emis.matem.unam.mxemis.matem.unam.mx/newsletter/newsletter34.pdf · EDITOR-IN-CHIEF ROBIN WILSON...

EDITOR-IN-CHIEFROBIN WILSONDepartment of Pure MathematicsThe Open UniversityMilton Keynes MK7 6AA, UKe-mail: [email protected]

ASSOCIATE EDITORSSTEEN MARKVORSENDepartment of Mathematics Technical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: [email protected] CIESIELSKIMathematics Institute Jagiellonian UniversityReymonta 4 30-059 Kraków, Polande-mail: [email protected] QUINNOpen University [address as above]e-mail: [email protected]

SPECIALIST EDITORSINTERVIEWSSteen Markvorsen [address as above]SOCIETIESKrzysztof Ciesielski [address as above]EDUCATIONVinicio VillaniDipartimento di MatematicaVia Bounarotti, 256127 Pisa, Italy e-mail: [email protected] PROBLEMSPaul JaintaWerkvolkstr. 10D-91126 Schwabach, Germanye-mail: [email protected] ANNIVERSARIESJune Barrow-Green and Jeremy GrayOpen University [address as above]e-mail: [email protected] [email protected] andCONFERENCESKathleen Quinn [address as above]RECENT BOOKSIvan Netuka and Vladimir Sou³ekMathematical InstituteCharles UniversitySokolovská 8318600 Prague, Czech Republice-mail: [email protected] [email protected] OFFICERMartin SpellerDepartment of MathematicsGlasgow Caledonian UniversityGlasgow G4 0BA, Scotlande-mail: [email protected] UNIVERSITY PRODUCTION TEAMKathleen Quinn, Liz Scarna

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CONTENTS

EMS December 1999

EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY

NEWSLETTER No. 34

December 1999

EMS News : Committee and Agenda .................................................................. 2Editorial by EMS Secretary David Brannan ..................................................... 3Introducing the Editorial Team : Part 2 ........................................................... 7EMS Executive meeting in Zurich ....................................................................... 8Felix Klein Prize ............................................................................................... 103ecm Barcelona: Second Announcement .......................................................... 12EMS Poster Competition .................................................................................. 14EMS Council Meeting in Barcelona: Second Announcement ........................... 15Interviews - Jan van Maanen........................................................................... 16Interviews - Olavi Nevanlinna .......................................................................... 18Interviews - Ian Frigaard ................................................................................ 191999 Anniversaries : Laplace and Poincaré .................................................... 201999 Anniversaries : Neugebauer .....................................................................231999 Anniversaries : Zariski .............................................................................24C.I.M.E. Summer Courses 2000 ....................................................................... 25Societies Corner : Kharkov Mathematical Society .............................................26Societies Corner : Luxembourg Mathematical Society ..................................... 26EMS - WiR Summer School .............................................................................. 28Education Section ............................................................................................. 29Forthcoming Conferences ................................................................................. 30Recent Books ..................................................................................................... 36Personal Column ............................................................................................... 43

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NOTICE FOR MATHEMATICAL SOCIETIESLabels for the next issue will be prepared during the second half of February 2000. Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Mathematics,P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: [email protected]

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EXECUTIVE COMMITTEEPRESIDENT (1999�2002)Prof. ROLF JELTSCHSeminar for Applied MathematicsETH, CH-8092 Zürich, Switzerlande-mail: [email protected]. ANDRZEJ PELCZAR (1997�2000)Institute of MathematicsJagellonian UniversityRaymonta 4PL-30-059 Krakow, Polande-mail: [email protected]. LUC LEMAIRE (1999�2002)Department of Mathematics Université Libre de BruxellesC.P. 218 � Campus PlaineBld du TriompheB-1050 Bruxelles, Belgiume-mail: [email protected] (1999�2002)Prof. DAVID BRANNANDepartment of Pure Mathematics The Open UniversityWalton HallMilton Keynes MK7 6AA, UKe-mail: [email protected] (1999�2002)Prof. OLLI MARTIODepartment of MathematicsP.O. Box 4FIN-00014 University of HelsinkiFinlande-mail: [email protected] ORDINARY MEMBERSProf. BODIL BRANNER (1997�2000)Department of MaathematicsTechnical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: [email protected]. DOINA CIORANESCU (1999�2002)Laboratoire d�Analyse NumériqueUniversité Paris VI4 Place Jussieu75252 Paris Cedex 05, Francee-mail: [email protected]. RENZO PICCININI (1999�2002)Dipto di Matem. F. EnriquesUniversit à di MilanoVia C. Saldini 50I-20133 Milano, Italye-mail: [email protected]. MARTA SANZ-SOLÉ (1997�2000)Facultat de MatematiquesUniversitat de BarcelonaGran Via 585E-08007 Barcelona, Spaine-mail: [email protected]. ANATOLY VERSHIK (1997�2000)P.O.M.I., Fontanka 27191011 St Petersburg, Russiae-mail: [email protected] SECRETARIATMs. T. MÄKELÄINENDepartment of MathematicsP.O. Box 4FIN-00014 University of HelsinkiFinlandtel: (+358)-9-1912-2883fax: (+358)-9-1912-3213telex: 124690e-mail: [email protected]: http://www.emis.de2

EMS NEWS

EMS December 1999

EMS Agenda2000

31 JanuaryNominations to the Secretariat for delegates of individual members contact: EMS Secretariat, e-mail: [email protected] � MarchVoting for delegates of individual memberscontact: EMS Secretariat, e-mail: [email protected] FebruaryDeadline for submission of material for the March issue of the EMS Newslettercontact: Robin Wilson, e-mail: [email protected] MarchDeadline for submission of nominations for the Felix Klein prizecontact: EMS Secretariat, e-mail: [email protected] � 25 MarchExecutive Committee Meeting, hosted by the Polish Mathematical Society and the Institute ofMathematics of the Polish Academy of Sciences, Bedlevo, near Poz�an (Poland)15 MayDeadline for submission of material for the June issue of the EMS Newslettercontact: Robin Wilson, e-mail: [email protected] 13 � 20 JuneEMS lectures by Prof. Dr. George Papanicolaou (Stanford, USA)13�16 June: ETH, Zurich (Switzerland): Financial mathematics18�20 June: University of Crete, Herakleion, Crete (Greece): Time reversed acousticscontact: David Brannan, e-mail: [email protected] � 22 JuneEURESCO Conference in Mathematical Analysis at Castelvecchio Pascoli (Italy):Partial Differential Equations and their Applications to Geometry and PhysicsOrganiser: J. Eichhorn, Greifswald (Germany), e-mail: [email protected][This series of conferences is financed by ESF.] 3 � 7 JulyALHAMBRA 2000: a joint mathematical European�Arabic conference in Granada (Spain),promoted by the European Mathematical Society and the Spanish Royal Mathematical Society contact: Ceferino Ruiz, e-mail: [email protected] website: www.ugr.es/~ruiz/6 July Executive Committee Meeting in Barcelona (Spain)7 � 8 JulyCouncil Meeting in Barcelona (Spain)contact: EMS Secretariat, e-mail: [email protected] � 14 JulyThird European Congress of Mathematics (3ecm) in Barcelona (Spain)contact: S. Xambó�Descamps, e-mail: [email protected] website: www.iec.es/3ecm/24 July � 3 AugustEMS Summer School in Edinburgh (Scotland): New analytic and geometric methods in inverse problemsOrganiser: Erkki Somersalo (Otaniemo, Finland), e-mail: [email protected] 15 AugustDeadline for submission of material for the September issue of the EMS Newslettercontact: Robin Wilson, e-mail: [email protected] August � 2 SeptemberEMS Summer School at Saint�Flour, Cantal (France): Probability theoryOrganiser: Pierre Bernard (Clermont�Ferrand, France), e-mail: [email protected]�bpclermont.frAutumnFifth Diderot Mathematical Forum, on Mathematics and Telecommunication.Date and programme to be announced. contact: Jean-Pierre Bourguignon, e�mail: [email protected] � 27 SeptemberEURESCO Conference at Obernai, near Strasbourg (France): Number Theory and Arithmetical Geometry: Motives and ArithmeticOrganiser: U. Jannsen, Regensburg, e-mail: [email protected] EURESCO Conference at San Feliu de Guixols (Spain): Geometry, Analysis and Mathematical Physics: Analysis and Spectral TheoryOrganiser: J. Sjöstrand, Palaiseau (France), e-mail: [email protected] SeptemberDeadline for proposals for the 2001 EMS Lecturescontact: David Brannan, e-mail: [email protected] � 15 OctoberExecutive Committee Meeting in the UK, hosted by the London Mathematical Society15 NovemberDeadline for submission of material for the December issue of the EMS Newslettercontact: Robin Wilson, e-mail: [email protected] 2001In the summer of 2001 there will be an EMS Summer School on Fluids at Charles University,Prague. Details to be announced.

EMS News: Committee and Agenda

It aall hhappened llike tthis ....The start of my interest in publicationsAfter gaining my PhD in London, I spent1967-68 in the USA. There I spent a lot oftime talking to a friend, Walter Schneider,about classical potential theory, approxi-mation, Vietnam, the state of the world,and other important matters � one ofwhich was the benefits to a MathematicsDepartment of a good mathematicslibrary. From there it was a short step tojust how one could build a good mathe-matics library even when university moneywas short.

Then in 1970 I was at a college inLondon whose library lacked some impor-tant journals for my interests. I thought ofthe idea of starting up a new mathematicsjournal, and using �exchange� copies tobuild up our library. Talking to mathe-maticians elsewhere in London, one toldme that it wasn�t that easy to do so and Ishould forget the idea, but that theLondon Mathematical Society was lookingfor a new Secretary if I was interested inburning off excess energy. I thought thissounded worth exploring, and six monthslater was elected Secretary. Two years laterthe job was divided into two � into a Counciland General Secretary and a Meetings andMembership Secretary � since the LMS hadentered an expansionary phase in its activ-ities.

What did the LMS publish?The LMS was founded in 1865, and beganto publish its Proceedings immediatelywith the firm C. F. Hodgson in northLondon. Things must have been difficultfinancially for a small society, and in 1874Lord Rayleigh gave the LMS £1,000 tosupport the printing bills. In 1926, at theurging of G. H. Hardy, the society startedpublishing its Journal. During the secondworld war, the Proceedings was moved fromHodgson�s in London to OxfordUniversity Press. As recently as 1953 theLMS Council was having anguisheddebates over the projected large annualdeficit on its two journals and consideringapproach industry for support.

Post Sputnik, the 1960s were a period ofmajor expansion in science: new universi-ties were founded world-wide, and theirlibraries needed long runs of journals.The LMS launched a major reprintingprogramme over ten years or so to reprintthe Proceedings and Journal; the incomefrom this and the money that it received

from G. H. Hardy on the death of his sis-ter completely transformed the Society�sfinancial position, so that covering print-ing costs was no longer a serious problem.In 1961 the LMS started to translateUspekhi Matematicheskii Nauk (as RussianMathematical Surveys) in conjunction withthe British Library; in 1964 it was a found-ing co-sponsor of the Journal of AppliedProbability; and in the late 1960s it begantranslation of the Transactions of the MoscowMathematical Societies, in conjunction withthe AMS. Then in 1968 it started two bookseries, the Monographs (originally withAcademic Press, and then OxfordUniversity Press when Academic Pressmoved most of its UK activities to USA)and the Lecture Notes (with CambridgeUniversity Press) � which in 1982 spawneda third series, the Student Texts. And in1969 the LMS started the Bulletin.

At first the Society had two Secretaries,who edited the journals. Then in 1937 aseparate office of Editor was created; sincea reorganisation in 1969, the journals haveeach had two Editors. For many years tillthe early 1970s, one Editor per journal hadan automatic seat on the Council; andPublications Committee consisted of a 15-minute meeting before the monthlyCouncil meeting; a list of all the papersaccepted but not yet published was laid onthe Council table at each meeting. Thingsare so much more professional now! � butthe system matched the needs of the time.

The 1970sI was on LMS Council from 1971 to 1981.During this time the LMS operated from ashared office in the Royal AstronomicalSociety in Burlington House in Piccadilly,London. For most of these years it hadone 0.8-time employee, Mrs Shalit, whodid all the routine administration that theSociety needed; in 1981 Susan Oakes tookup this post as full-time LMS Administrator,and has been a wonderful ambassador forthe Society in addition. I spent most of mytime as Council Secretary dealing withCouncil meetings and the dozens of �littlethings� that needed to be done to keep theCouncil affairs smooth.

These were the last days of the �hotmetal� printing process at Hodgson�s, andCouncil spent time wondering about thefuture of its publishing. It agonised overwhat was going to be the medium for itsjournals in future � would it be Microficheor would it be Microfilm? FortunatelyCouncil never decided to switch from theprinted page, since both media turned outnot to be the future after all.

In late 1973 there was one of a series of�oil crises�, together with a collapse in theUK stock market and an increase in theUK inflation rate to 28%. LMS Councildiscussed the fact that if it paid off its billsand printed all the journal issues for whichit had taken advance subscriptions, its networth was only around £75,000; so as anemergency measure it cut the sizes of theProceedings, Journal and Bulletin by one-third immediately. (Over the next 20 yearsthey increased in size again, but it tookmany years before they fully regained their

�lost pages�.)Council also wrung its hands at intervals

over the losses being made by its newBulletin. Its format of review articles andbook reviews as well as research articlesmeant that while mathematicians wouldsubscribe personally or would read a lot ofpages in each issue, they had trouble per-suading libraries to subscribe � even at itsvery low price. It also began to appearlater and later, encouraging libraries whosubscribed not to pay on time! But after aperiod of problems, its losses were sta-bilised, the Editor got it back on schedule,and Council decided that the losses wereaffordable � they would be covered by theprofits on the Proceedings and Bulletin, andascribed to the furtherance of the Society�smission in its Royal Charter to publish anddisseminate mathematics.

In 1973 the Society decided that itneeded to advertise to members the 1974International Congress of Mathematiciansin Vancouver. (This was the first ICM atwhich the Society had a reception formembers, to enable members to meet eachother and for foreign members to sign theLMS Membership Book � the originalbook, still in use since 1865). For manyyears the Society had posted to members amonthly postcard listing the monthlymeeting of the Society in London. But nowit decided to launch a �proper� LMSNewsletter. I took a sheet of A4 paper frommy desk, folded it over into A5 size, pen-cilled a page layout design on it, and sentthis off to Pat Hodgson asking him to printthe new Newsletter �like this�. TheNewsletter has appeared every month

(except August) since October 1973, andgoes from strength to strength � it is agood size so that you can sit and read itcover to cover easily, and it has a lot ofinteresting digestible information.Nowadays it is of course the main benefitthat LMS members receive for their sub-scription.

In 1979 I moved from London to theOpen University in Milton Keynes. I waspretty busy with a new job, organising a

EMS December1999 3

EDITORIAL

EditorialEditorialby

EMS SecretaryDavid Brannan

(Milton Keynes, UK)

NATO Instructional Conference inDurham, and as LMS Secretary. Shortlybefore my period of office ended I was theActing Meetings and MembershipSecretary as well as the Council andGeneral Secretary for six months, so dur-ing this heavy load I looked forward to�release� in summer 1981!

My first LMS Council meeting in June1971 was the last Council meeting attend-ed by J. A. Todd who had served a contin-uous 20-year period. But in the mid-1970s, Council was alarmed by the fact thatif its whole membership was elected annu-ally by the small number of members whobothered to vote, it would be quite easy fora small group of members acting in con-cert to elect their own nominees unrepre-sentative of the wishes of the membersgenerally. So it had introduced a systemof a mixture of one-year and two-yearterms for �ordinary� Council members,with a 6-year continuous office maximum;and a 10-year maximum period forOfficers, who continued to be electedannually to make sure that the Officers didnot begin to behave undemocratically!

Back again!In summer 1982 I was approached aboutthe possibility of taking on joint Editorshipof the Proceedings. Having had a year�sbreak, I agreed readily, and enjoyed a real-ly interesting period of four years (1983-86) as Editor with Don Collins. Editing alarge research journal is a really varied andinteresting role, not fully understood byanyone who has not tried to do the impos-sible themselves!

We had all the usual problems: � authors complaining that their wonderfulpapers had not been understood by thereferee � referees doing superficial work � referees failing to respond to appeals toreferee papers sent to them � agonising over which papers each monthwe would be forced to reject simplybecause we did not have sufficient space topublish them � trying to explain to authors and EditorialAdvisers why really good papers had beenrejected in spite of a glowing referee�sreport � at other times wondering how to fill thepages in an issue � wondering whether recently we had quiteenough of area X and so we should posi-tively try to cut back a bit on papers in X inthe next few issues;and so on.

In 1985 I had a view from PublicationsCommittee of the LMS Treasurer andPublications Secretary coping with the verydifficult problems of the bankruptcy ofHodgson�s who had worked for the Societysince 1865. As subscription income wasreceived by Hodgson�s on behalf of theSociety, the LMS found itself with signifi-cant publishing commitments to sub-scribers but without the correspondingincome. In the event the two Officersextricated the LMS from this extremelydifficult situation brilliantly, with a rela-tively small financial loss to the Society.

The Bulletin and Journal went toCambridge University Press, and theNewsletter to Armstrong Press inSouthampton. Unfortunately there wasconsiderable disruption to subscribers,since in the chaos the journal subscriptionlists were only recovered incomplete by theSociety to pass to CUP; this took two yearsto return to normal. However around thistime the Bulletin reached break-even point,and never made a deficit again!

From the frying pan into the fireIn 1986 I rejoined LMS Council asPublications Secretary when my predeces-sor John Pym went abroad on leave.Council had become much more business-like since 1981, meetings much longer,and business involved a much more out-ward-looking approach than in the 1970s.A completely new period of my life had infact started!

NonlinearityThe incoming President was ChristopherZeeman. He had the idea of the LMS try-ing to increase its membership in theApplied Mathematics community and cov-ering all mathematics, recognising theinherent unity of the subject (even today arather too radical approach in some quar-ters!). One component in his strategy wasto launch a new journal in applied mathe-matics, tentatively titled Transactions of theLMS. He did a lot of work on this; but atthe point of contacting possible Editors tohelp in the planning, he discovered thatthe Institute of Physics was planning tolaunch a new journal with some of thesame putative Editors! After preliminarydiscussions, it was decided that LMS andIOP should join forces, to harness the jointenergies of the mathematics and physicscommunities; and that non-linear mathe-matics and related areas should its subjectarea. The title Nonlinearity was adopted asits title on the suggestion of Mike Berry.

Nonlinearity was a baptism of fire for anincoming Publications Secretary! I tookover in July 1986 and the first issueappeared in March 1988. Meantime we

had to reach agreement with IOP over thediffering refereeing arrangements stan-dard in mathematics journals and inphysics journals (e.g. was timeliness moreimportant than complete accuracy? howmany referees? should the academicEditors-in-Chief see all papers that were tobe accepted? and so on). The LMS stillhad just one employee, whereas IOP hadover 150 (and 24 journals!); how could weensure that the venture would be fullyequal? and that financially each side wouldnot be �ripped off� by its new unfamiliarpartner? I had the job of buying a smallcompany �off the shelf�, changing its nameto LMS Publishing Ltd., changing itsArticles of Association, and writing a con-tract between LMSPL and IOP thatensured fair and equal liabilities and assetsto each partner; I was the CompanySecretary of LMSPL, responsible for itsonly business � handling the businessaffairs of Nonlinearity, together with theLMS Treasurer (who was also the LMSPLTreasurer, of course). The LMS felt thatthe whole venture was extremely risky, andthat it was not in the business of starting anew journal often whereas IOP started,sold and bought journals just like a com-mercial publisher; so LMSPL was to beused to insulate general LMS financialresources from this very uncertain threat.The contract between LMS and IOP wassigned after the first issue had appeared,things were happening so quickly at thattime!

In the event, things went brilliantly. Wehad chosen a subject area that was growingexplosively quickly, with much interestfrom the two subject communities. IOPhandled the practical publishing and dis-tribution arrangements extremely smooth-ly, the Managing Editors nominated by thetwo owners worked together like a dream,the Editorial Advisers formed a goodcoherent group meeting once a year butgelling by e-mail discussions, and the sup-ply of excellent papers from both areaspicked up very quickly � causing LMSPLand IOP regular problems over how quick-ly to expand the journal from quarterly tobimonthly! After two years the journal hadcovered its launch costs for the LMS, andhad an excellent subscription list base forthe future. The business side continued togive the owners an annual headache inview of their different pricing structuresand philosophies; and I regularly worriedwhether I would go to prison for not sub-mitting the LMS annual accounts on timeto Companies House! But all this wasminor � overall the launch of this greatnew journal had gone like a dream. Thejournal is instantly recognised on libraryshelves from its green and orange cover,and even non-readers look at the superbfront-cover designs; both the LMS andIOP should justifiably be proud of this col-laboration.

From the USSR to the RussianFederationOne of the first things I had to do whenbecoming LMS Publications Secretary inJuly 1986 was to find a successor to Kurt

EMS December 19994

EDITORIAL

Hirsch as editor of Russian MathematicalSurveys, as he died abroad quite unexpect-edly. Having taken advice but without hav-ing ever met him, I rang up Eric Primrose(Hirsch�s deputy) and asked him to take iton. Eric was a great Editor, and had awonderful relationship with his authorsand translators; for example, long before

e-mail made communications with Russiaeasy, Eric used to return helpful commentson translating Russian into English to hispanel of translators within Russia; severalof them have told me how much theyappreciated and learned from his wise sug-gestions.

Then in 1987 there was a problem overthe renewal of the contract for RMS �negotiations (handled by the BritishLibrary, our joint partners in RMS) hadcollapsed. The Russian �non-governmen-tal body� VAAP [Soviet Copyright Agency]that handled contractual matters inMoscow planned to transfer translationrights to some 14 translation journals inwhich BL had a share to someone else.This was a severe crisis, rescued only by aspeedily arranged visit by Edwin Shelock(Royal Society of Chemistry) and others toMoscow. But it meant that I knew I need-ed to adopt a more active role in RMSaffairs than the LMS had traditionallytaken in the past.

In 1989, Edwin Shelock, now Chairmanof ALPSP (see below), set up a visit for 17British publishers to visit VAAP in Moscowto discuss problems in existing collabora-tions or opportunities for future collabora-tions. Eric and I went, learned a lot aboutthe Soviet publishing and mathematicalset-ups, and made useful contacts in VAAP,the Academy of Sciences of the USSR, andthe Steklov Institute in Moscow.

Around the same time, John Coates(LMS President) was involved with LudwigFaddeev in the setting up of the EulerInternational Institute of Mathematics inLeningrad (now St Petersburg), and I wasfortunate enough to be invited to visit theEIIM and then in 1992 to attend its formal

opening ceremony. That was a great occa-sion with much deserved celebration! (I doregret that we were never able to set up aseries of publications jointly between theEIIM and the LMS.)

I made a point of visiting Moscow eachyear to keep an eye on possible futuredevelopments, and in 1992 was able toagree a new contract for RMS on behalf ofthe LMS and BL in Moscow. But thingshad now changed � the contract was notwith VAAP but with the Russian Academyof Sciences and its Department ofMathematics. I believe strongly in the ben-efits of personal contact, and continued tovisit Moscow. Then in 1994 I heard thatthe Academy was interested in discussingwith the LMS the possibility of some formof joint ownership of the translation jour-nals Izvestiya: Mathematics and Sbornik:Mathematics; the Academy had decided tomove from its previous arrangement withthe AMS. In the event, a multi-partnershiparrangement was arranged, involving theAcademy, its Department of Mathematics,the Editorial Board of each, the LMS, andTurpion � a body set up in both Londonand Moscow to enable such internationalscientific publishing collaborations. In1997 a similar ownership arrangement wasagreed for RMS as well.

This collaboration features the mathe-maticians in the UK and Russia being infull academic and financial control of theventure, on a partnership model that ismost successful; I think that each side isreally happy with it; a key ingredient is thearrangements for regular face-to-facemeetings of they key people at each level.It must be a model for future collabora-tions. I have to say that the UK editors(Eric Primrose on RMS, Gerald Gould onSbornik and Dave Johnson on Izvestiya)were a brilliant team of Editors to workwith � as were their Russian counterparts.

After my 10-year term as LMSPublications Secretary ended, I was askedto stay on a while as Deputy to the incom-ing Publications Secretary, Chris Lance; Istayed on for 18 months, with the principaltask of handling the Russian translationprogramme. I was very sad when Eric diedshortly after that, in late 1998: he left manyfriends in Britain and Russia.

I did not agree with every view put atLMS Council of the LMS Russian ventures!� but Council was tremendously supportiveof these complex international collabora-tions, often giving me significant authorityto conduct negotiations in Moscow andsign a contract without having to referthings back to London (they must have hadstrong nerves!). The ventures did notmake large profits for the LMS; butCouncil supported them since they cov-ered their costs and represented a signifi-cant contribution to disseminating mathe-matical research and to supportingRussian colleagues. Council also backedup its commitment by setting up a travelfund to enable mathematicians in the UKand Russia to visit each other for shortresearch visits.

Nonlinearity and the Russian translationprogramme were the main visible fruits of

my ten-year stint as LMS PublicationsSecretary!

MoneyA major part of the Publications Secretary�sjob was to handle the annual debate on thepricing of the journals. As the Treasurerused to say, this had to be �got right� - butnobody ever knew what the right decisionwas until about two years later when theysaw its effect! How could you predictmajor international financial crises thataffected university funding across theglobe? or currency fluctuations (after all,financial professionals cannot predict thisreliably!)? or the cost of paper? or thecosts in the printing industry? or postagecosts?

Given that universities were �rationalis-ing� their journal subscriptions, circulationof virtually all journals was declining.What strategy should the LMS adopt?Should the LMS each year increase pricesby X% to compensate for its anticipateddecline in subscription + Y% to allow forproduction and distribution cost increases± Z% to allow for the variation in theexchange rates of the pound and the USdollar (North America being the largestsingle market)? In the case of Nonlinearity,should it increase the price to match theincrease in size of the journal? Every Mayand June I used to talk to our printers andpublishers about their anticipated costs forthe year ahead, talk informally to commer-cial publishers about their pricing plans (acarefully guarded strategic commercialdecision to them, of course), agree with theTreasurer a strategy for what we thoughtthe LMS should do, then negotiate thedetail of this through LMS PublicationsCommittee, LMS Finance Committee andLMS Council � and then finalise negotia-tions with our various partners! This was areally interesting and testing experienceannually, to say the least.

Overall the LMS tried to increase pricesless than commercial publishers, mindfulof its learned society obligations to the

EDITORIAL

EMS December 1999 5

One of the books in the LMS-AMS History ofMathematics series.

mathematics community. We cannot havegot our pricing decisions too far wrongbecause, in spite of our cautious approach,our subscription levels declined less quick-ly than most mathematics journals and oursurpluses rarely declined. These surpluseswere fed back into general LMS funds; andwere used to support its meetings, confer-ences, visiting fellowships, and generalrunning costs.

InnovationIn spite of my tendency to conservatism,every so often an obvious development orinnovation came along. Thus in the early1990s a member suggested that the LMSlaunch a series of books in the History ofMathematics. It turned out that the AMSwas thinking along similar lines, and indue course we launched a joint LMS-AMSseries in the area. Its objective is to publishbooks in which the working mathematicianwill have an interest and at a price that(s)he can afford. And I had to create a con-tract with the AMS. . .

A major development was on the tech-nical side of journals. In the 1970s print-ers stopped using �conventional� hot-metalhandsetting and moved to computer-dri-ven typesetting. This was more economi-cal, but still had the problem that itemscould fall on the floor from the fonts orfrom the glue on the printer�s film failing.Then along came TeX, followed byLaTeX, followed by a whole range of ver-sions of each and so-called improved vari-ants from many sources! The enthusiastsfor these developments being adopted atonce by the LMS were vocal, but our print-ers were certainly less skilled in it than ourauthors!

It took many years before we were able(with CUP) to introduce the option ofLaTeX files being submitted to the LMSfor the Bulletin and the Journal, and it tookeven longer for the Proceedings. The con-tinuing problems of incompatibilitybetween versions and dialects plague everymathematics journal � TeX developersplease note!

And other things besides!What else did I do? Well, trouble-shootgenerally � the job was effectively that ofDirector of a small publishing house � orso it seemed! (No doubt that is why theLMS now has a full-time PublicationsManager, rather an academic doing it inthe corners of his time.) I was responsiblefor identifying and appointing Editors,Technical Editors and Editorial Advisersfor the journals and book series, subject toCouncil approval. This was sometimesquite difficult, to get a good balancebetween efficiency and academic standing!� and sometimes I had to �thank variouspeople for their services� (non-nativeEnglish speakers should replace thisphrase by �fire various people for notdoing their job�).

I also became involved in the Associationof Learned and Professional Society Publishers[ALPSP], an interesting body that celebrat-ed its 25th birthday last year. It runs aseries of courses, seminars and conferences

of value to �small learned societies� like theLMS (that is, as well as the big commercialpublishers, the big Engineering Institutes,etc.). My two-year spell on the ALPSPCouncil taught me a lot about publishingand publishers! Amongst other things Ilearned that the �amateur� LMS approachto journal pricing was in fact generally atleast as successful as the �professional�approach of the commercial publishers;and I grew to believe (and to tell Councilcolleagues) that the LMS should itselfexpand its publishing activities in a majorway, though of course it is up to my succes-sors to decide what they will actually do!

Since thenOver the decade 1986-96 LMS assetsincreased from £2M to £6M, with publish-ing profits rising from £200K to £500K peryear. The Society had expanded to twofull-time staff, and did a large amount ofbusiness in relation to mathematics in UK;it became simply too cramped, eventhough it had moved in the early 1990sinto a large office of its own in the RoyalAstronomical Society building. LMSCouncil decided to seek more appropriatepremises, both for the work of the Societyand as an investment.

It purchased two adjacent properties inRussell Square, near Euston Station, in1998 (see EMS Newsletter 31); in the newpremises it now has around seven staff �from an Executive Director through aPublications Manager to a receptionist.How did the LMS ever cope in the past?Also, in 1997 the LMS launched a newpurely electronic journal � the LMS Journalof Computation and Mathematics. This excit-ing new venture had been in planning forsome years, but its launch was delayed untilwe had the right academic objectives andtechnical systems in place to start a newjournal that the LMS would continue topublish indefinitely � its objective with allits publishing ventures. Rumour has it thatmost electronic journals find it difficult toattract authors, particularly authors ofpapers of sufficient quality to publish.Universities continue to regard printedjournals in many subjects (including math-ematics) as more authoritative, as betterrefereed, and as a better guide to the qual-ity of existing and prospective staff. Whileappointments and promotions are affectedby this view, electronic journals will find ithard to break the mould of conventionalpublishing.

The fratricidal debate over the cost ornon-cost of electronic journals seems to meto be a dead-end debate. (Interesting con-tributions to the question appear in�Electronic publishing and electronic pub-lications in mathematics�, Progress inMathematics 169 (1998), 315-337.) Thereare real costs involved in producing a qual-ity mathematics research journal, whetherpaper or electronic; and, in my view, thereare a number of myths around that sup-port the flawed view that electronic jour-nals should be free or priced at minimalcost:myth 1: all authors write clearly in goodgrammatical English with proper spelling

and punctuation, so that even readers newto the field or readers whose native lan-guage is not English can read and under-stand the mathematics without difficulty orambiguity arisingmyth 2: authors will do the TeX typeset-ting work for a journal, so the journal type-setting costs will be nil or negligiblemyth 3: individual journals will be avail-able indefinitely on the Editor�s server orhis/her University server and can beaccessed at any timemyth 4: editors do their work at zero cost,as their universities absorb the cost. In fact, quality costs money:� to �technically edit� manuscripts into aversion (fit to publish) that readers canunderstand� to prepare the electronic files, whetherfor paper, server, or both� to create accessibility of the material (thatis, its distribution in the short term)� to maintain its accessibility in the longtermso that publishers (whether commercial,learned societies or universities) will con-tinue to have to charge for mathematicsjournals. Nevertheless, the mathematicalcommunity owes it to itself, and to its suc-cessors, to agree a �system� that will makemathematics research literature availablenow and into the indefinite future at aprice that enables as many as possibleresearch libraries to afford to buy the keyjournals. The community does not seem tobe succeeding in this goal, yet.

I suspect that there will continue to be amarket for both paper and electronic ver-sions of journals for years to come, as eachformat has its own role � mathematicianslike to read papers slowly and carefully! �and that paper (backed up, admittedly, bysecondary, regularly-refreshed electronicfiles) will continue to be the principalarchiving format for some centuries yet.But neither I nor my 1999 readers knowwhether I�m right or wrong.

�Would you be interested . . . ?�Then out of the blue in 1998 I was asked ifI�d be willing to be nominated for the postof EMS Secretary. Though I had been anEMS member for years, I was not entirelyclear what the EMS actually did, butthought it seemed like an interesting chal-lenge and I agreed.

My first EMS Executive Committeemeeting in late 1998 in Copenhagen, as avisitor before taking office in January1999, showed how different was the natureof the EMS from the LMS � the EMS has acoordinating role for nations acrossEurope totally unlike what the LMS does.But what was a major agenda item at thatExecutive Committee meeting? � the firstissue of, and the contract for JEMS, thenew Journal of the EMS! This businessseemed strangely familiar . . .

And finallyDo I yet know how my EMS role will workout? � not really! Do I look forward tofinding out? � very much indeed. Good luckto the European Mathematical Society in thecoming millennium! Ad multos annos!

EDITORIAL

EMS December 19996

EMS NEWS

EMS December 1999 7

Ivan Netuka (Recent books editor) received (the equivalent of) a Ph. D. in Mathematics in1972 at Charles University, Prague, Czech Republic, where he has taught at the Facultyof Mathematics and Physics and is now Professor in the Mathematical Institute of CharlesUniversity. His mathematical interests lie in analysis, both classical and abstract and inthe history of mathematics. He has made contributions to the field of potential-theoret-ic methods applied to boundary value problems for partial differential equations, andparticularly in classical and abstract potential theory.

Vladimír Sou³ek (Recent books editor) grad-uated at Charles University, Prague, in1968 and has worked at the Faculty ofMathematics and Physics, CharlesUniversity since 1969. He received here(the equivalent of) a Ph. D. in 1974, and iscurrently Professor in the MathematicalInstitute of Charles University. Hisresearch interests lie in global analysis anddifferential geometry, with connections tomathematical physics. They are centredaround an investigation of properties ofinvariant differential operators onhomogenous spaces and their curved ana-logues. In particular, he has contributed tothe development of Clifford analysis (func-tion theory for solutions of the Dirac equa-tion).

Paul Jainta (Problems Corner editor) teaches mathematics and physics at Adam-KraftGymnasium, Schwabach, Bavaria. He has been involved with various mathematical com-petitions in Germany, and last year was appointed manager and secretary of the�Landeswettbewerb Mathematik Bayern e.V�. In February 1998 he was elected Vice-President of the association �Begabtenförderung Mathematik e.V� (Fostering mathemat-ically gifted youngsters). Another of his fields of activity is popularising mathematics.Apart from the Problem Corner in this Newsletter, he writes a column called �WerkstattMathematik� in the German mathematics journal �Wurzel�.

Introducing the Editorial Team : part 2

Jeremy Gray (Anniversaries editor) has a BAin mathematics from Oxford University,and obtained his PhD in mathematics fromthe University of Warwick in 1981. He ispresently a Senior Lecturer inMathematics at the Open University, UK.His main area of research is the history ofmathematics in the nineteenth century,particularly the growth of complex func-tion theory and algebraic geometry. In1998 he was an invited plenary speaker forthe History of mathematics section of theInternational Congress of Mathematiciansin Berlin.

Vinicio Villani (Education editor) is Professor of Mathematics Education in theDepartment of Mathematics, University of Pisa, Italy. He has been President of theItalian Mathematical Union.He has worked in the theory of functions of several complex variables. Currently hisinterests are mainly devoted to mathematics education, and specifically to aspects con-cerning the teaching-learning process of geometry at secondary and tertiary level, as wellas teacher preparation. He has been Chairman of the International ProgrammeCommittee appointed for the ICMI Study �Perspectives on the Teaching of Geometry forthe 21st Century� and editor of the resulting book with the same title, published in 1998.

Officers� reportsThe President reported briefly on recentcontacts with SIAM, GAMM and CICIAM.The Treasurer proposed the investment of60000 euro of the Society�s reserves in aFinnish financial fund, and this was agreedby the Committee. The Committee agreedto invite the Council meeting in July 2000to reconsider the level of membership fees.

Report of the former President (J.-P. Bourguignon)Plans for an exciting conference on theMathematics of the Alhambra in Granada as asatellite meeting for 3ecm in July 2000 arealmost complete.

ProjectsThe EU has funded LIMES (LargeInfrastructure in Mathematics � EnhancedServices) within its Fifth FrameworkProgramme with the aim of improving theservice of Zentralblatt-MATH and establish-ing it as a widely used infrastructure inmathematics. The project will probablystart in April 2000. The partners in theproject are likely to be FIZ Karlsruhe,MathDocCell Grenoble, TU Berlin,Eidetica (Amsterdam), DTV (Copen-hagen), SIBA (Lecce), USC/CESGA(Santiago de Compostela), HMS (Athens)and the EMS.

The Committee discussed a proposedproject Euclid designed to help indepen-dent mathematics publishers make thetransition to the electronic scene, and toact as a catalyst for the mathematics pub-lishing community to arrive at a commit-ment to use a common metadata standard.It decided that the Society should beinvolved in this project.

There was some preliminary discussionof the possibility that the Society become amathematics publishing house in its ownright. It was agreed that the Society shouldorganise a meeting of the non-commercialpublishers of mathematics journals pro-duced in Europe during 3ecm in Barcelonain July 2000.

It was agreed to provide a front-pagelink on EMIS to COMPUSCIENCE, adatabase produced by FIZ Karlsruhe inclose co-operation with Zentralblatt-MATH.This covers a part of computer sciencewhich is closely related to area 68 ofMATH, complements the offer in comput-er science provided by INSPEC, and has itsusers mainly near the borderline betweenmathematics and informatics. This willcomplement the data base access already

provided by EMIS.Committees R. Piccinini was elected chair of the EMSSummer Schools Committee for 2000�03, andD. Cioranescu was appointed a member ofthis committee. Emilia Mezzetti,University of Trieste, was elected to chairthe Committee on Women and Mathematics.O. Barndorff Nielsen was elected to chairERCOM for the years 1999-2002. ClaudeLobry has agreed to chair the Committee onDeveloping Countries, and A. Henault, M. S.Narasimhan, A. Pelczar and M. Robertswere elected members of the committee. J.Bruening, M. Chaleyat-Maurel, J.Davenport, I. Diaz, A. Quarteroni and K.-O. Widman were elected members of theCommittee on Special Events, chaired by J.-P.Bourguignon. The Committee for theSupport of Eastern European Mathematicianswas granted an additional sum of 5000euro for the year 2000.

The 4th Diderot Mathematical Forum on�Mathematics and Music� will be held on3�4 December 1999, in Lisbon, Paris andVienna. It is hoped that the 5th DiderotMathematical Forum will be onTelecommunications.

It was agreed to change the name of theCommittee on Applications of Mathematics tothe Committee for Applied Mathematics. Itsmission statement was accepted as follows:�Applied Mathematics and PureMathematics are two sides of the samecoin, they need each other. TheCommittee sees its role in promotingApplied Mathematics as a whole throughand within EMS, since applications cannotbe separated from the mathematical meth-ods. The Committee, instead of compet-ing, wants to cooperate with other, some-times more specialised, societies on theEuropean and international level and withapplications-oriented member societiesespecially in further improving the publicand political awareness about the impor-tance of mathematics to cultural, economicand social development.�

It was agreed to establish a four-yearlyprize, the Felix Klein Prize, in conjunctionbetween the EMS and the Institute forIndustrial Mathematics in Kaiserslautern,to be financed by the latter. The intentionis to award the prize to a young scientist(normally under the age of 38) or to asmall group of young persons (each under38 years), for using sophisticated methodsfor solving a concrete industrial problemto the industry�s satisfaction. The detailedrules for the Prize and mode of operation

of the Prize Committee will be publicisedseparately. The first Klein Prize will beawarded at the 3ecm in July 2000.

The Group on Relations with EuropeanInstitutions intends to form a strategytowards both DGXII and DGXIII of theEU, and to establish contacts with appro-priate new EU commissioners. V. Capasso,J.-P. Pier and O. Martio were added to theGroup�s membership. The Group wasasked to campaign against plans to cancelthe network programmes in the 6thFramework Programme. The ExecutiveCommittee agreed to invite ERCOM, as acommittee of EMS, to send a letter oppos-ing the cancellation of network pro-grammes.

World Mathematical Year 2000It was reported that a new resolution onWorld Mathematical Year 2000 was to bepresented to the November meeting ofUNESCO. The EMS was heavily involvedin the international preparation for this,via the activities of its Publicity OfficerMireille Chaleyat-Maurel � for example,via the WMY calendar of events, theAlhambra conference in July 2000, and itssupport for a pan-European campaign toraise public awareness of Mathematics by aposter campaign in European cities andrelated actions during the EuropeanScience and Technology Week

The EMS ran a poster competition foruse for WMY2000. The Prize Committeeof M. Chaleyat-Maurel, R. Brown, B.Branner and V. L. Hansen had decided onthe following awards. The posters will beforwarded to professional designers for usein the WMY2000 campaign, and thenames of the original designers will be vis-ible in the final version of each poster.

Summer schoolsThe Society had held two summer schoolsin 1999: the EMS-CIME summer school inMartina-Franca, Italy, and the EMS-WiRsummer school in Heidelberg, Germany.Both had been very successful, and hadreceived financial support from UNESCO-Roste as well as the EMS; ESF had alsogiven financial support to Heidelberg.

The EMS was planning two summerschools in 2000, one of which had alreadyreceived EU financial support. (For infor-mation on these, see the EMS Agenda,page 2.) One application to hold a 2001summer school, from Charles University inPrague, was approved. It was hoped thatanother 2001 proposal was in the pipeline.The Committee expressed the wish to havethe EMS summer schools move aroundEurope.

STOA Subcommittee of the EuropeanParliament STOA (Scientific and TechnologicalOptions Assessment), a group in theEuropean Parliament, has invited expres-sions of interest in membership of a panelfor research into science/mathematics poli-cy questions. R. Jeltsch, J.-P. Bour-guignon, H. Engl and L. Lemaire wereappointed to an ad hoc EMS group to inves-tigate this idea.

EMS NEWS

EMS December 19998

EMSEMSExExecutive Committee ecutive Committee

meetingmeetingZurich (Switzerland), 9 � 10 October 1999

Cooperation between EMS and othermathematical societiesPlans for joint events of EMS and SIAM areunder discussion. R. Jeltsch, H. Engl, O.Martio and D. Cioranescu were appointedto an ad hoc committee to progress a possi-ble joint meeting in 2001.

The Executive Committee discussed thepossibility of cooperation and/or a reci-procity agreement between the EMS andthe American Mathematical Society, andbetween the EMS and the AustralianMathematical Society. The Committeealso discussed possible future cooperationwith the European Regional Committee ofthe Bernoulli Society.

European Mathematical CongressesThe Committee received a progress reporton 3ecm, describing the scientific pro-gramme, financial matters and social pro-gramme. Everything seems to be progress-ing well, and the Committee believed thatthe Congress should be a mathematicallyexciting event that should attract very wideparticipation.

Bids for holding 4ecm in summer 2004were discussed by the Committee, and arecommendation will be made to theCouncil meeting in July 2000.

EMS Council meeting in Barcelona inJuly 2000The Catalan Mathematical Society hasoffered its help with the local arrange-ments.

Executive Committee electionsThe terms of office of one Vice-President(A. Pelczar) and of three ordinary mem-bers (B. Branner, M. Sanz-Solé and A.Vershik) terminate in 2000. A. Pelczar willhave served 8 years, and cannot be re-elected. The ordinary members can be re-elected, and have expressed their willing-ness to continue in service.

It was agreed that the composition ofthe Executive Committee is important, inorder to ensure a proper balance of areasof mathematics and geography. This willbe discussed again at the next ExecutiveCommittee meeting in March 2000.

EMS Council meeting in 2002The ICM 2002 will be held in Beijing. TheCommittee discussed whether to identify asite in Europe to be presented to membersas an alternative to a meeting in Beijing;this will also be discussed again in March2000.

Future Executive Committee meetingsLikely dates for meetings in 2000 are: 23-26 March in Poland; 6 July in Barcelona;and 13�15 October in the UK.

JEMS, Journal of the EMSIt was agreed to appoint a number of addi-tional associate editors to widen the fieldscovered by JEMS. Member societies will beasked if they are willing to collect pay-ments for JEMS with their subscriptions;and as a promotional measure, the EMSNewsletter should continue to print the con-

tents list of JEMS.

EMS NewsletterIt was agreed to offer institutions that arenot EMS members to subscribe to theNewsletter; the arrangements for this willbe publicised shortly.

EMS LecturesIt was reported that the three sets of EMS1999 Lectures had been very successful.

Publicity materialIt was agreed to print a new brochure forthe Society in time for 3ecm at Barcelona.(The current brochure was printed in1996.) A poster with the Society�s Agendafor the year 2000 will also be prepared.

The Committee felt that the �visibility�of the EMS is enhanced by having boothsat mathematics meetings. The EMS willhave booths at various meetings in 2000,including the AMS Annual Meeting inWashington, and at 3ecm.

And finally . . .The Committee expressed their heartfeltthanks to the Swiss Mathematical Societyfor supporting its meeting in Zurich, andto R. Jeltsch and A. Rast for making suchefficient arrangements for the accommo-dation, preparation of papers, social pro-gramme, transport and other arrange-ments for the meeting. Things had beenjust perfect.

David A Brannan

EMS NEWS

EMS December 1999 9

Some of the Executive Committee relax after a busy weekend

Carles Casacuberta & Tuulikki Mäkeläinen

Anatoly Vershik (left) & Renzo Piccinni (right)

David Brannan & Doina Cioranescu

The idea of a Felix Klein prize was born onthe first day of the ICIAM99 meeting inEdinburgh (see EMS Newsletter 33) duringa discussion between the winner of the1999 Pioneer prize, Helmut Neunzert,and the president of the EMS. Two dayslater, Heinz Engl, Chair of EMS�s AppliedMathematics Committee, joined in and afirst draft of the specifications was com-pleted. The executive committeeapproved the wording of the draft at itsmeeting in Zurich on 9�10 October.Renate Tobies�s article shows why thename Felix Klein was chosen. The first callfor nominations can be found below.

Why a Felix Klein Prize?Nowadays, mathematics plays an ever-greater role � often the decisive role � infinding solutions to numerous technical,economical and organisational problems.In order to encourage such solutions andto reward exceptional research in the areaof applied mathematics, the EMS decided,in October 1999, to establish the FelixKlein Prize.

The mathematician Felix Klein(1849�1925) is generally acknowledged asa pioneer with regard to the close connec-tion between mathematics and applica-tions that lead to solutions to technicalproblems. Klein�s success in his efforts toopen up modern mathematical methodsand theories to wider circles was based onhis international reputation as a renownedmathematician. His contributions to puremathematics include not only the well-known systematisation of geometricalfields in his Erlanger Programm (1872), butcovered nearly all fields of mathematics.These contributions were collected in threevolumes in his Gesammelte MathematischeAbhandlungen (1921�23). David Hilbert(1862�1943), whom Klein supported andwhose call to Göttingen he arranged in1895, was impressed with Klein�s strikinggeometrical perception. Hilbert empha-sised Klein�s outstanding results in the areaof automorphic functions and the scientif-ic vision that was evident in the undertak-ing Encyklopädie der mathematischenWissenschaften mit Einschluss ihrerAnwendungen (1895�1935), a comprehen-sive work of international authorship.When the Berlin mathematicians � whoover a long period had remained scepticalof Klein�s application-oriented endeavours� elected him as corresponding memberto the Berlin Academy of Science in 1913,their election recommendation stated:�Klein [is] one of the few mathematicianswho is still capable of an overall view ofmathematics� (full citation in Tobies,1999).

Klein was aware that abstract-orientedpure mathematics was in danger of becom-ing isolated. In the 1890s engineers andtechnicians, who lamented a mathematical

education that was remote from practica-lity, set in motion an anti-mathematicsmovement. In order to change the publicimage of mathematics and create greaterawareness for the usefulness of modernmathematical methods, Klein not onlyturned his own research to applied mathe-matics and application-oriented themes,but also smoothed the way for others withdiverse measures. His valuable results onthe application of mathematics were aptlydescribed by Richard von Mises(1883�1953), founder of the journalZeitschrift für angewandte Mathematik undMechanik, thus:�A good part of [Klein�s] work on lineardifferential equations must be countedhere . . . for the main part they are con-cerned with so-called oscillation theories,which are crucial to problems of stabilityand eigenfrequencies of mechanical (andother) systems. A few treatises deal withquestions relating to geometrical optics,[such as] the theory of refraction in opticalinstruments. It is within various areas ofmechanics, however, that Klein has ven-tured deepest into applied areas. He suc-ceeded in promoting the kinematics ofrigid bodies by developing Englishresearch which was virtually unknown inGermany at the time (Robert Ball, defini-tion of spiral or �dyname�) . . . and hesearched for related areas in �technicalmechanics�, i.e. direct solutions to real-world problems. . . The outstanding teach-ing material originating from the lecturesin Göttingen by Klein and Sommerfeld onthe theory of rigid bodies reaches . . . intotechnical problems dealing with gyro-scopes and gyro-compasses, yawing of ves-sels, etc. Together with K. Wieghardt,Klein published a theory of stresses inplane-truss assemblies based on an imagi-native combination of Maxwellian recipro-cal figures and Airy stress functions � a the-ory which has proved its fruitfulness upuntil the present time for dealing withproblems occurring in the statics of struc-tures� (Richard von Mises, �Felix Klein�,ZAMM 4 (1924), 87�88).

However, in order to bring aboutchange, it was not sufficient for Klein aloneto yield up research results. Numerousand diverse scientific measures were neces-sary to activate the long-neglected (inGermany) areas of applied mathematics.Around the turn of the century, Klein suc-ceeded, together with many allies, inbringing about much improved conditionsfor the development of applied mathemat-ics.One of these developments was a newexamination curriculum which was passedin 1898 and which introduced and regulat-ed � for the first time at a Prussian univer-sity � the teaching of applied mathematics.The course programme included a choiceof core subjects in descriptive geometry,

geodesy, and technical mechanics (kine-matics, graphical statics). The number ofsubjects was extended in following years toinclude numerical and graphical methods,insurance mathematics and statistics,hydrodynamics and aerodynamics. Theadvent of such specialised teaching inapplied mathematics made the establish-ment of corresponding subject areas neces-sary, and eventually led to the creation ofthe first professorships in Germany inapplied mathematics. Not only was Kleinsuccessful in convincing government min-istries, he also gained support for his plansfrom heads of industry. Within the frame-work of the �Göttinger Vereinigung zurFörderung der angewandten Physik undMathematik�, affluent circles supportedKlein�s endeavours with over 2 millionGoldmarks between 1898 and 1920.

The decision to produce a journaldevoted to applied mathematics was a fur-ther element of Klein�s programme. Forthis, in 1900 the already-existing Zeitschriftfür Mathematik und Physik was transformedand became what is acclaimed as the pre-cursor of the Zeitschrift für angewandteMathematik und Mechanik. In order tochange the public image of mathematics itwas not sufficient to limit activities to theuniversities. Klein strove in an interna-tional context � in 1908 at the FourthInternational Congress of Mathematiciansin Rome, he was elected as Chairman ofthe International Commission ofMathematical Instruction � for a reform ofthe teaching of mathematics �from primaryschool to university�. Special emphasis wasplaced on nurturing close relationsbetween high-level science and perspicu-ous applications-oriented mathematics.The fact that the group of Göttingen�smathematicians achieved internationalrenown was due, in a great measure, toKlein�s programme to develop mathemat-ics in all directions and enable results ofpure mathematical research to flow intoapplied areas combining the interests ofacademe and industry. Klein implement-ed an adroit appointment policy (DavidHilbert, Ludwig Prandtl and Carl Runge)to achieve an ideal balance in the combi-nation of theory, application and numeri-cal mathematics. Close cooperationbetween scientists and their students pro-duced valuable contributions for the devel-opment of mathematics and its applica-tions.

Scientists who can prove, in a promi-nent and commendable way, that mathe-matical theory and mathematical modelslead to practical solutions of problems, andwho thereby contribute to and influencethe future growth of the mutual stimula-tion of theory and practice, are followingin the footsteps of Felix Klein and are wor-thy candidates and eligible for the award ofthe Felix Klein Prize.

The above was written by Renate Tobies, from theDepartment of Mathematics, University ofKaiserslautern, who is habilitated in the History ofMathematics and has published five books, three ofwhich include material on Felix Klein, and a numberof essays. [English translation by A. Rast-Margerison]

NEWS

EMS December 199910

FFelix Klein Pelix Klein Prizerize

Felix Klein PrizeSpecifications

Principal guidelinesThe prize, established in 1999 by the EMSand the endowing organisation, theInstitute for Industrial Mathematics inKaiserslautern, is awarded to a young sci-entist or a small group of young scientists(normally under the age of 38) for usingsophisticated methods to give an outstand-ing solution, which meets with the com-plete satisfaction of industry, to a concreteand difficult industrial problem.

Selection procedures for composing theprize committeeThe prize committee consists of six mem-bers, with one designated as �Chair�. Theprize committee is composed of the follow-ing people.

Three committee members are chosenby unanimous agreement of the presidentof EMS and the chair of the AppliedCommittee of the EMS. The endowingInstitute for Industrial Mathematics inKaiserslautern elects two members to theprize committee, at least one of whomshould be a representative from industry.The European Consortium forMathematics in Industry, ECMI, elects onemember to the prize committee. The prizecommittee constitutes itself.

Appointments to the prize committeeshould be made at least eighteen monthsbefore the prize award date. Tenure of the Prize CommitteeFrom the date of appointment to the PrizeCommittee, the members serve until theprize is awarded. If no prizewinner is cho-sen, the duties of the committee are com-pleted. Rules of OperationsA prize committee will be appointed everyfour years. If no prize is awarded, theaward date moves ahead four years.The prize committee determines its ownprocedures and rules of operations.

Nomination of the AwardThere are no restrictions on eligibilityother than those specified in the PrincipalGuidelines.

The prize committee is responsible forsolicitation and evaluation of nominations.Nominations may be made by anyone,including members of the prize committeeor by candidates themselves. It is theresponsibility of the nominator to provideall relevant information to the prize com-mittee, including a resumé and documen-tation of the benefit to industry and themathematical method used.

The nomination for the award shouldbe reported by the prize committee to theEMS president at least three monthsbefore the date of the award. The nomi-nation for the award must be accompaniedby a written justification and a citation ofabout 100 words that can be read at theaward date.

The prize is awarded to a single personor to a small group and cannot be split.

Description of the awardThe award comprises a certificate contain-ing the citation and a cash prize, theamount of which is to be determined bythe endowing Institute for IndustrialMathematics in Kaiserslautern in consulta-tion with the presidents of EMS and ECMI.Normally, the prize sum will be approxi-mately 5000 euro.

Award presentationThe prize is presented every four years atthe European Congress of Mathematics. Arepresentative of the endowing Institutefor Industrial Mathematics inKaiserslautern or the president of EMSpresents the award. The recipient is invit-ed to present his or her work at the con-ference.

Prize historyThe first prize will be awarded in the year2000.

Prize fundThe endowing Institute for IndustrialMathematics in Kaiserslautern is responsi-ble for managing the prize fund as well asits administration, should such a fund beestablished.

Changes to these specificationsAll changes to these specifications musthave the approval of the EMS ExecutiveCommittee and the endowing Institute forIndustrial Mathematics in Kaiserslautern.

Approved by the EMS Executive Committee atits meeting in Zurich, 9�10 October 1999.

NEWS

EMS December 1999 11

2000 : World Mathematical YearMireille Chaleyat-Maurel

The year 2000 will be a crucial year for mathematics and math-ematicians. For eight years the mathematical community hasknown that this year, the first (or last) of the century and themillennium, has been declared World Mathematical Year by

the International Union of Mathematics. This decision, taken under the presidencyof Prof. J.-L. Lions, is supported by UNESCO, whose support has been confirmed bya vote in General Assembly. A solemn declaration, called �Déclaration de Rio� pro-poses three main lines of actions centred on mathematics:� the major challenges in mathematics for the 21st century;� mathematics and development;� the image of mathematics among the general public.

The first theme is mostly directed toward the mathematics community that wants itsconjectures turned into theorems with simple proofs � short, elegant and accessible toall. This past century has witnessed the establishment of Fermat�s last theorem, thathad baffled people for over 300 years. Hopefully, at the end of the next century, peo-ple will speak of �Riemann�s theorem� no longer as a hypothesis! During 2000 a com-mittee, directed by Prof. V. -I. Arnold, is assessing the work accomplished during the20th century and prospecting for the coming century; a synthetic work is in prepara-tion on these topics.

The second theme involves the applications of mathematics and problems raised byteaching mathematics. This point will be emphasised at the 2000 InternationalCongress of ICMI in Tokyo.

The third theme is aimed at teaching mathematics to a general public not alwayswilling to learn. This calls for great creativity and originality from mathematicians, inthe domain of communication and media such as: introducing mathematical sectionsand exhibitions in science museums, developing movies, videos and books, andorganising conferences that popularise mathematics; all initiatives are welcome. Inthis direction, an idea proposed some years ago by the European MathematicalSociety is already under way: posters on mathematical topics in subway stations and incars and other forms of public transportation. A similar campaign has already beendeveloped for poetry. Many European cities are willing to participate in this cam-paign, and some have already started to do so. The EMS has sponsored a poster con-test for this mathematical metro campaign � see page 14.

The year 2000 is also very important for the European Mathematical Society,because its third Congress 3ecm will be held in Barcelona in July. The announcedprogramme shows that it should be as successful as the Congresses of Paris andBudapest. We hope that, for this event, many mathematicians will join the EMS.

There is still time to propose mathematical congresses, workshops, conferences andexhibitions. World-wide events can be announced in the WMY 2000 newsletter: justask the Editorial Committee at WMY 2000, Institut Poincaré, 11, rue Pierre et MarieCurie, 75005 Paris, France. For European events, please contact the author of thisnote [e-mail: [email protected]] or the EMS Newsletter editor. For national events, weurge national societies to create a Year 2000 Committee and to publish informationin their newsletters.

In conclusion, all European mathematicians should become involved with WorldMathematical Year 2000, and should participate, actively and at all levels, to every-thing that may contribute to the development of mathematics and its impact onworld-wide problems of education, society and economy.

The Second Announcement of the 3ecmwill soon be mailed to those who have pre-registered through the Congress web site.It will contain detailed instructions for reg-istration, grant requests, information onaccommodation, and other features of theCongress. Here we present a summary ofthe relevant information that is currentlyavailable.

Plenary Lectures� Robbert Dijkgraaf (Universiteit van

Amsterdam)� Hans Föllmer (Humboldt-Universität

zu Berlin)� Hendrik W. Lenstra, Jr. (University of

California at Berkeley and UniversiteitLeiden)

� Yuri I. Manin (MPI für Mathematik,Bonn)

� Yves Meyer (École NormaleSupérieure de Cachan)

� Carles Simó (Universitat de Barcelona)� Marie-France Vignéras (Université

Paris 7 Denis Diderot)� Oleg Viro (Uppsala Universitet and

POMI St Petersburg)� Andrew J. Wiles (Princeton University)

Parallel Lectures� Rudolf Ahlswede (Universität

Bielefeld)� François Baccelli (INRIA and École

Normale Supérieure, Paris)� Volker Bach (Universität Mainz)� Viviane Baladi (Université Paris-Sud

XI)� Joaquim Bruna (Universitat Autònoma

de Barcelona)� Xavier Cabré (Universitat Politècnica

de Catalunya, Barcelona)� Peter J. Cameron (Queen Mary and

Westfield College, London)� Ciro Ciliberto (Università degli Studi

di Roma �Tor Vergata�)� Zoé Chatzidakis (CNRS and Université

Paris 7 Denis Diderot)� Gianni Dal Maso (SISSA, Trieste)� Jan Denef (Katholieke Universiteit

Leuven)� Barbara Fantechi (Università degli

Studi di Udine)� Alexander B. Givental (University of

California at Berkeley and Caltech)� Alexander Goncharov (Brown

University, Providence)� Alexander Grigor�yan (Imperial

College, London)� Michael Harris (Université Paris 7

Denis Diderot)� Kurt Johansson (Kungl Tekniska

Högskolan, Stockholm)� Konstantin M. Khanin (Heriot-Watt

University, Edinburgh, Isaac NewtonInstitute, Cambridge, and LandauInstitute, Moscow)

� Pekka Koskela (Jyväskylän Yliopisto)� Steffen L. Lauritzen (Aalborg

Universitet)� Gilles Lebeau (École Polytechnique,

Palaiseau)� Nicholas S. Manton (University of

Cambridge)� Ieke Moerdijk (Universiteit Utrecht)� Eric M. Opdam (Universiteit Leiden)� Thomas Peternell (Universität

Bayreuth)� Alexander Reznikov (University of

Durham)� Henrik Schlichtkrull (Københavns

Universitet)� Bernhard Schmidt (Universität

Augsburg)� Klaus Schmidt (Universität Wien)� Bálint Tóth (Budapesti Müszaki

Egyetem)

Mini-SymposiaThe following list of topics was chosen bythe Scientific Committee. The speakers at each mini-symposium willbe selected by the corresponding Chair(listed in brackets below).� Quantum chaology [Sir Michael Berry,

University of Bristol]� Computer algebra [Wolfram Decker,

Universität des Saarlandes]� Mathematics in modern genetics

[Peter Donnelly, University of Oxford]� String theory and M-theory [Michael

Douglas, Rutgers University]� Mathematical finance: theory and

practice [Hélyette Geman, Universitéde Paris IX and ESSEC]

� Quantum computing [Sandu Popescu,University of Cambridge]

� Free boundary problems [JoséFrancisco Rodrigues, Universidade deLisboa]

� Symplectic and contact geometry andHamiltonian dynamics [Mikhail B.Sevryuk, Russian Academy of Sciences]

� Curves over finite fields and codes[Gerard van der Geer, Universiteit vanAmsterdam]

� Wavelet applications in signal pro-cessing [Andrew T. Walden, Universityof London]

Round TablesThe following list of topics has been agreedby the Round Table Committee.� Mathematics teaching at the tertiary

level� What is mathematics today?� The impact of mathematical research

on industry and vice versa� The impact of new technologies on

mathematical research� Building networks of cooperation in

mathematics� How to increase public awareness of

mathematics� Shaping the 21st century

Call for Software, Video and Multi-mediaAs has already been announced, a sessionon mathematical software will take placeduring the Congress. In this session,mathematical software systems relating toall fields of mathematics, and applicable toa variety of purposes, will be presented.The scheduled length of a presentation(including discussion) is 30 minutes.Submissions must be received by theorganisers before 1 February. They maybe made electronically by using the formprovided on the web site http://www.iec.es/3ecm/mathsoft.htm, or by e-mail [email protected] with the singleword mathsoft in the Subject field.

The organisers also plan to produce aDVD containing both short videos and

EMS December 199912

3ecm

3r3rd Eurd European opean CongrCongress ofess ofMathematicsMathematicsShaping the 21st CenturyBarcelona, 10 � 14 July 2000Second announcement

multi-media with mathematical content.This DVD will be exhibited in general pub-lic sessions. Submissions of contributionsfor this DVD may be made from all areas ofmathematics, and must be received by theorganisers before 1 February. Submissionforms are available at http://www.iec.es/3ecm/video.htm, where additionaldetailed information can be found. Theaddress [email protected] may be usedto contact the organisers of this comple-mentary activity or to ask any related ques-tions.

Call for PostersAll registered participants will have theopportunity to present their mathematicalwork in the form of a poster. Decisions onacceptance will be made by the OrganisingCommittee on the basis of an abstractwhich should reach the organisers before 1March. Abstracts submitted after this datewill not be considered. Acceptance will beconfirmed before 20 March.

Abstracts should conform with the fol-lowing instructions. It is strongly recom-mended that abstracts be submitted elec-tronically by using the form provided inthe web site http://www.iec.es/3ecm/posters.htm. Abstracts may also be sent bye-mail to [email protected], with theSubject field containing exclusively the rel-evant section number (see the list of sec-tions at the web site). Abstracts shouldpreferably be written in English, and pre-pared in LaTeX using only standard com-mands and AMS macros, symbols andfonts.

GrantsThe organisers of the 3ecm will awardgrants of either partial or full support toattend the Congress. The aim of thesegrants is to promote the participation ofyoung researchers in mathematics, withspecial attention to their professional situ-ation and their country of origin.Financial support will be offered in the fol-lowing ways.A. Grants of 25,000 PTA covering the

registration fee.B. Grants of 30,000 PTA covering accom-

modation expenses at university resi-dences.

C. Grants up to 35,000 PTA for travelexpenses.

Mathematicians working in Catalonia canapply only for type A grants.Mathematicians working in Spain but out-side Catalonia can apply for type A and/ortype B grants. Mathematicians workingabroad can apply for all types.

People interested in obtaining financialsupport are requested to fill in an applica-tion form which can be found at the 3ecmweb site http://www.iec.es/3ecm. Applic-ations should be submitted before 31January. Decisions will be taken before 10March. Grant holders should confirm theirregistration before 1 April. The registra-tion fees of people with type A grants willbe paid by the organisers. Grants of typeB and C will be paid to their holders onarrival at the Congress.

Satellite ActivitiesThe following list of satellite activities hasbeen acknowledged by the ExecutiveCommittee by October 1999. Proposalsfor further satellite congresses or othermathematical events will be welcome until1 February.

26 June � 1 July: Summer School onInteractions between AlgebraicTopology and Invariant Theory,Ioannina, Greece Contact: Nondas Kechagias (University ofIoannina), [email protected] site: http://www.uoi.gr/conf_sem/topology2000/.

29 June � 1 July: 2nd InternationalConference on Symmetry andAntisymmetry in Mathematics, FormalLanguages and Computer Science,Brasov, RomaniaContact: Gabriel V. Orman (TransylvaniaUniversity), [email protected].

29 June � 4 July: Workshop onBifurcation, Symmetry and Patterns,Porto, Portugal. Contact: Jorge Buescu (IST, Lisboa), [email protected].

3 � 7 July: Functional Analysis Valencia2000, an international functional analy-sis meeting on the occasion of the 70thBirthday of Professor Manuel Valdivia.Valencia, Spain. Contact: José Bonet (UniversidadPolitécnica de Valencia), [email protected] or Klaus D. Bierstedt (UniversitätPaderborn), [email protected]. Web site: http://www.upv.es/VLC2000/.

3 � 7 July: 6th International Conferenceon Harmonic Analysis and PartialDifferential Equations, El Escorial,Madrid, Spain. Contact: Eugenio Hernández (UniversidadAutónoma de Madrid), [email protected].

3 � 7 July: Alhambra 2000, a JointMathematical European-ArabicConference, Granada, Spain Contact: Ceferino Ruiz (Universidad deGranada), [email protected]. Web site: http://www.ugr.es/~alhambra2000/.

3� 7 July: EVEQ 2000, InternationalSummer School on Evolution Equations,Prague, Czech Republic Contact: Hana Petzeltová (Academy ofSciences, Prague), [email protected].

3 � 7 July: Colloquium on NumberTheory, Debrecen, HungaryContact: Attila Pethö (Lajos KossuthUniversity), [email protected].

3 � 7 July: Conference on Algebraic K-Theory and Homotopy Theory ofSchemes, Toulouse, FranceContact: Max Karoubi (Université Paris 7Denis Diderot), [email protected].

3 � 9 July: Summer School onMathematical Aspects of EvolvingInterfaces, Funchal, PortugalContact: Pierluigi Colli (Università diPavia), [email protected]. Web site: http://maei.lmc.fc.ul.pt.

4 � 6 July: Catop 2000, a Conference onCategorical Topological Methods,Fribourg, SwitzerlandContact: H.-P. Künzi (Universität Bern),[email protected].

4 � 7 July: First Euro-MediterraneanTopology Meeting, Bellaterra, Barcelona,SpainContact: Carlos Broto (UniversitatAutònoma de Barcelona), [email protected]. Web site: http://mat.uab.es/euro-mtm.

3 � 5 or 5 � 7 July: cem 2000, Congrésd�Educació Matemàtica, I Jornadesd�Educació Matemàtica a Catalunya.Mataró, Barcelona, SpainContact: Xavier Vilella (FEEMCAT), [email protected].

5 � 8 July: 6BLM, 6th Barcelona LogicMeeting, Barcelona, SpainContact: Josep Maria Font (Universitat deBarcelona), [email protected].

6 � 8 July: IX Fall Workshop onGeometry and Physics (Special Session),Vilanova i la Geltrú, SpainContact: Miguel C. Muñoz-Lecanda(Universitat Politècnica de Catalunya),[email protected] site: http://www-mat.upc.es/dgdsa/geomphys2000.html.

6 � 8 July: New Women in Mathematics:an International Forum for WomenStarting in Mathematical Research,Barcelona, SpainContact: Laura Fainsilber (University ofGothenburg), [email protected]. Web site: http://www.math.helsinki.fi/EWM/.

17 � 19 July: Distributions with GivenMarginals and Statistical Modelling,Barcelona, SpainContact: Carles M. Cuadras (Universitat deBarcelona), [email protected].

17 � 22 July: Colloquium on Lie Theoryand Applications, Vigo, SpainContact: Ignacio Bajo, EsperanzaSanmartín (Universidad de Vigo), [email protected]. Web site: http://www.dma.uvigo.es/~clieta/index.

Contact AddressesCongress e-mail: [email protected] web site: http://www.iec.es/3ecm/or http://www.si.upc.es/3ecm/Mailing address: Societat Catalana deMatemàtiques, Institut d�Estudis CatalansCarrer del Carme, 47 E-08001 Barcelona,SpainPhone: (+34)-93-270-16-20Fax: (+34)-93-270-11-80


3ecm

In the spring of 1999, the EuropeanMathematical Society announced a compe-tition to encourage the idea of creatingposters with a mathematical theme thatwould catch the eye and be representativeof mathematics and its uses. Such ideascan prove valuable in many situations as away of presenting mathematics to the pub-lic. The direct reason for the competitionwas, however, to get ideas for suitableposters to be displayed in subways andother public places, as one of the eventsduring the World Mathematical Year 2000.In the announcement of the competition,the EMS offered prizes for the three bestproposals, but naturally the hope was toget more good proposals than those thatwould finally be selected for a prize . . . andthe EMS was not disappointed!

The deadline for submission of propos-als was 1 May 1999. Twenty-six proposalswere received, many containing multiplesuggestions for posters. Altogether the juryappointed by the Executive Committee ofthe EMS to evaluate the proposals hadabout 100 posters to consider.

The jury consisted of Bodil Brannerfrom the Executive Committee, andRonnie Brown, Mireille Chaleyat-Maureland Vagn Lundsgaard Hansen (Chair)from the EMS committee on WMY 2000.

It was a difficult task for the jury tocome up with a decision. If a poster is tobe both instantly attractive to a lay person,and also signal an important math-ematical message to a personreflecting on the poster, fruitfulideas are not particularly easy tocome by. In several proposals, thegraphics were attractive but themathematical message was too sim-ple. In other proposals the mathe-matical content was substantial, butthe graphics were not sufficientlyappealing to the general public. Inthe end, the jury selected three pro-posals that satisfied both expecta-tions, being attractive as well as car-rying an important mathematicalmessage. The recommendations bythe jury were approved by theExecutive Committee of the EMS atits October meeting in Zurich. TheExecutive Committee expressed itssatisfaction with the diversity in thesubmissions and by the high degreeof creativity shown by the pro-posers.

The winners are:First prize: Stéphane Durand, Centrede Recherches Mathématiques,Université de Montréal, C.P. 6128,Succ. Centre-Ville, Montréal, Qc, H3C3J7, Canada

[Durand receives the first prize for a seriesof seven posters that deal with Sunflowerseeds and Fibonacci sequences, Animalswith a spotted body, The Nautilus shelland the golden mean, Viruses and knots,Escher�s Circle Limit III (hyperbolic plane)and the Big Bang, Fractal geometry inmany situations, and Snowflakes and chaostheory.]Second prize: Andreas Frommer, StefanieKrivsky and Petra Zöllner, BergischeUniversität, Gesamthochschule Wuppertal,Fachbereich 7 (Mathematik), Gauss-Strasse 20,42097 Wuppertal, Germany[Frommer, Krivsky and Zöllner receive thesecond prize for a series of five postersdivided into two concepts: three posters onMathematical thinking, which deal withThe bridges of Königsberg, Primes andtwin primes, The Four Colour Theorem,and two posters on Advertising mathemat-ics as being the foundation of high tech ineveryday life, which deal withTomography: the brain, Mathematical carcrash test.]Third prize: Nadja Kutz, FachbereichMathematik, Sekr. MA 8-5, TechnischeUniversität Berlin, Str. des 17. Juni 136,10623 Berlin, Germany[Kutz receives the third prize for a series ofposters with short slogans. She submittedthree posters: Play with Mathematics (ababy holding a model of a doubly discretesmoke ring flow in her hand), Grow with

Mathematics (a flower picture which isactually a rotational invariant Willmoresurface), The World is different withMathematics (a �world pretzel�, in the formof a double torus, that exhibits the variouscontinents).]Runner-up: Wolfgang Joppich, Institute forAlgorithms and Scientific Computing-GMD-SCAI, Sankt Augustin, Germany, for anapplied mathematics poster on numericalweather forecasting.Many of the ideas for posters are suitablefor use in other contexts as well, such aspostcards, mugs, T-shirts etc. TheEuropean Mathematical Society hopes toobtain permission from the proposers tomake all such uses of their ideas as may beof benefit to mathematics and mayenhance the public understanding of oursubject. If permissions are granted, theEMS will allow the use of the ideas in allworthy contexts.It was an unusual and exiting experiencefor the jury in the competition. We feelcertain that we selected some very goodproposals, but we also know that there areother very valuable ideas in the total col-lection. Early in the evaluation procedure,the jury realised that it is difficult for math-ematicians to judge what will catch theattention of the general public in connec-tion with mathematics. But nevertheless, itis important to try, for the future of math-ematics.

NEWS

EMS December 199914

EMS PEMS Poster Competition roster Competition resultsesultsVagn Lundsgaard Hansen

One of the prize-winning entries. Others will appear in future issues

The EMS Council meets every second year.The next meeting will be held in Barcelonaon 7-8 July 2000, before the 3rd EuropeanCongress of Mathematics. The exact loca-tion will be announced later.

Delegates to the Council will be electedby the following categories of members, asper the Statutes.(a) Full Members: Full Members are nation-al mathematical societies, which elect 1, 2or 3 delegates according to their size andresources. Each society is responsible forthe election of its delegates. Each societyshould notify the Secretariat of the EMS inHelsinki of the names and addresses of itsdelegate(s) no later than 10 March 2000.As of 1 July 1999, there were 47 such soci-eties � which could designate a maximumof 69 delegates.(b) Associate Members: There are two associ-ate members, namely the Gesellschaft fürMathematische Forschung and theEuropean Mathematical Trust. Their cur-rent common delegate is elected until1999, so their delegate has to be elected in2000. According to the Statutes, �delegatesrepresenting associate members shall beelected by a ballot organised by theExecutive Committee from a list of candi-dates who have been nominated and sec-onded, and have agreed to serve.�(c) Institutional Members: There are three

institutional members, Institut Non-Lineare de Nice, the Moldovian Academyof Sciences and the Mathematical Instituteof the Serbian Academy of Sciences andArts. Their common delegate is elected till1999, so their delegate has to be elected in2000. According to the Statutes, �delegatesrepresenting institutional members shallbe elected by a ballot organised by theExecutive Committee from a list of candi-dates who have been nominated and sec-onded, and have agreed to serve.�(d) Individual Members: A person becomes

an individual member either through acorporate member, by paying an extra fee,or by direct membership. On 30 June1999, there were some 1900 individualmembers and, according to our statutes,these members will be represented by19�20 delegates. The final count of indi-vidual members for these elections wasmade on 1 November 1999.

The mandates of 11 of the present 17delegates ended on 31 December 1999,and so elections must be held for theirpositions. They are: G. Anichini, G.Bolondi, B. Branner, J.-M. Deshouillers, K.Habetha, M. Karoubi, T. Kuusalo, A.Lahtinen, L. Màrki, R. Piccinini, and D.

Puppe. Of the eleven, B. Branner, J.-M.Deshouillers and M. Karoubi cannot be re-elected because they have served in thiscapacity for 8 years.

The Executive Committee is responsi-ble for preparing the matters to be dis-cussed at Council meetings. Items for theagenda of this meeting of the Councilshould be sent as soon as possible � and nolater than 10 March � to the EMSSecretariat in Helsinki.

The Council is responsible for electingthe President, Vice-Presidents, Secretary,Treasurer and other members of theExecutive Committee. The present mem-bership of the Executive Committee,together with their individual terms ofoffice, is as follows.

PresidentProfessor Rolf Jeltsch (1999�2002)

Vice-PresidentsProfessor Andrzej Pelczar (1997�2000)Professor Luc Lemaire (1999�2002)

SecretaryProfessor David Brannan (1999�2002)

TreasurerProfessor Olli Martio (1999�2002)

MembersProfessor Bodil Branner (1997�2000)Professor Marta Sanz-Solé (1997�2000)Professor Anatoly Vershik (1997�2000)Professor Doina Cioranescu

(1999�2002)Professor Renzo Piccinini (1999�2002)

Under Article 7 of the Statutes, membersof the Executive Committee shall be elect-ed for a period of 4 years. Committeemembers may be re-elected, provided thatconsecutive service shall not exceed 8years. Andrzej Pelczar has served on theExecutive Committee for 8 years, so hecannot be re-elected.

It would be convenient if potential nom-inations for office in the ExecutiveCommittee, duly signed and seconded,could reach the Secretariat by 10 March. Itis strongly recommended that a statementof intention or policy is enclosed with eachnomination. If the nomination comesfrom the floor during the Council meetingthere must be a written declaration of thewillingness of the person to serve, orhis/her oral statement must be secured bythe Chair of the Nominating Committee (ifthere is such) or by the President. It is rec-ommended that a statement of policy ofthe candidates nominated from the floorshould be available.

The Council may, at its meeting, add tothe nominations received and set up aNominations Committee, disjoint from theExecutive Committee, to consider all can-didates. After hearing the report by theChair of the Nominations Committee (ifone has been set up), the Council will pro-ceed to the elections to the ExecutiveCommittee posts.

Delegates to the Council meeting, whoare planning to attend the EuropeanCongress of Mathematics, are advised thattheir accommodation arrangementsshould be made through the ECM. Fordelegates to the Council who are not

attending the ECM, an address for accom-modation arrangements will be providedlater.

Secretariat: Ms. Tuulikki Mäkeläinen Secretary of the EMSP.O. Box 4 FIN-00014 University of Helsinki Finland

Annex: 22000 ttimetable ffor ttheCouncil MMeeting

31 January: Deadline for nominations fordelegates of individual members. February: The ballots for delegates of indi-vidual members are sent to individualmembers. March: Candidates for delegates of indi-vidual members are announced in the EMSNewsletter. The venue and meeting timesof the Council meeting are repeated. April: A letter is sent to each delegate, con-taining the agenda of the Council meeting. June: The results of the elections for dele-gates of individual members areannounced in the EMS Newsletter. Thevenue, the meeting times, and the agendaof the Council meeting are given. Materialfor the Council meeting is sent to the del-egates.


EMS NEWS

Meeting Meeting of the of the

EMS CouncilEMS Council7 � 8 July 2000, Barcelona

Second announcement

EMS CountryRepresentatives

The following have become Country rep-resentatives for the EMS Newsletter. Ifyou would like to become a CountryRepresentative, please contact yourcountry�s mathematical society and thencontact the EMS Secretariat in Finland(see page 2).

Catalonia: Agusti Reventos[[email protected]]

Czech Republic: Lubos Pick [[email protected]]

Finland: Mikko Pere [[email protected]]

Germany: Ehrhard Behrends [[email protected]]

Italy: Giuseppe Anichini [[email protected]]

Luxembourg: Jean-Paul Pier [[email protected]]

Norway: Erik Bedos [[email protected]]

United Kingdom: Susan Oakes [[email protected]]

Jan van Maanen graduated in mathematicsfrom the University of Utrecht in 1977, andtook his PhD in 1987 with a thesis on �Facets ofseventeenth-century mathematics in theNetherlands�. For fifteen years a teacher at theChristelijk Gymnasium, Utrecht, he now teachesat the University of Groningen and is chair ofthe national exam board for �Mathematics B�(the pre-university school-leaving examinationin calculus and geometry). Jan van Maanen isco-chair of an international study on the rela-tions between history of mathematics and theteaching and learning of mathematics, as wellas chair of HPM, the International StudyGroup on the Relations between History andPedagogy of Mathematics, which provides thecontext for the opening question.

First, Jan, could you explain what �HPM�is? You can look at HPM in two ways. I couldreply by saying that it is an official studygroup of ICMI � the InternationalCommission on Mathematics Instruction �which is itself a committee of the IMU(International Mathematical Union). Itwas established in the early 1970s, at thesecond ICME (International Congress onMathematics Education). From that per-spective it is a cog in the internationalmachinery of mathematical and education-al interests. But I could reply in anotherway too: HPM is a collection of teachersand academics from around the worldunited in a common enthusiasm for therole of history in mathematics teaching,people who want to absorb the lessons ofthe past in order to improve the mathe-matics education of the future.

How is the HPM group organised?Interestingly, it more or less works withoutadministration or finances � which is rareamong such international organisations!The group runs through communicationsbetween people, through conferences. Ithas had a newsletter for the past 20 years,thanks to the hard work of a number ofindividuals, both in editing it and distrib-uting it, and thanks, too, to the support ofinstitutions who have provided assistancewith reprographic and postage costs. Tobe an HPM member has been, in effect, tobe on the mailing list of a distributor; theworld is covered with a network of distrib-utors. But the newsletter is in a fallow peri-od at the moment, I hope temporarily, somembership is even less formally pinneddown than usual. Nonetheless a greatnumber of activities take place.

In Europe, for example, how does thatwork?

There is a lot of enthusiasm in manyEuropean countries for developing histori-cal contexts for mathematics teaching andincorporating historical insights in a wholerange of ways, into everything from nation-al curricula, as in Denmark and Norway, tothe work of individual teachers. Thisenthusiasm is fostered and shared by theorganisation of meetings which attract par-ticipants from across Europe: I rememberespecially one in Braga, Portugal, in 1996which attracted roughly equal numbers ofPortuguese mathematics teachers, andmathematicians and mathematics educa-tors from the rest of Europe and else-where, some 550 people in total fromaround thirty countries.

What kind of people are we talking about?� teachers? researchers?The HPM movement is very interesting �and important in an exemplary way, Ithink � for its mix between teachers, acad-emics, generators and users of research: anenvironment where people who are profes-sionally engaged in mathematics, in itsteaching and in history of mathematicscome together to learn from each other,exchange insights and move forwardtogether. You can see this in the annualHIMED (�History in MathematicsEducation�) meetings in the UK, in theUniversité d�été in history and epistemologyof mathematics which is an annual event inFrance, and which, since 1993, is organ-ised at a European level every three years,this July in Belgium. And there are numer-ous sessions devoted to the topic withinbroader conferences such as ICMs, ICMEsand national mathematical conferences.

So we�ve established that there is a livelyand wide-ranging social structure for peo-ple with common interests, but � if I may actas devil�s advocate for a moment � just whatis the point?The point is that mathematics teaching canbe better if the teacher is aware of theadded dimension of where the mathemat-ics has come from, and has a range ofinsights and resources to share with stu-dents as is appropriate for their needs anddifficulties at any moment. In my owncase, I was doing research into the historyof mathematics for my PhD at the sametime as teaching mathematics at a Dutchgymnasium (a six-years grammar schoolthat gives direct entrance to university). Ibegan to find that sharing with my pupilsthe historical insights I was gainingthrough my researches was a good strategywith several benefits for the lessons. Pupilslearned that great mathematicians made

mistakes just as we do and they do � thatproblems were solved with different meth-ods � that things taken for granted in someperiod were open questions at other peri-ods. Overall they gained a quite differentperspective on mathematics � much betterthan only learning by doing problemsfrom a textbook, and often with more plea-sure too! . . . though I had them do manysums as well.

I think people would be interested in havingthis pinned down a bit: can you give anexample?One of my pupils, Janneke, comes to mymind. She was not at ease with the qua-dratic equation formula which she foundextremely hard to remember; she felt it asan alien collection of characters and othersigns. One day I came back to class, full ofenthusiasm for just having read one of myancient texts, Johan Stampioen�s Algebraof 1639, and got the students to read andwork through the way he solved a quadrat-ic problem, with a geometric diagram (lit-erally �completing a square�), then to com-pare his process with our formula.Stampioen described his solution rhetori-cally, in a �first do this, then do that� kindof style. Janneke was spellbound, asked�why don�t we solve these equations theway Stampioen did it?� We then comparedthe rhetorical solution with the quadraticequation formula, and found out that youcan also remember that formula as a seriesof actions, instead of having to store a sta-tic formula in your photographic memory.Here the comparison with the past helpedto clarify the present procedures. Janneke,by the way, later on went to university andstudied econometrics: I feel history helpedher at a crucial stage in her mathematicaldevelopment. But maybe that is a biasedimpression!

Another example � I have read Eulerwith my class. I like Euler very much,because he has a very clear and open style,which is such a wonderful example of howto write and do mathematics. When myclass came to learn logarithms the students

INTERVIEW

EMS December 199916

InterInterview with Jan van Maanenview with Jan van Maanen(Gr(Groningen)oningen)Chair of HPM

interviewer: John Fauvel, Open University, UK

Jan van Maanen (in check shirt) discussingstrategy with international colleagues in theHPM movement

read Euler�s marvellous exposition ashomework (some helping by translating itout of Latin) then checked his reasoningand calculations. They seemed to me tounderstand logarithms, as a result, muchmore clearly than the way I myself wastaught the subject thirty years ago. Alsomy colleague teachers of classical lan-guages profited, since this Euler passagewas the first text these students read foranother sake than just learning Latin.

Is history only or most useful, then, for aschool such as Christelijk Gymnasiumwhose pupils study Latin as well, and mostof whose students go on to university? No, I do not think so. In fact, teachersworking with a range of disadvantaged orlow attaining or unconfident studentsreport considerable success in exploringmathematics from a historical perspective.My colleague Marjolein Kool, for example,has done just this kind of thing with low-attaining teenagers, and found old Dutchmathematics texts an ideal source of stim-ulation and reassurance. Part of the rea-son for the success, of course, is that thiskind of historical material enthuses andmotivates us, the teacher, so the teaching isbound to have an infectious spark, andthat�s so much of the battle. The difficultpoint is whether it transfers: take a schoolat random, a teacher at random � wouldhistory also be interesting for such ateacher? For the pupils? How would youreach this teacher? That�s the challenge.It�s true that other mathematics teachersmight find they can inspire pupils throughtheir involvement in something like sailingor sundials or football, so it�s tempting tosay that enthusiasm is the main qualityneeded. But history has a whole range offurther benefits too, as our ICMI Study isshowing.

So tell me about the ICMI Study. You could easily answer this yourself, sincewe are co-chairing this event, but I appre-ciate that answers are to come from me inthis interview. Last year there was a con-ference at the French MathematicalSociety�s retreat in Luminy, nearMarseilles, at which 75 mathematics teach-ers, educators and historians from aroundthe world came together for a week toexchange experiences and perceptions.There they made a systematic and compar-ative survey of the improvements in math-ematics teaching and learning through his-torical dimensions and resources � andalso of the problems connected with thisapproach. The results are being written upin a book which should be published intime for the next ICME to be held inTokyo in August 2000.

What kind of results have you got, or do youexpect, from the ICMI Study? I�ve hinted at the main thing, which is thegreat range of students � across ages,across abilities, across subjects, acrosscountries � whose mathematical learningand understanding is helped by havinghistorically resourced teachers. The sec-ond main finding is the enormous range of

ways in which such teachers can make useof history, from telling stories to settingprojects and designing curricula.

Should history of mathematics itself betaught in schools? Mathematics should be taught as a living,dynamic subject, and history can con-tribute to that. If history is taught as such,it is only as a means of evoking mathemat-ical understanding. A teacher who monot-onously reads from a history book willhardly be helping pupils! But suitably cho-sen history can be really beneficial. Theteacher who is teaching L�Hôpital�s Rule,for example, can bring a good and memo-rable kind of pathos into the classroom bytalking about Johann Bernoulli who � as ayoung man with advanced knowledgeabout the new field of differential calculus- taught the rich nobleman L�Hôpital, whomade a contract that Bernoulli would sendletters about his mathematical discoveries.L�Hôpital sent money in return, and coulddo with Bernoulli�s findings what he want-ed. So L�Hôpital wrote, in 1696, the firsttextbook about differentiation, in which heincluded Bernoulli�s method for calculat-ing limits, which is still known underL�Hôpital�s name � and Bernoulli could donothing about it (although he tried, afterL�Hôpital�s death). For some pupils this isjust a rule, one of many. Pupils who knowthe story behind the rule will not easily for-get it. The story gives the rule a profile,and in this manner supports the memory.

Is there any particular reason for yourinterest in Johann Bernoulli?Since you ask, he was one of the early starsof the University of Groningen, where Iteach. Bernoulli�s Groningen was the sec-ond university in the world (after his broth-er Jakob�s Basel University) to teach calcu-lus � that was in 1698 � and we�re ratherproud of that. In fact in 1996 the

University commissioned a sculpture tocommemorate Bernoulli�s association withGroningen, and in particular his celebrat-ed work on the brachistochrone problem,showing the curve of quickest descent to bea cycloid. Bernoulli�s solution is represent-ed in a great steel sculpture by the gener-ating circle of the cycloid and two vastcycloidal arcs. It�s quite eye-catching.

And has much of mathematical interesthappened in Groningen since Bernoulli�sday? Not different from many other academicinstitutions, I guess. But let me tell youabout just one episode. In 1914 AliciaBoole, the daughter of George Boole, wasawarded an honorary degree atGroningen, which was rather revolutionaryat that time, for her work on polytopes (herword for four-dimensional regular poly-hedra). A few years ago Dirk Struik, thegreat Dutch historian of mathematics nowin his 105th year, asked me if there werestill any traces of Alicia Boole atGroningen; I found that indeed her ownwonderfully colourful drawings of poly-topes are still kept at our department, andthat a set of models of three-dimensionalsections of them is in the university muse-um.

How does the presence of so much history ofmathematics influence or benefit today�sGroningen students? I have no firm evidence for that. The his-tory of maths course is fairly popular, andsome of my colleagues do integrate historyin their lectures. The clearest thing Inotice is that students use the Bernoullisculpture as a backdrop for taking pho-tographs of each other! Maybe also busi-ness administration students who havetheir own fantasy with the statue. The bigcircle as a symbol for generating moneyinstead of cycloids?

INTERVIEW


The cycloidal lines of Henk Ovink�s Bernoulli sculpture (1996) are seen against the buildings ofthe University of Groningen.

Olavi, let me congratulate you on your elec-tion as President of ICIAM. The appliedmathematics community always associatedthis name with the conferences likeICIAM99 in Edinburgh. Why did yourorganisation change its name from thenearly unpronounceable CICIAM?CICIAM was the abbreviation of�Committee for International Conferenceson Industrial and Applied Mathematics�.It was felt that the new name describesmore accurately the aims of the organisa-tion as set out in its bylaws. The congress-es will be advertised in the old way; forexample, the next international congresson industrial and applied mathematics,will take place in Sydney, 7�11 July 2003,and will be called ICIAM2003.

What are the aims of ICIAM?To promote industrial and applied mathe-matics internationally, to promote interac-tions between member societies and theirgoals, and to coordinate planning for reg-ularly occurring international meetings onindustrial and applied mathematics.

What do you personally want to achieve aspresident of ICIAM over the next fouryears?If one thinks of the ICIAM congresses asan emerging process, it has surely startedwell. These congresses answer a strongneed and this positive development mustcontinue. CICIAM acted mainly as astanding committee for these congresses.Now, however, it is time to focus also onother aims of the organisation. With thisshift of focus, we have seen that the opera-tional mode followed by CICIAM is nolonger sufficient.

In Edinburgh we changed our bylawsand from now on we have four elected per-manent officers: a President, a formerPresident/President elect, a Secretary and aTreasurer. My intention is to get the offi-cers to work as a team which prepares andexecutes those decisions reached by the

ICIAM Board at its annual meeting. Ourvision of ICIAM is, I think, shared by allinvolved: to become a truly globally oper-ating organisation in its field. I think wewill achieve this goal in an organic way, bybuilding on the tradition of applied math-ematics where many important societiesand are � and have been � multinational bynature.

How do you position ICIAM in the societiesin the world? Some of your member soci-eties are also corporate members of EMS.Would it still make sense for EMS to joinICIAM associate member?ICIAM has only scientific societies as mem-bers. In Edinburgh our by-laws werechanged so that societies significantly � butnot primarily � dedicated to applied orindustrial mathematics can be associatemembers of ICIAM. I am convinced thatEMS becoming an associate member wouldbenefit both ICIAM and EMS.

If I remember correctly, the ICIAM confer-ence series was started in 1987 in Paris outof protest to the ICM congresses of IMU.What is the relation nowadays betweenICIAM and IMU?It is true there has been some frustrationover the minor role accorded to appliedmathematics at ICM congresses, but themain motivation was undoubtedly the needfor international congresses dedicated toapplied mathematics. The community hadgrown large and strong enough to emergein its own right. At present there are noformal links between ICIAM and IMU, butin Edinburgh a decision was reached toestablish contacts.

I�ve noticed that the applied mathematicscommunity has grown in size and the num-ber of mathematicians in this area is surelyalmost equal to the number of the mathe-maticians in areas outside applied mathe-matics. Can you confirm this?Yes, I think we can say that their size is of

the same magnitude.

Do you think that one should adapt the sub-ject classification used at ICM and ECMcongresses to reflect this change?Well, yes, I think the classification used atICM congresses surely has a strong sub-conscious influence on what is viewed asvaluable within mathematics. And fromthis perspective the situation is far fromsatisfactory. It is interesting to look backon the history of IMU. There have been anumber of attempts to increase connec-tions to applications. However, these haverather been attempts to reach out to suchfields as theoretical mechanics or theoreti-cal computer science, instead of support-ing the existing applied mathematics com-munity within mathematics.

The acronym ICIAM comprises �Industrialand Applied Mathematics�. Where do youposition this type of mathematics within thewhole of mathematics?Perhaps the customary way of thinking isto put it at the periphery, where it livesclosely connected with its neighbouringfields within other sciences. However, if weask ourselves why mathematics exists in thefirst place, in this socio-economic world, itis at the very centre.

Is Industrial Mathematics not simply oneaspect of Applied Mathematics?Not really. To me, applied mathematicsrefers to a certain, specific area within thescience of mathematics, whereas industrialmathematics relates more to its applicationin industry. For example, a smaller con-ference within some field of applied math-ematics would typically take a slice ofapplied mathematics following some classi-fication as in science, while a reasonableslice of industrial mathematics might col-lect different types of mathematical toolsvital to one fixed industrial area.

For the newest arrival on the scene,Computational Science and Engineering, orCSE, many centres have been created andnew curricula set up. Is CSE a science?Should it be taught?It is true, CSE is arriving in many placesnow. I know you have a programme atETH and we are starting a program atHelsinki University of Technology as well.I think the name of this discipline, CSE, isvery honest in that it emphasises computa-

INTERVIEW

EMS December 199918

InterInterview with Olavi Nevanlinnaview with Olavi NevanlinnaPresident of ICIAM

interviewer: Rolf Jeltsch, EMS President

Olavi Nevanlinna (right) and Rolf Jeltsch during a working break inHelsinki, summer 1978.

Celebrating the election of Prof. Olavi Nevanlinna (right) as President ofICIAM at Rolf Jeltsch�s house in Zurich, autumn 1999.

tion as a tool to obtain new scientific resultsand to propose new or develop existingengineering practices. Naturally it has tobe taught. The fact that it is an interdisci-plinary subject makes teaching more diffi-cult, but no less important.

You were elected just a few days ago andhence I feel very flattered that your firsttrip, directly after the visit to your prede-cessor, Reinhard Mennicken, should be tome.Mister President. I am flattered that youare flattered. I like this city. Zurich issurely one of the centres of mathematics.For example, it has hosted the ICM no lessthan three times � no other venue was cho-sen more than once. Maybe we should tellthe readers that we used to work together,quite a lot actually, in the late 1970s andearly 1980s, and I am aware that we thinkalong similar lines: that applied mathe-matics really does need a push and thatthis push will eventually benefit pure math-ematics.

This occasion [raising their glasses to drinkto their close co-operation] reminds me ofan old photo of the two of us, taken inHelsinki in 1978 where we celebrated some-thing, although I don�t remember what.It must have been the fair number of beau-tiful theorems we proved during the twomonths on the beach at our summer place.

May I ask you a more personal question?You come from a very famous family of fivegenerations of mathematicians. When Iused to lecture on our joint work, peoplealways wanted to know about your familyconnection with Rolf Nevanlinna. I assumethat our readers would like to know this too.Well, Rolf, I have been asked this questiona few times too. Rolf Nevanlinna was mygrandfather�s brother. When I decided tostudy mathematics I entered the HelsinkiUniversity of Technology in order to gaindistance from the function theory schoolwhich dominated mathematics at theUniversity of Helsinki at that time. I want-ed to pursue my own career in appliedmathematics.

Only after a dozen years as full profes-sor did I allow myself to work in that area.Actually, while lecturing here at ETH dur-ing the summer term in 1992 I noticed alink between value distribution theory ofmeromorphic functions and perturbationtheory of linear operators. Bearing inmind applications to iterative methods inlarge-scale computation, I wanted to beable to estimate the growth of a resolventin such a way that small rank perturbationswould be seen as small perturbations. Letme remind you that value distribution the-ory is often called Nevanlinna theory.

I am looking forward to an excellent coop-eration between our two societies.So am I, but should we say organisationsrather than societies?

Yes, that might be more appropriate.Thank you very much for this interview.

The EMS Committee on Applications ofMathematics plans to conduct a series of inter-views with recent mathematics graduates whonow work in industry. These interviews withapplied mathematicians will continue in futureissues.

What kind of work do you currently do inyour company?The technical work involves solving practi-cal engineering problems, usually involv-ing continuum mechanics and more specif-ically, fluid mechanics of non-Newtonianfluids. The background to this is thatSchlumberger Dowell are involved in pro-viding cementing and drilling fluid ser-vices to the oil industry.

How much does it relate to mathematics? The content of the work that I do is large-ly mathematical. However, this does notmean that I spend my time �doing mathe-matics�. Significant proportions of mytime are spent writing reports and papers,presenting and explaining my work,directing and helping others, program-ming, training, travelling, e-mail andbureaucratic activity. I think this is com-mon in any large multinational company.

Tell us about your mathematical educationand prior experience before your currentemployment.I have a B.Sc. in Mathematics fromUniversity of Wales, which is a general 3-year UK mathematics degree. Followingthis I specialised in applied mathematicswith an M.Sc. in Mathematical Modellingand Numerical Analysis at the Universityof Oxford. Finally I studied for my D.Phil.at Oxford. Although this was within theDepartment of Engineering Science, it waslargely industrial mathematical modelling.

My current position is my fourth job. Ispent three years working at AlcanInternational�s Banbury ResearchLaboratory (UK), during and after myD.Phil. The work here coincided largelywith my D.Phil. thesis work and wasinvolved with modelling a novelAluminium spray process. Following this Ispent two years as an ECMI post-doctoralresearch fellow at the Institute forIndustrial Mathematics, University of Linz,Austria. Here I did some feasibility typeresearch for Voest Alpine Industrean-lagenbau, on a Steel continuous castingprocess. I spent some time involved inactivities with the ECMI research networkactive at the time and some time publish-ing work from my thesis. I also lectured influid mechanics at the university. I joined

Schlumberger Cambridge Research afterthis and spent eighteen months therebefore starting my current job. My experi-ence there was quite varied, with muchlearnt about the oil industry and oilfield-type engineering, rather than undertakingany particular or significant mathematicalwork.

How do you view all this in view of yourcurrent work? What was especially impor-tant, what was missing and should havebeen emphasised more?Most of my work in the past seven or eightyears has been in the area ofindustrial/applied mathematics. I think Iwas fortunate to do the M.Sc. course, whichgave me enough confidence (and a toolboxof skills) to go out and tackle some realproblems. After this, every experience hashelped to build my problem-solving abili-ties. I�ve changed industry two or threetimes now and each time I find the learn-ing curve of �what the problems are� is eas-ier to climb. Two important things frommy perspective are: � in an applied mathematician�s education�modelling� and �problem-solving� areessential, but if they want to work in indus-try the first thing to recognise is that the�problem� is not a mathematical one, atleast at first. This is hard to put into a con-ventional maths education and should notbe at the expense of learning mathematics. � once working in industry as a mathe-matician, the opportunities to stay in touchand work with academic mathematiciansbecome very important intellectually.

How much of your work needs numerics?Nearly all, but the numerical mathematicsis rarely used or useful when I don�talready understand the problem or itssolution, at least partly, through analysis orintuition.

What skills in addition to mathematicalones do you need most?Diplomacy, communication and presenta-tion skills. The ability to see through busi-ness bullshit.

Dr. Frigaard also expressed his view that inhis experience, companies rarely hiremathematicians as such, but they are look-ing for people with expertise in a specificproblem area, so that mathematicians haveusually to compete with engineers.

Heinz W. Engl is Chairman of the EMSCommittee on Applications of Mathematics.

INTERVIEW


InterInterview with Ian Fview with Ian FrigaarrigaarddSchlumberger Dowell, Paris

interviewer: Heinz W Engl

There are many mathematical anniversaries in2000. If you are interested in writing a columnon any of the following, please contact either ofthe column editors, June Barrow-Green andJeremy Gray, in the first instance: NiccoloTartaglia (b.1500), John Napier (b.1550),John Maior (b.1550), Adrian Vlacq (b.1600),René Descartes (d. 1650), Daniel Bernoulli (d.1700), Simon L�Huilier (b. 1750), AbrahamKaestner (d.1800), Lorenzo Mascheroni(d.1800), Karl Feuerbach (b. 1800), SonyaKowalewskaya (b.1850), Alfred Pringsheim(b.1850), Bernt Holmboe (d.1850), EugenioBeltrami (d.1900), Joseph Bertrand (d.1900),Elwin Christoffel (d.1900), Jean-FrédéricFrenet (d.1900), Mary Cartwright (b.1900),Constantin Carathéodory (d.1950), ErnstHellinger (d.1950), Aleksandr Khinchin(d.1950) and Nikolai Luzin (d.1950).

Of the myriad of subjects that feature in19th-century mathematical research, nonemore completely embraces the period thancelestial mechanics. The century bothopened and closed with seminal works ofmonumental proportion. When it began,the first two volumes of Laplace�s Traité deMécanique Céleste were barely a few monthsold � they were published in October 1799� and when it ended, the final volume ofPoincaré�s Les Méthodes Nouvelles de laMécanique Céleste had just appeared. Therewas of course a substantial quantity of workproduced in between, initially promptedby Laplace�s work which became thespringboard for research in both theoreti-cal and practical astronomy. His followersfocused themselves on extending theresults, improving the methods of investi-gation, and illustrating the more obscurepoints of the theory. But research intocelestial mechanics was not done only bythose, such as Delaunay, Le Verrier,Newcomb, Hill and Tisserand, who spe-cialised in the subject. Such was the sub-ject�s appeal that it frequently engaged theattention of mathematicians whose reputa-tions resided elsewhere. Arthur Cayley, forexample, was renowned as a pure mathe-matician, but wrote almost forty papers forthe Royal Astronomical Society.

Considered together, the treatises ofLaplace and Poincaré provide a remark-able example of the expansion and evolu-tion of mathematical thought during thecentury. At the end of the eighteenth cen-tury, research into celestial mechanics wassufficiently limited that it was realistic forLaplace to aim to set down all there was toknow about the subject. Furthermore, itwas also a time of great faith in the ability

A century of celestialmechanics:

Laplace (1799) to Poincaré (1899) June Barrow-Green

of mathematics to quantify the world. Inkeeping with such a belief, Laplace, whowas �always less enamoured with the beau-ty of mathematical speculation than he wasanxious to unfold the system of the world�[7, p.111], actively pursued methods thatcould be used to yield quantitative infor-mation. But by the end of the century asignificant change had taken place. Notonly had the subject grown well beyond thescope of a single researcher, but the gener-al thrust of the activity had changed. Nolonger dominated by a single methodolo-gy, a split had emerged between the quan-titative and the qualitative approaches.There were those, such as George Darwin,who calculated orbits using numericalanalysis [3], but the innovative theoreticaldevelopment lay with the qualitative analy-sis of Poincaré. In contrast to the methodsof Laplace, the methods of Poincaré, whichrelied heavily on geometric intuition andreasoning, were quite unsuitable for use inquantitative analysis at the time when theywere conceived.

Pierre-Simon Laplace (1749-1827)Laplace began his career as professor ofmathematics at the École Militaire in Pariswhere he taught from 1769-76. His firstpublished paper, on the integral calculus,was published in 1771, and he was electedto the Académie des Sciences in 1773.During the 1770s he established his math-

ematical reputation, embarking on a pro-gramme of research in celestial mechanicsand in probability, the two subjects forwhich he would become most famous.With regard to celestial mechanics, he wasparticularly fascinated by the problem ofthe stability of the solar system. He wasconvinced that stability could be proved byNewton�s laws and his quest for a resolu-tion of the problem was to prove a fertileground for his ideas, most notably in hisintroduction of perturbation methods.

In the 1780s Laplace pushed forward

his earlier work and achieved many of hismost important results. These includedhis discovery of the long period inequalityoccurring in the mutual perturbations ofJupiter and Saturn, and the cause of thesecular variation of the mean motion of themoon. These discoveries added furtherconviction to his belief in stability, and by1788 he had become certain that stabilitywas beyond doubt. It was also the timeduring which he engaged in experimentalphysics, most notably in the chemicalphysics of heat, in active collaboration withLavoisier. In the early 1790s he was alsoheavily involved in the preparation of themetric system.

By 1795 Laplace had begun to compilematerial for Mécanique Céleste and in thatyear embarked on giving his first and onlylecture course at the École Normale. Thecourse was never completed, due to theclosure of the École, and for the missinglectures the students were referred to abook that Laplace was in the process ofwriting. The book, Exposition du Système duMonde, which was published the followingyear, contains a non-mathematical accountof planetary motion, rational mechanicsand gravitational theory, as well as a sum-mary of the history of astronomy. Itproved a resounding success. Although awork in its own right, it also acts as an out-line or prospectus for the Mécanique Céleste,and Laplace arranged for the second edi-tion to be published specifically to accom-pany the launch of the treatise.

Laplace was also involved in politics,although not to great effect. WhenNapoleon seized power in 1799 Laplacebecame Minister of the Interior but afteronly six weeks he was replaced byNapoleon�s brother. He was later appoint-ed to the Senate and in 1803 became chan-cellor of the Senate, a position of littlepower but of substantial salary. Napoleon,having realised the limits of Laplace�scapabilities, described him as having �car-ried the spirit of the infinitesimal intoadministration� [5, p.176].

Traité de Mécanique Céleste (1799-1825)In October 1799 Laplace presentedNapoleon with copies of the first two vol-umes of Mécanique Céleste. Napoleon�sresponse is legendary. He accepted thegift with the promise that he would readthem �in the first six months I have free�.He also invited Laplace and his wife todine the following day �if you have nothingbetter to do� [5, p.176]. The third volume,which was dedicated to Napoleon,appeared in 1802, the fourth in 1805, andthe final volume in 1825. Although imme-diately recognised as a masterpiece, itsmathematical difficulty combined with itsbroad range of subject matter meant thatonly a very few were able to read it all withany degree of facility [8, I, p.62].

The whole was conceived as two parts:the first, consisting of Volumes I and II,

ANNIVERSARIES

EMS December 199920

1999 Anniversaries

Pierre-Simon Laplace

deals with the methods and formulae nec-essary to determine the different types ofmotion, while the second is concerned withthe application of the formulae to planets,satellites and comets. As Laplace himselfdeclared, he had dual objectives in writingthe treatise. First, to provide a connectedview of all the existing theories of celestialbodies which derive from the law of gravi-ty, and, second, to improve the precision ofastronomical tables. Much of the work isderived from Laplace�s earlier research. Insome cases he used almost complete publi-cations, while in others he made revisionsto the papers so that they fitted in with hisoverall schema. He also included exten-sive applications of techniques he had pre-viously developed [5, Chapter 21].

The treatise opens with a mathematicalexposition of the general principles of sta-tics and dynamics as applied to materialpoints, systems of bodies and fluids. Thelaw of gravity is deduced from observation,the differential equations of gravitationalattraction are derived, and there are dis-cussions of the theory of elliptical motionand of perturbation theory, with specifictechniques � such as approximating peri-odic inequalities � illustrated using partic-ular examples.

Volume II covers the shape of celestialbodies, and the oscillations of the sea andthe atmosphere. It begins with an exami-nation of the attraction of spheroids andincludes a comparison of spheroidal attrac-tion theory with the results of geodetic sur-veys of meridional arcs. The latter, whichdraws on previously unanalysed data fromthe survey of the terrestrial meridian fromDunkirk to Barcelona (on which the metricsystem was based), also contains the appli-cation of error theory. Further discussionsinclude the shape of Saturn�s rings, andthe shape of the atmosphere of celestialbodies. These are followed by chapters onthe ebb and flow of tides, the stability ofequilibrium of the sea, the influence oflocal conditions, and a comparison withobservation. The volume concludes withan analysis of the rotation of celestial bod-ies, with examples drawn from the earth,the moon, and the rings of Saturn.

In Volume III Laplace deals with bothplanetary and lunar theory with a view toproviding a tool for accurate positionalastronomy. In order to obtain the neces-sary degree of precision he had to extendthe methods he had developed in VolumeI since these encompassed only thoseinequalities independent of the eccentrici-ties or inclinations of the orbits, or thosedependent on the first power of thesequantities. Here he carried the approxi-mations to higher powers, and applied toall the planets the method he had previ-ously used on Saturn in his work on Jupiterand Saturn. Having derived the formulae,he then employed the calculator AlexisBouvard to substitute in the values of theelements according to each planet, inorder to get numerical expressions foreach radius vector and its motions in lon-gitude and latitude.

The first part of Volume IV is mostlytaken up with the theory applied to the

Jovian satellites, but it also includes shortchapters on the satellites of Saturn and ofUranus, as well as a brief discussion of thetheory as applied to comets. The secondpart of the volume, which contains mostlynew material and moves into a quite differ-ent mode, examines �several questions rel-ative to the system of the world�. Theseinclude astronomical and terrestrial refrac-tions, barometric measurements of alti-tude, and the influence of the earth�s rota-tion on the descent of bodies falling from agreat height.

The fifth volume, originally intended toprovide a history of the subject togetherwith an account of the work of his contem-poraries, ended up rather differently. Ithad been delayed due to Laplace�s changein priorities � probability and physics hadovertaken celestial mechanics in his inter-ests � and by the time he came to publishthe final volume he was in the twilight ofhis career and felt unable to carry out thetask he had promised. Instead he tookrecourse in the papers on celestialmechanics he had published in the early1820s (which consisted mostly of correc-tions and improvements to theory he hadpreviously covered in Volumes I to IV) andreconceived Volume V as a unification ofthese researches accompanied by historical

summaries. The early parts of Laplace�s work were

rapidly translated into English by severalauthors, but these were supplanted by themasterful translation of the first four vol-umes by the American mathematicianNathaniel Bowditch (1773-1838). Inrecognition of the difficulty of the mathe-matics, Bowditch provided an extensivecommentary, including many diagrams,which was of a similar length to the treatiseitself. He also corrected some calculatingerrors. An estimate of the remarkably highstandard of Bowditch�s commentary can begauged from the fact that Legendre con-sidered it equivalent to a new edition, andthat requests were made for it to be trans-lated into both French and Italian.Although Bowditch completed his transla-tion between 1814 and 1817, his insistenceupon publishing it at his own expensemeant that it did not appear until severalyears later (1829-39). He wrote severalnotes on the fifth volume but died beforehe was able to complete the translation.Laplace�s material was also reworked byother authors for different audiences, as inthe edition that brought Mary Somervilleto fame, The Mechanism of the Heavens(1831).

Activity in the rest of the century strong-

ANNIVERSARIES


ly reflected the influence of Laplace and itwas not until the end of the century that amajor new development took place.

Henri Poincaré (1854-1912)Poincaré was awarded his doctorate from

the University of Paris in 1879, and after abrief appointment at the University ofCaen, returned to the University of Pariswhere he remained for the rest of his life.In 1886 he became Professor ofMathematical Physics and Probability, andin 1889 Professor of MathematicalAstronomy and Celestial Mechanics.

Almost from the beginning of his acad-emic career, Poincaré had been concernedwith the fundamental problems of celestialmechanics � in particular the three-bodyproblem and the stability of the solar sys-tem � and many of the papers he pub-lished during the 1880s relate to his inter-est in the subject. These include many of abroad theoretical nature, such as those onthe qualitative theory of differential equa-tions, as well as those in which he respond-ed to explicit questions of dynamicalastronomy.

In 1890 Poincaré�s celebrated Oscarprize-winning memoir on the three-bodyproblem was published, although the storyof its conception and publication hadbegun some five years earlier [1]. Todaythe memoir is famous for providing thefoundations for his Les Méthodes Nouvellesde la Mécanique Céleste, and for containingthe first mathematical description of chaos.The memoir, which is centred on therestricted three-body problem, introducedseveral new ideas into the study of dynam-ical problems, including the use of varia-tional equations and the use of invariantintegrals. But above all the memoir isdominated by his theory of periodic solu-tions. By taking a reductionist view andstudying the periodic solutions of a systemwith two degrees of freedom, Poincaré�sglobal qualitative perspective led him tothe brilliant discovery of asymptotic solu-tions. His analysis of the complex natureof these solutions then resulted in his dis-covery of homoclinic points and the begin-nings of the mathematical theory of chaos.

Les Méthodes Nouvelles de la MécaniqueCéleste (1892-99)The three volumes of Les MéthodesNouvelles de la Mécanique Céleste were pub-lished in 1892, 1893 and 1899. WhenGeorge Darwin presented the medal of the

Royal Astronomical Society to Poincaré in1900, he said, �It is probable that for half acentury to come [Les Méthodes Nouvelles]will be the mine from which humblerinvestigators will excavate their materials�[4]. With the benefit of hindsight it is pos-sible to say that had Darwin omitted theword �half�, his prediction would still havebeen fulfilled. Nevertheless, althoughhighly acclaimed, Les Méthodes Nouvellesreceived relatively few reviews, and almostnone engaged critically with the content,indicating the difficulty of the subject mat-ter. (In recognition of the work�s generalinaccessibility, Poincaré produced anotherthree volume set, Leçons de MécaniqueCéleste, which covered similar topics butwhich was aimed at a mathematically lesssophisticated audience. The Leçons, whichwere based on lectures given at theSorbonne, appeared between 1905 and1910 and is an altogether more practicalwork.) Les Méthodes Nouvelles contain theprincipal ideas from the 1890 memoir butin a more fully explained and developedform. Further applications of the theoryare included besides a substantial amountof new material, and the focus of attentionis more on the general three-body problemthan on the restricted problem.

Volume I covers the analytical part ofthe theory with many of the topics dis-cussed in the 1890 memoir revisited, butwith a greater emphasis on the role of theHamiltonian form of the equations. Thereis an amplified treatment of periodic solu-tions, with a stronger affirmation of theconjecture about the denseness of the peri-odic solutions, and, as in the memoir,there are chapters on characteristic expo-nents, asymptotic solutions and the non-existence of new single-valued integrals.The one completely new chapter is on theexpansion of the perturbation function.

In Volume II Poincaré concentrated on

the methods of contemporary dynamicalastronomers � namely, Newcomb, Gyldén,Lindstedt and Bohlin. Throughout hisresearches he had become increasinglyaware of the differences that had evolvedbetween the perceptions of mathemati-cians and of astronomers as to what consti-tuted a solution to a problem in celestialmechanics, and that these differences oftenled to what appeared to be inconsistentresults. In this volume he attempted toclarify the situation and to explain the dis-crepancies. In particular, he forcefullydemonstrates the importance of under-standing the nature of the convergence ofthe different series used in the expressionsfor the co-ordinates of the planets. Most ofthe material is completely new, apart fromthe discussion of the divergence ofLindstedt�s series. In the latter Poincaréreaches fundamentally the same conclu-sion with regard to divergence as he hadearlier but, displaying more caution thanbefore, he now casts doubt over the casewhere the frequencies are chosen inadvance. (Almost seventy years later it wasshown by Kolmogorov, Arnold and Moserthat Poincaré had been right to be guard-ed about his conclusions.)

The final volume is characterised byPoincaré�s geometrical ideas. HerePoincaré returned to the subjects of invari-ant integrals, stability, periodic solutions ofthe second class � periodic solutions thatmake more than one orbit around the pri-mary � and doubly asymptotic solutions.The volume also included a discussion ofwhat he now called periodic solutions ofthe second species. These are solutionswhich arise from a system involving two

very small bodies orbiting one large oneand which narrowly avoid collisions at def-inite intervals, the existence of which hehad conjectured at the end of the 1890memoir.

Poincaré�s discussion of doubly asymp-totic solutions contained essentially thesame analysis as the memoir but with oneimportant addition. In the memoir

ANNIVERSARIES

EMS December 199922

Henri Poincaré, 1872

Henri Poincaré

Poincaré had shown that corresponding toeach unstable periodic solution there was asystem of asymptotic solutions. However,he had only considered the possibility ofdoubly asymptotic solutions arising fromdifferent families of asymptotic solutionsassociated with the same unstable periodicsolutions. These are what he called homo-clinic solutions. Now he proposed that adoubly asymptotic solution of a differenttype could arise from asymptotic solutionsassociated with two different unstable peri-odic solutions, and these he called hetero-clinic solutions. In both cases he showedthat the existence of one of these solutionsis sufficient to prove the existence of aninfinite number, and, in contrast to thememoir, he is absolutely explicit abouttheir bewildering complexity.

The difference a century makesAlthough the aims of the two authors werefundamentally the same � to determinewhether Newton�s law of gravity explainsall astronomical phenomena � theirmethodologies were palpably different.Laplace developed the theory and then,combining observation and calculation,demonstrated its usefulness, whilePoincaré, mindful of the shortcomings ofboth observation and calculation, focusedalmost entirely on the theoretical develop-ment. Nevertheless there are similaritiesbetween the two treatises. They both owetheir genesis to an abiding interest in theproblem of the stability of the solar system.They both rely heavily on previously pub-lished work and both are showcases forexciting results: Laplace�s discovery of thelong period inequality of Jupiter andSaturn, and Poincaré�s discovery of homo-clinic point to name but two. Both worksare extremely mathematical and virtuallyimpossible for all but the specialist toassimilate, but in each case the author didprovide a simplified counterpart: Laplacewith the Systéme du Monde and Poincaréwith the Leçons de Mécanique Céleste. Bothtreatises are characterised by a conspicu-ous lack of diagrams. Laplace, who did notinclude any, assumed his audience suffi-ciently well versed in analysis not to needthem. Poincaré, who included a few, reliedlittle on pictorial representation himself �he was renowned for his inability to draw �and was probably oblivious to the needs ofothers not blessed with his gift of geomet-ric visualisation.

Another way in which the two works dif-fer is in the speed and type of responsethey received with respect to translation.Poincaré�s treatise, unlike that of Laplace,did not receive immediate attention. Thefirst English translation of MéthodesNouvelles, which was published in 1967 byNASA, appeared more than sixty yearsafter the original and contained little byway of commentary. The different rates ofresponse with respect to translation reflectthe perceived utility of the two works.Laplace�s treatise is not a homogeneouswhole but rather �a textbook, a collectionof research papers, a reference book, andan almanac� [5, p.184] rolled into one. Ithas an obvious practical dimension � there

are techniques and results that peoplewanted to use and indeed Laplace expect-ed them to use � and it was clearly a toolfor further research. Poincaré�s work onthe other hand was deeply theoretical andfiercely difficult, and while it containedmathematical techniques of great interestto mathematicians, the inability ofresearchers to engage in a quantitativeanalysis due to inadequate computingtechniques meant that it had only spe-cialised appeal. The demand for transla-tion was generated when, with improvedcomputing power and the stimulus of adeveloping space programme, Poincaré�smethods could actually be applied. Morerecently, with the advent of the moderndigital computer and the explosion ofresearch into non-linear systems resultingin the unfolding of the mathematical theo-ry of chaos, interest in Poincaré�s work hasintensified and in 1993 a second transla-tion was published [6].

Both Laplace�s Traité de MécaniqueCéleste and Poincaré�s Les MéthodesNouvelles de la Mécanique Céleste opened anew era in the study of celestial mechanics.Each work stands as a testament to thegenius of its author. Poincaré did notsupersede Laplace, he launched out in adifferent direction. In the words of GastonDarboux, each merits a place alongside theother [2].Bibliography1. J. Barrow-Green, Poincaré and the Three Body

Problem, American Mathematical Society,Providence, 1997.

2. G. Darboux, �Éloge Historique d�HenriPoincaré� Mémoires de l�Académie des Sciences del�Institut de France 52 (CXX-CXXI), 1914.

3. G. H. Darwin, �Periodic orbits�, ActaMathematica 21 (1897), 99-242.

4. G. H. Darwin, �Presentation of the medal ofthe Royal Astronomical Society to M. HenriPoincaré�, Monthly Notices of the RoyalAstronomical Society 60 (1900), 406-415.

5. C. G. Gillispie, Pierre-Simon Laplace 1749-1827. A Life in Exact Science, Princeton,1997.

6. D. L. Goroff, �Henri Poincaré and chaos the-ory: An introduction to the English transla-tion of Les Méthodes Nouvelles de la MécaniqueCéleste�, New Methods of Celestial Mechanicsby Henri Poincaré, American Institute ofPhysics, 1993.

7. R. Grant, History of Physical Astronomy,London, 1852.

8. P.-S. Laplace, Traité de Mécanique Céleste, 5vols., Paris, 1799-1825; translated by N.Bowditch, Boston, 1829-39.

9. H. Poincaré, Les Méthodes Nouvelles de laMécanique Céleste, 3 vols., Paris, 1892-99;translated by the American Institute ofPhysics, 1993.

10.H. Poincaré, �Sur le problème des trois corpset les équations de la dynamique�, ActaMathematica 13 (1890), 1-270.

June Barrow-Green [[email protected]] is a research fellow in the history of math-ematics at the Open University, UK.

Otto Neugebauer was one of the few greathistorians of mathematics there has everbeen. Born in Innsbruck, Austria, on 26May 1899, he was attracted to mathematicsat school but joined the Austrian Army in1917 in order to be excused the schoolleaving examination in Greek, which heclaimed he had no chance of passing. Hewas taken prisoner at the armistice andspent almost a year in a prisoner of warcamp; Ludwig Wittgenstein was a fellowprisoner.

By 1922 he had made his way to

Otto Neugebauer (b. 1899)Jeremy Gray

ANNIVERSARIES


This Babylonian tablet, described by Neugebauer, illustrates a knowledge of Pythagorean triples1000 years before Pythagoras.

Göttingen, where he struck up life-longfriendships with Richard Courant, HaraldBohr, and the Russian mathematicianAlexandroff. His only publication in puremathematics is a joint paper with Bohr onalmost periodic functions. Bohr hadalready asked him to review T. E. Peet�snew edition of the Rhind papyrus, know-ing that Neugebauer had embarked on aserious study of Egyptian; his Göttingendissertation, on the vexed topic ofEgyptian unit fractions, was conductedwith the approval of Courant and Hilbert.In 1927 he began lecturing on ancientmathematics, and it was these lectures thatbrought van der Waerden to the subject.

In 1927 Neugebauer began to learnAkkadian, the language of Babylonianmathematics, and embarked on his great-est contribution to the history of mathe-matics. Whereas Egyptian sources werewell known and often well studied,Babylonian sources hidden away in numer-ous museums were seldom read and stan-dards were very low. Neugebauer was topublish his 3-volume collection on mathe-matical tablets in the mid-1930s. Theyestablished the great richness ofBabylonian mathematics, far exceedinganything one could have guessed fromGreek or Egyptian sources. The ramifica-tions of this discovery continue to animatethe study of ancient mathematics to thisday, and as Neugebauer�s own estimationof Babylonian mathematics and astronomycontinued to deepen he refused any longerto consider them as �pre-Greek�; indeed hefound their level of mathematical abstrac-tion and power exceeded Ptolemy�s.

Neugebauer was also active in thedesign of the new Mathematics Institute atGöttingen, completed with money fromthe Rockefeller Foundation in 1929. Hewas the driving force behind the creationof Zentralblatt für Mathematik und ihreGrenzgebiete, which came out for the firsttime in 1931. When the Nazis came topower students attacked him for beingpolitically unreliable (he was very liberal inhis views) and he refused to sign the loyal-ty oath. Bohr was able to arrange forNeugebauer to move to Copenhagen inJanuary 1934 on a three-year appoint-ment, and he was able to bring Zentralblattwith him. He fought a long struggle toprotect the journal from the Nazis andtheir supporters, Blaschke in particular,and eventually resigned as part of anorganised protest at the dismissal of Levi-Civita from the editorial board.

In 1939 Neugebauer sailed to America,where Brown University was offering him aprofessorship, and threw himself into thecreation of Mathematical Reviews. The firstedition appeared on time in January 1940,and Neugebauer is recognised as thefounding editor (as he is of Zentralblatt, asthe revived journal proudly says). AtBrown he built up what became the lead-ing institution in the world for the study ofthe history of the exact sciences, especiallyof the ancient world. It was a magnet forscholars around the world, and capable ofdrawing people in, despite the narrow-minded traditionalism of their home uni-

versities. Neugebauer published profuse-ly, and much of our knowledge of ancientastronomy and chronology is due to him.

He received numerous honours and waselected to many learned societies, but itmay be supposed that his greatest pleasurewas in entirely reshaping and extendingour knowledge of the history of science.Indeed, the message that Babyloniansknew more (and, as he impishly insisted,the Egyptians knew less) than most peoplebelieve still needs amplification today.The high level of scholarship that now pre-vails in the subject gives every prospectthat received opinion will change, and thathigh level is largely due to the standardshe set himself, his organisational skills, andthe support he was able to attract.

Ascher Zaritsky was born in Kobrin inWhite Russia on 24 April 1899, the sixthchild of Bezalel and Hannah Zaritsky, andspent his first eleven years there. Hisresourceful mother was able to afford atutor for him in Russian and arithmeticfrom the age of seven. Oscar learned thesesubjects quickly and they proved his pass-port out of the Pale. The family fled thewar to Chernigov in Ukraine, and Oscarreturned briefly in 1918 before enrollingin the philosophy department at theUniversity of Kiev in 1921 (there was noroom in the mathematics faculty). Politicalupheaval eventually soon him to Rome,where he enrolled under Castelnuovo and

the more sociable Enriques. They wereamong the great figures of algebraic geom-etry and this was the subject that Zariskiwas to work on more than any other. It wasEnriques who suggested that he Italianise

Oscar Zariski (b. 1899)Jeremy Gray

his name to Oscar Zariski, when they cameto prepare their first joint paper for publi-cation. It was also in Rome that Zariskimet Yole Cagli. He married her on a visitto his home town of Kobrin in September1924.

When the Fascists took power in Italylife became increasingly difficult for Jews,and with Lefschetz�s help Zariski obtaineda postgraduate fellowship at JohnsHopkins University. Lefschetz�s work intopology was just one sign that Zariski wasmoving beyond his Italian mentors:Castelnuovo once said to him �You arehere with us but you are not one of us�,referring to his algebraic inclinations andhis insistence on rigour. In 1935 Zariskiwas to write an account that satisfied him ofthe algebraic theory of surfaces, whichCastelnuovo and Enriques had done somuch to start, but, as he put it, �The pricewas my own personal loss of the geometricparadise in which I had so happily beenliving�.

By then Zariski had become a professorat Johns Hopkins, and in 1937 he becamea full professor. He embarked on a pro-gramme of adapting and creating conceptsin commutative ring theory to formulateand solve problems in algebraic geometry.He introduced the integral closure of aring in 1937 and in 1939 applied it to theresolution of singular points on curves andsurfaces. It was also in this context that heintroduced the topology on an algebraicvariety that now bears his name: the Zariskitopology. He did this in 1944 to facilitatethe study of what he called at the time theRiemann surface associated to a field, andby then he was thoroughly committed todeveloping algebraic geometry over arbi-trary fields.

In 1945 Zariski was in Sao Paolo for ayear. His duties included giving one lec-ture course of three hours a week; his audi-ence consisted of one student, André Weil.They had already met at the Institute forAdvanced Study in Princeton in 1937 andin Harvard in 1941, and the year theyspent together was a stimulating one foreach of them, despite, or perhaps becauseof, their often heated disagreements.

In 1947 Zariski made his final move, toHarvard, where he was to stay for the restof his life and greatly influence theprogress of algebraic geometry. Amonghis students there were Michael Artin,Robin Hartshorne, Heisuke Hironaka,Steven Kleiman, and David Mumford.Zariski�s high standards and ambition forthe subject, coupled with his urge to gen-eralise beyond the familiar complex case,were instrumental in bringingGrothendieck�s new vision of algebraicgeometry to America, a transition in whichall of his students played major roles. Hestayed on at Harvard for five years afterthe usual retirement age, becoming a pro-fessor emeritus in 1969, but in the late1970s his health began to fail andAlzheimer�s disease was eventually diag-nosed. He died on 4 July 1986.

Jeremy Gray [[email protected]] is a seniorlecturer at the Open University, UK.

ANNIVERSARIES

EMS December 199924

Oscar Zariski

The Fondazione CIME will hold five cours-es in 2000: two courses will be held atMartina Franca (Taranto, Italy), two will beheld at Cetraro (Cosenza, Italy), and onewill be held at Funchal (Portugal), jointlyorganised by CIME and CIM (CentroInternacional de Matematica, Portugal).

Brief information concerning thesecourses is presented below. Further infor-mation can be found on the Web server ofthe CIME, http: //www.math.unifi.it/CIME

If you are interested, please contact: Fondazione C.I.M.E. c/o Dipartimento diMatematica �U. Dini�, Viale Morgagni, 67,A-50134 Firenze, Italy tel: (+39)-55-434975 / (+39)-55-4237123fax: (+39)-55-434975 / (+39)-55-4222695 e-mail: [email protected] Director: Prof. Arrigo Cellina[[email protected]] Secretary: Prof. Vincenzo Vespri[[email protected]]

If you wish to attend, you should sendan application to the C.I.M.E Foundationat the address above, one month before thebeginning of each course (not later than 20July for courses starting in September). Inthe application your field of currentresearch must be specified.

An important consideration in theacceptance of applications is the scientificrelevance of the Session to the field ofinterest of the applicant. Participation willbe allowed only to persons who haveapplied in due time and have had theirapplication accepted. CIME will be ablepartially to support some of the youngestparticipants. Those who plan to apply forsupport must mention this explicitly in theapplication form.

Sites and LodgingMartina Franca is a charming, beautifullypreserved ancient city on the hills of Puglia(South Italy), an architectural jewel.Participants are lodged at the Park HotelS. Michele, a nice hotel with a well-keptgarden and a large swimming pool. TheLectures will be at the Palazzo Ducale (CityHall), within short walking distance, at theSala Arcadia. Cetraro is a beatiful locationon the Tirrenian coast of Calabria (SouthItaly). The nearest train station is Paola onthe line Roma-Salerno-Reggio-Calabria,easily reached even by fast trains (Eurostartrains stop in Paola).

CIME activities are made possiblethanks to the generous support receivedfrom The European Commission, DivisionXII, TMR Programme �Summer Schools�;Consiglio Nazionale delle Ricerche;Ministero dell� Università e della RicercaScientifica e Tecnologica; UNESCO-ROSTE, Venice Office.

Course 1: Dynamical Systems, Cetraro(Cosenza), 19�26 June

Jack Macki (Alberta) Pietro Zecca (Florence) [[email protected]]Stability and entropy in spatially discretedynamical systems (6 lectures in English)Shui-Nee Chow, Singapore Planar dynamical systems (3 lectures inEnglish) Roberto Conti, Florence Non-autonomous dynamical systems (6 lecturesin English) Russell Johnson, FlorenceWaves in spatially discrete dynamical systems (6lectures in English) John Mallet Paret, ProvidenceRecent trends in the theory of non-linear delayequations (6 lectures in English) Roger Nussbaum, Rutgers

Course 2: Diophantine Approximation,Cetraro (Cosenza), 28 June � 6 July Scientific Direction: Francesco Amoroso (Caen) [[email protected]] Umberto Zannier (Venice) [[email protected]] (6 lectures in English for each course)Diophantine Approximation on CommutativeGroups VarietiesDavid Masser, BaselThe Absolute Subspace TheoremHans Peter Schlikewei, MarpurgZeros of linear recurrence sequences Wolfgang Schmidt, ColoradoLinear Independence measures for Logarithmsof algebraic numbersMichel Waldschmidt, Paris

Course 3: Mathematical Aspects ofEvolving Interfaces, Funchal (Portugal),3 � 9 July Organised by CIME and CIM (CentroInternacional de Matematica, Portugal) Scientific Direction: Pierluigi Colli (Pavia)[[email protected]]

Jose-Francisco Rodrigues (Lisbon) [[email protected]] (3 lectures (90 minutes) in English for eachcourse)Distance function and evolution of fronts byimplicit time discretisation Luigi Ambrosio, PisaNumerical approximation of mean curvatureflow of graphs G.Dziuk, Freiburg Dynamics of patterns and interfaces in reaction-diffusion systems from chemical and biologicalviewpoints. Masayasu Mimura, Hiroshima Evolution free boundary problem for parabolicand Navier-Stokes equations V. A. Solonnikov, St PetersburgVariational and dynamic Problems for theGinzburg-Land Functional. H. M. Soner, Princeton

Course 4: Mathematical Methods forProtein Structures Analysis and Design,Martina Franca (Taranto), 9 � 15 JulyScientific Direction: Concettina Guerra (Padua) [[email protected]] Sorin Istrail (Sandia) [[email protected]] (4 lectures in English for each course) Mathematical protein Structure Analysis.Arthur Lesk, Cambridge (Title to be announced) Michael Levitt, Stanford High Speed Computations for the Design ofProteins.John Moult, MarylandGeometric Computing in Structural MolecularBiology. Haim Wolfson, Tel Aviv

Course 5: Noncommutative Geometry,Martina Franca (Taranto), 3�10SeptemberScientific Direction: Sergio Doplicher (Rome) [[email protected]] Roberto Longo (Rome) [[email protected]] (6 lectures in English for each course) Noncommutative Geometry Alain Connes, ParisK-Theory and Cyclic Cohomology Joachim Cuntz, MunsterGroup C*-algebras and K-Theory Nigel Higson, PennsylvaniaThe Algebraic Approach to Quantum FieldTheory. John E. Roberts, Rome

NEWS


C.I.M.E. C.I.M.E. Summer Courses 2000Summer Courses 2000

Journal of the European Mathematical Society (JEMS)

The contents list of the fourth issue of the JEMS is as follows: Volume 1, Number 4

Edson de Faria and Welington de Melo, Rigidity of critical circlemappings I Stefan Müller and Vladimir Sverák, Convex integration with con-straints and applications to phase transitions and partial differentialequations

Societies corner is a column concerning themathematical societies in European countries.The articles in this column could describe thehistory of a particular society or discuss someevent connected with the society. If you feel thatyour society would interest others, please contactthe column editor, Krzysztof Ciesielski (e-mail:[email protected]) in the first instance.

In Luxembourg organised mathematicalactivities, other than pedagogical ones,started around 1970, under the name of�Séminaire de Mathématique deLuxembourg�. In 1988, the members ofthat group created the SociétéMathématique du Luxembourg (SML),which became a founding member of theEuropean Mathematical Society.Currently the Luxembourg MathematicalSociety has 35 members, of whom 21belong to the EMS. The regular activitiesof the SML consist of weekly seminars.The topics vary, but usually relate to har-monic analysis or differential geometry.

The SML endeavours to popularisemathematics in a small country, and fromtime to time organises conferences for thegeneral public. Among the symposia ongeneral mathematical subjects, eachattended by about one hundred people, we

LuxembourgMathematical

SocietyJean-Paul Pier

mention: �Mathematics and Reality�(1974), �Mathematical Language andMathematical Thought� (1976), and�Poincaré�s Philosophy of Science� (1986).The speakers have included J. Dieudonnéand R. Thom.

A regular congress of GMEL(Groupement des Mathématiciensd�Expression Latine) was held inLuxembourg in 1981. It involved mainlymathematicians from neo-Latin speakingcountries (French, Spanish, Italian,Portuguese and Romanian). The SML ismuch concerned with cooperation in the�Grande Région� centred in Luxembourg,and regional meetings have includedUniversité de Liège, Centre universitairede Luxembourg, Université de Metz,FUNDP Namur, Université HenriPoincaré Nancy, Universität desSaarlandes and Universität Trier.Specialised symposia have also takenplace, such as �Harmonic Analysis� (1987),with the participation of G. Mackey(Springer Lecture Notes 1359). Besidesthe publication of symposia proceedings,the SML has for ten years edited a yearlyissue of �Travaux mathématiques�, whichshould now be expanded further.

In the context of World MathematicalYear 2000 (WMY2000), the SML has givenmuch consideration to understanding theevolution of mathematical ideas during thenow-ending century. Two symposia havealready been organised: � �The Development of mathematics1900-1950�, at Bourglinster Castle in 1992;foreign speakers were J. L. Doob, G.

Fichera, I. Gelfand, M. Guillaume, W. K.Hayman, C. Houzel, A. Lichnerowicz, L.Nirenberg and W. Schwarz (see picture); � �Developments in mathematics at theeve of 2000�, at Centre universitaire deLuxembourg in 1998; foreign speakerswere J. P. Bourguignon, C. Houzel, V.Kac, J.-P. Kahane, J. Mawhin, N. Nikolskii,R. Penrose and R. Remmert.

At the end of 1997 UNESCO unani-mously adopted a motion introduced byLuxembourg, declaring its sponsorship forWMY2000 (draft resolution 29C/DR126).A new motion has recently been proposedby Luxembourg, asking UNESCO toincrease its support for mathematical pro-jects during WMY2000.Jean-Paul Pier is President of the SociétéMathématique de Luxembourg.

In this note, we give a short history andsome general information on the KharkovMathematical Society (KMS) and the math-ematicians who have played an importantrole in its activities.

The KMS was founded in 1879 on theinitiative of V. G. Imshenetskii (1832-92).He was a professor at Kharkov Universityand worked in partial differential equa-tions. According to the Charter of the

KharkovMathematical

SocietyI. V. Ostrovskii

EMS December 199926

SOCIETIES

Societies Corner

KMS, �the goal of the mathematical societyis support of development of pure scientif-ic and pedagogical questions in the field ofmathematics�. Meetings with scientificreports were held monthly, as a rule.Starting from 1880, the KMS has pub-lished Communications of KMS, first as asupplement to the Transactions ofKharkov University, and then as a separatejournal.

In 1885, A. M. Lyapunov (1857-1918), aformer student of P. L. Chebyshev, movedfrom St Petersburg to Kharkov and playeda leading role in the KMS. During his yearsin Kharkov (1885-1902) Lyapunov carriedout research in stability theory, potentialtheory and probability theory, gaining hima world-wide reputation. He gave 27reports on this work at the meetings of theKMS. Because of Lyapunov, mathematicalresearch and reports at KMS meetingsreached a much deeper level. In the nextperiod (1902-06), the chairman of KMSwas V. A. Steklov (1863-1926), a formerstudent of Lyapunov. Steklov is wellknown for his work in mathematicalphysics and analysis, and also as one of theorganisers of scientific research in theSoviet Union. In particular, he foundedthe Institute of Mathematics in Moscownamed after him.

During the forty-year period 1906-46,the chairman of KMS was D. M. Sintsov(1876-1946), who worked in geometry andin the geometrical theory of Pfaff andMonge equations. Sintsov was an activeparticipant of the movement for thereform of school education in mathemat-ics, and worked on the international com-mittee for the promotion of these reforms,headed by F. Klein. Through Sintsov�s ini-tiative, the KMS was deeply involved in theimprovement of mathematical educationin the schools of the Kharkov region.Sintsov also put considerable effort intomaintaining the KMS mathematical librarywhich is still one of the most completemathematical libraries in the Ukraine.

From 1908 to 1933, S. N. Bernstein(1880-1968), one of the leading mathe-maticians of the 20th century, worked inKharkov. Scientific activity, and all otherkinds of KMS activity, were under hisstrong influence during these years. Manyof his famous results were first reported atKMS meetings and then published in theCommunications of KMS. Among his stu-dents were V. L. Goncharov (1896-1955)and Ya. L. Geronimus (1898-1984), both ofwhom became well-known mathemati-cians. After 1917, S. N. Bernstein used hisgreat international reputation to maintainand promote further development ofmathematics in Kharkov. In 1929, heorganised the Institute of Mathematics atKharkov which provided an opportunityfor scientific research for many mathemati-cians. Due to Bernstein�s world-wide repu-tation, the First All-Union MathematicalCongress took place in 1930 at Kharkov(rather than in the capital of the USSR, asone would expect according to the tradi-tions of that time). A number of mathe-maticians from the West participated inthis Congress, among them beingHadamard, Denjoy and Montel.

Soon, after a conflict with the KharkovCommunist party leaders, Bernstein hadto leave Kharkov. But before doing so, heinvited N. I. Akhiezer (1901-80) to move toKharkov. In 1933, Akhiezer became theDirector of the Institute of Mathematics,and in 1947, the chairman of the KMS.Akhiezer�s work on approximation theory,the moment problem and operator theoryare well known today. His books on theseand other topics are outstanding pieces ofmathematical literature. Akhiezer man-aged to create a strong mathematical com-munity in Kharkov. We mention here a fewnames that should be of interest today tospecialists in related fields: Ya. P. Blank(1903-87), A. M. Danilevskii (1906-41), G.I. Drinfeld (b. 1908), A. M. Efros (1906-41), I. M. Glazman (1916-68), M. I. Kadets(b. 1923), N. S. Landkof (b. 1915), B. Ya.

Levin (1906-93), B. M. Levitan (b. 1914),M. S. Livshic (b. 1917), V. A. Marchenko(b. 1922), A. D. Myshkis (b. 1920), A. Ya.Povzner (b. 1915), A. V. Pogorelov (b.1919), A. K. Sushkevich (1889-1961) andE. M. Zhmud� (b. 1918).

In 1950, the Institute of Mathematics inKharkov was closed by a decision of theSoviet Government. Conditions for scien-tific work started to deteriorate. In thisconnection, an important event was thefoundation in Kharkov, in 1960, of theInstitute for Low Temperature Physics andEngineering (ILTPE). The founder andfirst Director of the Institute was the physi-cist B. I. Verkin (1919-91). A broad-mind-ed person with great respect for puremathematics, he invited the leadingKharkov mathematicians, Akhiezer,Glazman, Levin, Marchenko, Myshkis and

Pogorelov, to join the Institute with agroup of their former students and to con-tinue their mathematical research in theInstitute. The scientific activity of Levin,Marchenko, Myshkis and Pogorelov led tothe further flourishing of mathematicalstudies in Kharkov which lasted till thebeginning of the 1990s. An importanthonour for the KMS was when V. G.Drinfeld (b. 1954), a member of theMathematical Division of ILTPE, wasawarded a Fields Medal in 1990.

Until 1992, the KMS usually heldmonthly scientific meetings with talks byKharkov mathematicians and others fromall over the Soviet Union. Publication ofCommunications of KMS was stopped in the1960s by officials, in spite of the energeticprotests of N. I. Akhiezer. However, hesucceeded in starting a new journal,Function theory, functional analysis and theirapplications, which was published till 1992.From 1994 to 1999, the KMS participatedin the publication of the journalMathematical Physics, Analysis and Geometry,and in 2000 a new journal, MathematicalAnalysis and Geometry, will be published.

After the break-up of the Soviet Unionand the cut-off of finance for scientificresearch, many Kharkov mathematicianshave found positions abroad. Certainly,this has caused serious damage to the workof the KMS. Nevertheless, the KMS con-tinues to hold scientific meetings and tosupplement its mathematical library withnew mathematical literature. The KMSalso participates in the distribution ofurgent support that comes from othermathematical societies to the Kharkovmathematicians. I. V. Ostrovskii is Chairman of the KharkovMathematical Society.


SOCIETIES

The four Fields Medalists in 1990, V. G. Drinfield is on the right.

A Russian postagestamp featuringA. M. Lyapunov.

NEWS

EMS December 199928

Sixty mathematicians, computer scientists,physicists and engineers from twelve coun-tries took part in the EMS-WiR SummerSchool, Numerical Simulation of Flows, heldin September 1999 at the chair ofTechnical Simulation, IWR, of theUniversity of Heidelberg, Germany. Thesummer school was organised in coopera-tion with the European MathematicalSociety (EMS), the research associationWiR Ba-Wu (Wissenschaftliches RechnenBaden-Wurttemberg), ESF-AMIF (Euro-pean Science Foundation � AppliedMathematics for Industrial FlowProblems), and SFB 359 (Reactive Flow,Diffusion and Transport) of HeidelbergUniversity. The members of the EMS-WiRSummer School Scientific Committee wereDr. P. Bastian (Heidelberg), Prof. G. Dziuk(Freiburg), Prof. W. Hackbusch (Leipzig),Prof. R. Jeltsch (Zurich), Prof. D. Kroener(Freiburg), Prof. C.-D. Munz (Stuttgart),Prof. R. Rannacher (Heidelberg), Prof. W.Rodi (Karlsruhe), Prof. S. Sauter (Zurich),Prof. S. Wagner (Stuttgart), Prof. G.Wittum (Heidelberg) and Prof. H.Yserentant (Tubingen).

The numerical simulation of flows isone of the central problems in scientificcomputing. The complexity of flow simu-

lations is so great that a realistic descrip-tion requires sophisticated mathematicalmethods and models. In particular, themodelling and simulation of turbulentflows, as well as nearly incompressibleflows, are challenging problems for mathe-matical models and numerical methods.The numerical simulation of flows requiresthe co-operation of several mathematicaldisciplines such as analysis, numerics,mathematical physics, and computationalscience.

The programme comprised a theoreti-cal and a practical part. The first week (inHeidelberg) consisted of basic instruction.During this week mathematical modelsand methods were presented in lectures byspecialists. In particular, Prof. Yserentantpresented a survey of the mathematicaldescription of flows and Prof. Jeltsch gavea talk on the modelling of compressibleflows and the method of transport for sim-ulation. The lectures by Prof. Kinzelbachand Prof. Helmig, focused on the model-ling of groundwater flows and transport,and the theoretical basis of multi-phaseflows in porous media. Prof. Wagner pre-sented a survey on turbulent flows. Prof.Quarteroni spoke on flows in biosystems.Surveys of finite element and finite volume

methods were presented by Prof.Rannacher and Prof. Kroener.

Further topics were interface flows, lowmach number flows, conjugate gradientand other Lanczos-type methods for largelinear systems, multi-grid methods, andalgebraic multi-level methods. Dr. Bastiangave an overview on software concepts andtools suited to the solution of flow prob-lems. Further lectures on grid generationand methods for the visualisation of flowswere presented. An evening reception atthe chair of Technical Simulation, IWR,and an excursion to Heidelberg Castle andthe Königstuhl in bright seasonable weath-er completed the first week.

During the second week the partici-pants worked on different flow problemsformulated by the lecturers in differentplaces (Heidelberg, Freiburg, Stuttgartand Zurich). Finally the results of thepractical work were presented in a plenarymeeting in Heidelberg. The summerschool ended with a dinner in a restaurantin Heidelberg. The financial support ofEuropean Mathematical Society (EMS),ESF-AMIF (European Science Foundation� Applied Mathematics for Industrial FlowProblems) and SFB 359 of HeidelbergUniversity is gratefully acknowledged.

EMS-EMS-WWiR Summer SchooliR Summer SchoolNumerical Simulation of Flows

6 - 21 September 1999Rolf Jeltsch

European Mathematical SocietySummer School

24 July � 2 August 2000

Edinburgh, Scotland

New Analytic and GeometricMethods in inverse problems

LECTURERS and TOPICSDima Burago � Topics in Riemannian geometryGilles Lebeau � Carleman estimates and boundary control ofdifferential equationsVladimir Sharafutinov � Topics in intergral geometryGunter Uhlmann � Anisotropic inverse geometryAnders Melin � Intertwining operator methods and inversescatterringAlexander Katchalov & Matti Lassas � Boundary controlmethods for Gel�fand inverse problemLassi Päiärinta � Analytic techniques in inverse scattering

REGISTRATIONDeadline � 15 May 2000Contact � Erkki Somersalo, Summer School Edinburgh 2000,Helsinki University of Technology.Fax: +358-94 51 30 16 www.math.hut.fi/projects/inverse

European Mathematical SocietySummer School

17 August � 3 September 2000

St Flour, Cantal, France

Probability Theory

LECTURERS and TOPICSSergio Albeverio � Dirichlet forms and infinitedimensional processesWalter Schachermayer � Mathematical FinanceMichel Talagrand � Spin Glasses

REGISTRATIONDeadline � 15 April 2000Contact � Danièlle Courageot, St Flour SummerSchool on �Probability Theory�, Laboratoire deMathématiques Appliquées, Les Cézeaux,F�63177 AubiereFax: +33-4 73 40 70 64wwwlma.univ-bpclermont.fr/stflour

PresentationThe differing structure of school systems invarious European countries presentsremarkable heterogeneity, but also note-worthy similarities, concerning the overallgoals for the education of young genera-tions.

With the increasing mobility of studentsand workers at all levels throughoutEurope, it is urgent to identify commonreference levels concerning general abili-ties, as well as knowledge of specific topicsrelated to specific age groups.

Regarding mathematics, more than ayear ago the European MathematicalSociety promoted an international studyinvolving all E.C. countries and someselected non-E.C. countries. TheEducation Committee of the EMS hasagreed to take responsibility in the study.A first two-year project, concerning the 16-year-old age group has been submitted tothe E.C., under the Socrates programme.It has been accepted and was funded for1999. Besides the E.C. countries, the fol-lowing non-E.C. countries are involved:the Czech Republic, Hungary, Poland,Russia and Switzerland.

In future, other age groups may also beconsidered. The choice to start with the16-year age group is because this age coin-cides, at least de facto, with the end of full-time compulsory education in most E.C.Countries.

However, already at age 16, three dis-tinct sub-populations must be considered:� those who are going to quit school � those who will use mathematics mainly asa tool

� those who plan to enrol in a scientific fac-ulty.

A possible structure of the study, includ-ing its main goals is illustrated in the figurebelow.

What is it about?A first task of the working team has been tospecify and delimit the meaning of �refer-ence levels�.

Two main aspects have been identified:1. References concerning the general mathemat-ical curriculumAs a starting point the working team is col-lecting �national references�, general infor-mation about mathematics education in allcountries involved, along with specificquestions to be asked at country level. The�European reference� will be a synthesisfrom these national references. 2. References concerning students� abilities andknowledgeThese �references� will consist of state-ments concerning the students� mathemat-ical behaviour and in samples of tasks thatcan be submitted to 16-year-old students.Some of these statements and tasks mayconcern students� achievement, eitherobserved or expected. They will obviouslyvary across countries, and according to thedifferent aims of mathematics education,as highlighted in the national curriculumreference levels.

We do not claim that the whole set ofstatements and tasks can (or should) beranked in order. It seems more meaning-ful to organise specific subsets, giving riseto several distinct �reference scales�; eachstatement from a reference scale will

define one reference level, relative to theappropriate field.

Until now, priority has been given toaspect 1, since aspect 2 should be seen inthe light of the outcomes of aspect 1. Theworking team plans to consider aspect 2during the second year of the project.

To help gathering, selecting, dissemi-nating (and where appropriate, translat-ing) relevant background information, aresource centre devoted to MathematicsCurriculum and Evaluation (both exami-nations and large-scale assessments) inEurope, as well as in other places (U.S.A.,Japan), is currently being developed at theInstitute of Mathematical Research andEducation (IREM) in the MathematicsDepartment of the University of Franche-Compté in France. For the moment, theCentre focuses mainly on ages 14-16, tokeep with the reference levels project, butit is planned to extend its scope up to thefirst university years.

What is peculiar about this project?Several international large-scale studieshave been already performed in the past(IEA, TIMSS). They provide us with usefulinformation about curricula and achieve-ment, although not specifically mirrored atage 16. Meanwhile, it is well acknowl-edged that those studies were largely dri-ven by governments and psychometricians,and that their influence on the mathemat-ical community has been dramatically low.In addition, those studies have not ade-quately taken into account the specificneeds and sensitivities of European coun-tries.

Moreover, any information concerningeducational systems rapidly becomes obso-lescent. Part of the information releasedtoday already belong to history!

Our project will have to cope with thesame problem. We are thus already plan-ning to put on track a continuous updatingof the outcomes of our study, via an inter-active involvement of the mathematicalcommunity at large, through the EMS web-site.

We plan to present a preliminary reporton the project at the EMS Congress inBarcelona in July. Antoine Bodin is at the Institute ofMathematical Research and Education (IREM)at the Université de Franche-Compté inBesancon, France. Vinicio Villani is in the Department ofMathematics at the Università di Pisa, Italy.

Editor�s note: We regret that the ProblemCorner, due for publication in this issue,has had to be held over to the March issue.

EDUCATION


Education SectionReference levels in school education in mathematics

A project of the EMS

Antoine Bodin (Besancon) and Vinicio Villani (Pisa)

Position of the studyWidth of the arrows relate to the relative importance as seen at 16.

This relative importance would not be the same if the age were 14, 18 or 20.

Please e-mail announcements of European conferences,workshops and mathematical meetings of interest toEMS members, to [email protected]. Announce-ments should be written in a style similar to those below,and sent as Microsoft Word files or as text files (but notas TeX input files). Space permitting, each announce-ment will appear in detail in the next issue of theNewsletter to go to press, and thereafter will be brieflynoted in each new issue until the meeting takes place,with a reference to the issue in which the detailedannouncement appeared.

5-8: Non-Fermi Liquid Effects in MetallicSystems with Strong Electronic Correlation,Cambridge, UKInformation:Web site: http://www.newton.cam.ac.uk/programs/scew01.html

7-9: 2nd Mediterranean Conference onMathematics Education, Nicosia, CyprusInformation:Web site: http://www.kutzler.com/medconf2000-mathedu/

17-22: Workshop on Computational Stochastics,Aarhus, Denmark Information: contact Eva B. Vedel Jensen,Department of Mathematical Sciences, Universityof Aarhus, Ny Munkegade, DK-8000 Aarhus C,Denmark e-mail: [email protected] site: http://www.maphysto.dk/events/CompStoc2000/[For details, see EMS Newsletter 32]

27-29: Congreso RSME2000 de la RealSociedad Matemàtica Española, Madrid, SpainSpeakers: Fernando Chamizo (Madrid), OscarGarcìa-Prada (Madrid), Juan Josè LòpezVelàzquez (Madrid), Rafael de la Llave (Texas),Mark Melnikov (Barcelona), Sebastiàn Montiel(Granada), Marta Sanz-Solé (Barcelona), LuisCaffarelli (Texas), John H. Conway (Princeton)Organisers: Carlos Andradas (Univ.Complutense), Emilio Bujalance (UNED),Antonio Còrdoba (Madrid), Ildefonso Dìaz (Univ.Complutense), Alberto Ibort (Univ. Carlos III),Manuel de Leòn (CSIC), Juan Llovet (Univ. deAlcalà), Francisco Martìn (Fed. Española Soc.Profs. Matemàticas, FESPM), David Rìos (Univ.Rey Juan Carlos), Josè Manuel Vega (Madrid)Site: Universidad Complutense de Madrid Information:Web site: http://www.mat.ucm.es/rsme2000

3-5: Mathematics Today, Trondheim, NorwayNote: primarily intended for a ScandinavianaudienceInformation:Web site: http://www.math.ntnu.no/talltiltusen/

28-3 March: Eighth International Conference

February 2000

January 2000

on Hyperbolic Problems, Magdeburg, Germany Information: contact HYP-2000 c/o Institut fürAnalysis und Numerik, Otto-von-Guericke-Universität, Magdeburg, PSF 4120, D-39016Magdeburg, Germany; fax: HYP-2000 at +49-391-67-18073e-mail: [email protected] site: http://rubens.math.uni-magdeburg.de/~hyp2000[For details, see EMS Newsletter 33]

6-10: International Conference on DifferentialGeometry and Quantum Physics, Berlin,Germany Scope: this will reflect a good part of theresearch activities of SFB 288 (see below). Theconference is centred around the interests ofDirk Ferus, Ruedi Seiler and Robert Schrader, tohonour their contribution to the SFB and to sci-ence in general, on the occasion of their sixtiethbirthdays Topics: differential geometry and geometricanalysis: submanifolds, integrable systems, spec-tral geometry; partial differential equations inmathematical physics: Dirac and Schrödingerequations, transport equations, soliton equations,microlocal analysis, spectral theory; quantummechanics and quantum field theory: semiclassi-cal, adiabatic, perturbative and Born-Oppenheimer approximations, n-body andmany-body quantum theory, algebraic quantumfield theorySpeakers: J. Avron, W. Ballmann,J. Bourguignon, J. Cheeger, J.-M. Combes,L. Faddeev, J. Froehlich, E. Lieb, W. Mueller,S. Novikov, B. Simon, C.-L. TerngProgramme: plenary talks and special sessionson the above mentioned topics Organisers and sponsors:Sonderforschungsbereich (SFB) 288 �DifferentialGeometry and Quantum Physics� of DeutscheForschungsgemeinschaft, which links theMathematics Departments of HumboldtUniversität zu Berlin, Technische UniversitätBerlin, the Universität Potsdam, and the PhysicsDepartment of Freie Universität BerlinApplications: titles and abstracts for special ses-sions should be sent (preferably by e-mail) to oneof the organisers, Volker Bach and JochenBruening (for addresses, see below)Site: Technische Universität (TU) BerlinDeadlines: for submission of titles and abstracts,31 December 1999; for registration, 31 January2000; for payment of the fee, 6 March 2000Information: contact Volker Bach, FBMathematik (17), Universität Mainz, D-55099Mainz, Germany, or Jochen Bruening, Institutfür Mathematik, Humboldt-Universität zu Berlin,Unter den Linden 6, D-10117 Berlin, Germany e-mail: [email protected], [email protected], [email protected] Web site: http://www.math.TU-Berlin.DE/~bach/FSS.html

March 2000

11-12: School Mathematics 2000, Helsinki,FinlandInformation:e-mail: [email protected]

13-16: Geometry and Applications,Novosibirsk, Russia[on the 70th anniversary of the birthday of VictorAndreevich Toponogov]Topics: geometry, geometrical questions ofanalysis (including differential equations), topol-ogy, applications (mathematical methods ofchemistry in particular)Organisers: The Sobolev Institute ofMathematics of the Siberian Branch of theRussian Academy of Sciences, Novosibirsk StateUniversity Programme committee: Yu. G. Rushetnyak(chair) (Novosibirsk), A. A. Borisenko (Kharkov),Yu. D. Burago (St Petersburg), V. M. Goldshtein(Beer-Sheva), M. L. Gromov (Paris), I. G.Nikolaev (Urbana-Champaign), S. P. Novikov(Maryland) Information: e-mail: [email protected]

27-31: ICMS Instructional Course: QuantumComputing, Edinburgh, UKTheme: in the past five years the new subject ofquantum computing has emerged; this offers thepotential of immense practical computing powerand also suggests deep links between the well-established disciplines of quantum theory andinformation theory and computer science. Anotable feature of the subject is its interdiscipli-nary nature with contributions from physicists,mathematicians and computer scientists Aim: to provide a comprehensive introduction tocurrent developments in quantumcomputation/quantum information theoryLecturers: Charles Bennett (tbc), quantum com-munication; Harry Buhrman, complexity/com-munication complexity; Chris Fuchs, quantumcommunication; David DiVincenzo, implementa-tions; Richard Jozsa, algorithms and complexity;Noah Linden, introduction to quantum mechan-ics and entanglement; Hoi-Kwong Lo, cryptogra-phy; Sandu Popescu, quantum information;Andrew Steane, error correction/faulttolerance/decoherence Scientific organising committee: Richard Jozsa(Bristol), Noah Linden (Bristol), AngusMacintyre (Edinburgh), Andrew M. Pitts(Cambridge)Audience: accessible to computer scientists aswell as graduate students and post-Docs fromother relevant disciplinesSponsor: the course is an activity of UKQuantum Computing Network, funded by theEPSRCInformation:Web site: http://www.ma.hw.ac.uk/icms/current

31-1 April: LMS Two-Day Meeting: ModellingSpatiotemporal Dynamics in InteractingSystems, Oxford, UK

5-14: ICMS Instructional Conference: OperatorAlgebras and Operator Spaces, Edinburgh,ScotlandScientific organising committee: V. Jones (UCBerkeley), C. Lance (Leeds), G. Pedersen(Copenhagen), G. Pisier (Paris), S. Popa (UCLA),A. Sinclair (local organiser, Edinburgh),

April 2000

CONFERENCES

EMS December 199930

FForthcoming conferorthcoming conferencesencescompiled by

Kathleen Quinn

G. Skandalis (Paris)Aim: to introduce this active field of mathematicsto younger scientists and to provide an opportu-nity for specialists to exchange ideasTopics: operator spaces, free probability, exactC*-algebras, subfactors and related areas of oper-ator algebrasProgramme: several series of lectures (each seriesconsisting of 2 or 3 one-hour lectures) designedto introduce and elaborate upon a particularfield. These series will be complemented by morespecialised talks examining current trends. Inaddition to the formal lectures, there will beample opportunity for informal tutorials and dis-cussionsSpeakers: include C. Anantharamam-de la Roche(Orleans), D. Bisch (Santa Barbara), K. Dykema(Texas), U. Haagerup (Odense), V. Jones(Berkeley), E. Kirchberg (Berlin), V. Paulsen(Houston, Texas), G. Pisier (Paris), S. Popa(UCLA), M. Rieffel (Berkeley), D. Voiculsecu(Berkeley) Sponsor: supported by the EuropeanCommissionInformation: contact Allan M. Sinclair,Department of Maths and Statistics, JCMB, KB,Edinburgh EH9 2DE, Scotland e-mail: [email protected] Web site: http://www.ma.hw.ac.uk/icms/current

10-20: NATO Advanced Study Institute/ECSummer School, New Theoretical Approachesto Strongly Correlated Systems, Cambridge, UKInformation:Web site: http://www.newton.cam.ac.uk/programs/scew.html

11-14: Workshop on Harmonic Maps andCurvature Properties of Submanifolds 2, Leeds,UK Information: contact J. C. Wood, School ofMathematics, University of Leeds, Leeds LS29JT, UK e-mail: [email protected] Web site: http://www.amsta.leeds.ac.uk/pure/geometry/leeds2000.html [For details, see EMS Newsletter 33]

17-20: 52nd British Mathematical Colloquium,Leeds, UKInformation: e-mail: [email protected] site: http://www.amsta.leeds.ac.uk/bmc/ [For details, see EMS Newsletter 33]

23-29: Spring School on Functional Analysis:(Non)smooth Analysis in Banach Spaces,Paseky nad Jizerou, Czech RepublicAim: to bring together adepts with an interest inthe fieldSpeakers: Alexander Ioffe (Haifa), TerryRockafellar (Seattle), Philip Loewen (Vancouver),Robert Deville (Bordeaux) Programme: a series of lectures on the abovetopicOrganiser: Faculty of Mathematics and Physicsof Charles UniversityNotes: there will be opportunities for informaldiscussions. Graduate students and others begin-ning their mathematical careers are encouragedto participate Site: Paseky nad Jizerou, in a chalet in theKrkonose MountainsInformation: contact Katedra matematickèanalýzy, Matematicko-fyzikàln fakulta UK,

Sokolovskà 83, 186 75 Praha 8, Czech Republic,tel./fax: +420 - 2 - 232 3390 e-mail: [email protected] site: http://www.karlin.mff.cuni.cz/katedry/kma/ss/

26-28: Mathematical Education of Engineers,Loughborough, UKInformation: Web site: http://www.ima.org.uk/mathematics/conferences.htm[For details, see EMS Newsletter 33]

25-6 May: NATO Advanced Study Institute,Nonlinear Dynamics in Life and SocialSciences, Moscow, RussiaInformation:Web site:http://www.cas.mcmaster.ca/~sulisw/asi.html

20-25: MaPhySto and StocLab Summer Schoolon Stereology and Geometric Tomography,Sandbjerg Manor, Denmark Aim: to give an overview of modern stereologyand its relation to geometric tomography, includ-ing both the mathematical and statistical theoryand the practical applicationsScope: stereology is the area of stochastics deal-ing with statistical inference about spatial struc-tures from geometric samples of the structuresuch as two-dimensional sections and one-dimen-sional probes. The development of stereologicalmethods involve the use of advanced mathemati-cal tools, especially from geometric measure the-ory and integral geometry. Stereology is now inworld-wide use in many areas of biology andmedicine, most importantly in neuroscience andcancer grading. Other areas of application aregeology, metallography and mineralogy.Geometric tomography is closely related to stere-ology, as is apparent from its definition: �geomet-ric tomography is the area of mathematics deal-ing with the retrieval of information about a geo-metric object from data about its sections, or pro-jections, or both�. Geometric tomography hasconnections with convex geometry, geometricprobing in robotics, computerized tomography,and other areasTeaching team: includes Adrian Baddeley(Australia), Richard Gardner (Washington), HansJørgen G. Gundersen (Aarhus), Eva B. VedelJensen (Aarhus), Kiên Kiêu (Versailles) Programme: lectures by invited researchers inrelated fields such as convex geometry, stochasticgeometry and spatial statistics are also planned,as well as lectures by the participants of the sum-mer schoolOrganisers: StocLab (Laboratory forComputational Stochastics) and MaPhySto(Centre for Mathematical Physics andStochastics), both Department of MathematicalSciences, University of AarhusAudience: PhDs, post-Docs and otherresearchers in mathematics. Scientists from thenatural sciences with a strong background andinterest in mathematics are also welcome. Thenumber of participants is limited to 50Site: Sandbjerg Manor, a conference centreowned by University of Aarhus, situated in thesouthern part of Jutland, DenmarkGrants: a limited number available for students Deadline: for application, 1 March 2000Information: e-mail: [email protected]

May 2000

Web site: http://www.maphysto.dk/events/S-and-GT2000/

28-3 June: Spring School on Analysis: SomeRecent Techniques in Harmonic Analysis,Paseky nad Jizerou, Czech RepublicAim: to bring together adepts with an interest inthe field Speakers: Sergei Treil (Michigan), title to beannounced; Igor Verbitsky (Missouri), Best con-stant inequalities for some classical Fourier multi-plier operators; Alexander Volberg (Michigan),Bellman function and some sharp estimates inharmonic analysis Programme: a series of lectures on the abovetopicOrganizer: Faculty of Mathematics and Physics,Charles University Notes: there will be opportunities for informaldiscussions. Graduate students and others begin-ning their mathematical careers are encouragedto participateSite: Paseky nad Jizerou, in a chalet in theKrkonose MountainsInformation: contact Katedra matematickèanalýzy, Matematicko-fyzikàln fakulta UK,Sokolovskà 83, 186 75 Praha 8, Czech Republic,tel/fax: +420-2-232 3390 e-mail: [email protected] site: http://www.karlin.mff.cuni.cz/katedry/kma/

29-2 June: Deuxième Rencontre Internationalesur les Polynomes à valeurs entières CIRM,Luminy, FranceMain themes: integer-valued polynomials, multi-plicative ideal theory, dimension theory, factori-sation properties, commutative monoidsOrganisers: P. J. Cahen (Aix-Marseille III), J. L.Chabert (Picardie)Information:e-mail: [email protected]

29-9 June: Foliations: Geometry and DynamicsRevisited, Banach Centre, Warsaw, PolandInformation:Web site: http://fol2000.math.uni.lodz.pl/

5-9: Sixth International Conference onProbability, Poraj (near Czestochowa), Poland[dedicated to Professor Kazimierz Urbanik]Topics: the latest scientific output of peopleworking creatively in the field of probabilitytheoryOrganisers: the Institute of Mathematics ofPolish Academy of Sciences, the Faculty ofMathematics and Information Science of WarsawUniversity of Technology, the Institute ofMathematics of Wroclaw University and theUniversity of Commerce in KielceProgramme committee: Dobieslaw Bobrowski,Krzysztof Burdzy, Zbigniew Ciesielski, WieslawDziubdziela, Ryszard Jajte, Michal Karonski,Boleslaw Kopocinski, Stanislaw Kwapien,Zbigniew Morawiecki, Agnieszka Plucinska,Tomasz Rolski, Jan Rosinski, Zdzislaw Rychlik,Lukasz Stettner, Jan Suwala, Dominik Szynal,Kazimierz Urbanik, Jan Waluszewski, AleksanderWeron, Wojbor A. Woyczynski, Jerzy Zabczyk,Ryszard ZielinskiInformation: e-mail: [email protected]

7-11: PhD Euroconference on Complex

June 2000

CONFERENCES


Analysis and Holomorphic Dynamics,Catalonia, SpainFocus: complex analysis and holomorphicdynamics are classical domains of the mathemati-cal sciences which are now going through anexciting phase of fruitful interplayAim: to bring together young researchers inorder to expose and discuss work in progress andrecent advances on these fieldsMain speakers: Xavier Buff (Toulouse), GregeryBuzzard (Cornell), Mattias Jonsson (Michigan),Ricardo Perez Marco (UCLA & Paris), StephenRohde (Seattle)Programme: lectures given by the main speakers,shorter talks and one session of exposition anddiscussion of open problemsOrganising committee: Nuria Fagella(Barcelona), Xavier Jarque (Barcelona), XavierMassaneda (Barcelona), Joaquim Ortega Cerda(Barcelona)Organising institution: Centre de RecercaMatematica (CRM)Site: Platja d�Aro (Costa Brava), Catalonia, Spain Note: the conference is restricted to youngresearchers (normally those aged up to 35)Information: e-mail: [email protected] Web site: http://crm.es/cad2000 (from 1 January2000)

13-16: First AMS-Scandinavian InternationalMathematics Meeting, XXIII ScandinavianCongress of Mathematicians, Odense, DenmarkInformation: contact Hans J. Munkholm,Odense University, Campusvej 55, DK 5230Odense M, Denmark, tel: +45-65572309/+45-65932691e-mail: [email protected] site: http://www.imada.ou.dk/~hjm/AMS.Scand.2000.html[For details, see EMS Newsletter 33]

14-17: International Workshop for OperatorTheory and Applications (IWOTA), Bordeaux,FranceInformation: e-mail: [email protected] Web site: http://www.math.u-bordeaux.fr/~iwota/[For details, see EMS Newsletter 33]

18-21: International Conference on MonteCarlo Simulation, Monte Carlo, MonacoInformation: Web site: http://www.uibk.ac.at/c/c8/c810/conf/mcs_2000.html[For details, see EMS Newsletter 33]

18-24: Perspectives of Mathematics, Goslar,GermanyInformation: contact K. Hulek, Institut fürMathematik, Universität Hannover, Postfach6009, D-30060 Hannover, Germany e-mail: [email protected] site: http://www-ifm.math.uni-hannover.de/info/perspectives.html[For details, see EMS Newsletter 33]

20-25: Mathematical Physics in Mathematicsand in Physics: Quantum and OperatorAlgebraic Aspects, Siena, Italy [dedicated to Sergio Doplicher and John E.Roberts on the occasion of their 60th birthdays]Scope: the conference is centred around theinterplay between mathematics and physics,mainly with reference to operator algebras and

quantum field theory, but there will be talks onother subjects in mathematical physicsInvited speakers: include J. Boeckenhauer, D.Buchholz, A. Connes, K. Fredenhagen, G.Gallavotti, U. Haagerup, M. Izumi, A. Jaffe, V.Jones, Y. Kawahigashi, M. Mueger, G. Pedersen,S. Popa, H.-K. Rehren, M. Rieffel, I. Singer, R.Stora, E. Stoermer, M. Takesaki, D. Voiculescu,R. Verch, S. WoronowiczSocial event: dinner on 22 JuneSite: the Certosa di Pontignano, a splendid 15th-century building in the countryside near Siena(pictures athttp://www.unisi.it/servizi/certosa/Certosa.html)Deadline: for registration, 15 April 2000Information : contact Roberto LongoDipartimento di Matematica, Università di Roma�Tor Vergata�, I-00133 Roma, Italy, fax: +39-0672594699e-mail: [email protected] site: http://mat.uniroma2.it/~mp/siena2000.html

25-28: IMACS-ACA�2000 6th InternationalConference on Applications of ComputerAlgebra, St Petersburg, RussiaScope: actual or possible applications of nontriv-ial computer algebra techniques to other fieldsand substantial interactions of computer algebrawith other fieldsGeneral chair: Nikolay Vassiliev,[email protected] Programme chairs: Victor Edneral,[email protected], Richard Liska,[email protected], Michael Wester, [email protected] Meeting format: standard IMACS format; indi-viduals are invited to organise a special session.Individuals can propose a special session by con-tacting the program chairs. All paper submis-sions must be directed to an organiser of anappropriate special sessionSponsors: Steklov Institute of Mathematics at StPetersburg, Euler International MathematicalInstitute, St Petersburg Mathematical Society, StPetersburg State University Information: web site: http://www.pdmi.ras.ru/EIMI/2000/imacs/

26-28: Sixth International Conference onAdvanced Computational Methods in HeatTransfer, Madrid, Spain Aim: to provide a forum for the presentation ofnew approaches to the numerical solutions ofheat transfer problems. Methods of interestinclude all well-established and efficient numeri-cal techniques such as finite differences, finitevolume, finite elements and boundary elements.Special attention will be paid to complex thermalproblems from engineering practice. HeatTransfer 2000 is of importance to all scientistsand engineers who are actively involved in devel-oping innovative approaches, as well as in solvinga variety of industrial problemsTopics: conduction including non-linear prob-lems, diffusion-convection, natural and forcedconvection, thermal radiation, fire and combus-tion simulation, phase change, thermal problemsin porous media fibres and composites, metalcasting, welding, forging and other processes,energy power systems, inverse problems andother ill-posed problems, combined heat andmass transfer, advances in heat transfer software,coupling different numerical methods, hot spotsand thermal shocks, heat exchangers, heat trans-

fer in manufacturing, cooling of electric and elec-trical equipment, gas turbine heat transfer, heattransfer enhancement, modelling and experi-ments in heat transfer Organizer: Wessex Institute of Technology,Southampton, UK Sponsor: Developments in Heat Transfer BookSeriesConference proceedings: will be published to ahigh standard by WIT Press Information: contact Conference Secretariat,Heat Transfer 2000, Wessex Institute ofTechnology, Ashurst Lodge, Ashurst,Southampton SO40 7AA,UK tel: 44-(0)-23-80-293223, fax: 44-(0)-23-80-292853 e-mail: [email protected] web site: http://www.wessex.ac.uk/conferences/2000

26-30: Formal Power Series and AlgebraicCombinatorics (FPSAC �00), Moscow, RussiaTopics: algebraic and bijective combinatoricsand their relations with other parts of mathemat-ics, combinatorial and computer algebra, com-puter science and physicsProgramme: invited lectures, contributed pre-sentations, poster sessions, problem sessions andsoftware demonstrationsChairmen, program committee: Daniel Krob(LIAFA), Alexander A. Mikhalev (MSU, Russiaand Hong Kong) Chairman, organizing committee: Alexander V.Mikhalev (MSU, Russia) Site: Moscow State UniversityInformation: web site: http://www.liafa.jussieu.fr/~fpsac00/

26-30: POISSON 2000, FranceInformation:e-mail: [email protected]

28-1 July: First World Congress of theBachelier Finance Society, Paris, FranceInformation:e-mail: [email protected]

29-3 July: International Workshop onNonlinear Spectral Theory, Würzburg,Germany Information: contact Jurgen Appell, Departmentof Mathematics, University of Würzburg, AmHubland, D-97074 Würzburg, Germany; tel:+49-931-8885017; fax: +49-931-8885599e-mail: [email protected] site: www.mathematik.uni-wuerzburg.de/~appell/nlst.html[For details, see EMS Newsletter 33]

2-7: Sixth International Conference on p-AdicAnalysis, Ioannina, GreeceScope: analysis over valued fields other than thefields of real or complex numbers (such as thefield of p-adic numbers)Topics: Banach spaces, Hilbert spaces, locallyconvex spaces and modules, operators, spaces ofcontinuous functions, distributions and measures,function theory, classical and harmonic analysis,applications in mathematical physicsSpeakers: (preliminary list) Shavgat Ayupov(Uzbekistan), Jesus Araujo (Spain), Jose ManuelBayod (Spain), Kamal Boussaf (France),Abdelbaki Boutabaa (France), Gilles Christol(France), N. De Grande-De Kimpe (Belgium),Bertin Diarra (France), B. Dragovich(Yugoslavia), Alain Escassut (France), Jose

July 2000

CONFERENCES

EMS December 199932

Aguayo Garrido (Chile), Thomas Gilsdorf (USA),L. Van Hamme (Belgium), Jerzy Kakol (Poland),A. K. Katsaras (Greece), Hans A. Keller(Switzerland), Andrei Khrenikov (Sweden),Anatoly Kochubei (Ukraine), Sara Krantz(Sweden), Nicolas Mainetti ( France), M. S.Moslehian (Iran), L. Narici (USA), P. N.Natarajan (India), S. Navarro (Chile), RobertNyqvist (Sweden), H. Ochsenius (Chile), C.Perez-Garcia (Spain), C. G. Petalas (Greece),Marie-Claude Sarmant (France), W. H. Schikhof(The Netherlands), Stany De Smedt (Belgium),V. K. Srinivasan (USA), Susana Vega (Spain), AnnVerdoodt (Belgium), T. Vidalis (Greece)Scientific committee: A. K. Katsaras (Ioannina),W. H. Schikhof (Nijmegen), L. Van Hamme(Brussels) Organising committee: A. K. Katsaras(Ioannina), C. G. Petalas (Ioannina), T. Vidalis(Ioannina) Site: University of IoanninaInformation: contact A. K. Katsaras, Dept. ofMath., Univ. of Ioannina, 45110, Ioannina,Greece, tel: +30-651-98289, fax: +30-651-46361 e-mail: [email protected] web site: http://www.uoi.gr/conf_sem/p-adic

2-15: NATO Advanced Study Institute 20thCentury Harmonic Analysis-a Celebration,Tuscany, ItalyInformation:web site: http://www.cs.umb.edu/~asi/analysis2000

3-7: ALHAMBRA 2000, Granada, Spain[joint European-Arabic conference]Scope: (morning sessions) historical perspectiveson contributions of both cultures to the presentmathematical knowledge, the state of the morerelevant mathematical concepts over the cen-turies and the way they have evolved; (afternoonsessions) current mathematical subjects from thelist below Topics: computational mathematics, geometry ofsubmanifolds, mathematical demography, non-linear problems, orthogonal polynomials, publicmathematics, representation theory of algebras,symmetryProgramme: plenary lectures on the above sub-jects, short communications Information: contact ALHAMBRA 2000Conference eurocongres Avda. Constitución, 18 -Blq.4 E-18012 - Granada, Spain, tel: +34-958-209-361, fax: +34-958-209-400 e-mail: [email protected],[email protected] site: http://www.ugr.es/local/alhambra2000

3-7: ANTS IV Algorithmic Number TheorySymposium, Leiden, The NetherlandsInvited speakers: include Frits Beukers, PeterBorwein, Jin-Yi Cai, Noam Elkies, Victor Flynn,Jacques Stern Topics: algorithmic aspects of number theory,including elementary number theory, algebraicnumber theory, analytic number theory, geome-try of numbers, algebraic geometry, finite fields,cryptography and computational complexityDeadline: for submission of contributed papers,1 January 2000Proceedings: to appear in the series of LectureNotes in Computer Science of Springer-VerlagOrganising committee: Bart de Smit (Leiden),Herman te Riele (CWI), Jaap Top (Gronigen),Peter Stevenhagen (chair, Amsterdam); WiebBosma (Nijmegen)

Information: e-mail: [email protected] web site: http://www.math.leidenuniv.nl/ants4/

3-7: Functional Analysis Valencia 2000, SpainInformation: contact: K. D. Bierstedt or J. Bonet,Univ. Paderborn, FB 17, Math., D-33095Paderborn, Germany or Universidad Politècnicade Valencia, Departamento de MatemáticaAplicada, E-46071 Valencia, Spain e-mail: [email protected] site: http://math-www.uni-paderborn.de/VLC2000[For details, see EMS Newsletter 32]

3-9: Euro-Summer School on MathematicalAspects of Evolving Interfaces, Madeira,Portugal [Joint school of CIM (Centro Internacional deMatematica, Portugal) and CIME (CentroInternazionale Matematico Estivo, Italy), SatelliteActivity of the Third European Congress ofMathematics in Barcelona, Spain, 10-14 July] Aims: interfaces are geometrical objects model-ling free or moving boundaries which arise in awide range of phase change problems in continu-um physics, in particular in material sciences.Recent mathematical advances in the theory ofgeometric evolution problems will be presentedin a set of lectures with an interdisplinary per-spective, covering several aspects from theory toapplicationsProgramme: a series of five complementarycourses each consisting of three 90-minute lec-tures plus tutorials; a limited number of selectedtalks of 20-30 minutes each by young researchersor post-DocsSpeakers and course titles: Luigi Ambrosio(Pisa), Distance function and evolution of frontsby implicit time discretization; Gerhard Dziuk(Freiburg), Numerical approximation of meancurvature flow of graphs; Masayasu Mimura(Hiroshima), Dynamics of patterns and interfacesin reaction-diffusion systems from chemical andbiological viewpoints; Vsvolod A. Solonnikov (StPetersburg), Evolution free boundary problemsfor parabolic and Navier-Stokes equations; HalilM. Soner (Princeton), Variational and DynamicProblems for the Ginzburg-Landau FunctionalOrganisers: Pierluigi Colli, Jose-FranciscoRodrigues Audience: the school is mainly intended forEuropean postgraduate students, includingrecent PhDs, but selected participants from out-side Europe and senior scientists wishing to learnabout the subject are not excludedLecture notes: expected to be publishedFinancial support: some grants for youngerresearchers are available. Applications should bemade to the organising committeeSite: University of Madeira, Funchal, Portugal Information:e-mail: [email protected] web site: http://maei.lmc.fc.ul.pt

4-6: Catop 2000, Fribourg, SwitzerlandScope: categorical topological methodsAim: to discuss categorical topological methodsthat are likely to be mathematically important inthe next century. Furthermore, on Thursday, wecelebrate the 70th birthday of Prof. HeinrichKleisli (Fribourg)Programme committee: Hans-Peter A. Kuenzi(Bern), Ernst A. Ruh (Fribourg) Information:

web site: http://www.unifr.ch/math/catop2000/

4-7: Second International Conference onMathematical Methods in Reliability,Bordeaux, FranceAims: to serve as a forum for discussing funda-mental issues of reliability mathematical methodswith respect to its applications; to assembleresearchers in probability, statistics and appliedmathematics, working in the field of reliability,from university laboratories and research institu-tions in Europe and elsewhereScope: common methods and models used insurvival analysis and reliability will be consideredfrom a general point of view. Theoretical, mod-elling, computational and case study contribu-tions will be presented, ranging from academicconsiderations to industrial approachesProgramme: invited talks, plenary sessions, par-allel sessions and posters Information: contact Dr Valentina Nikoulina,Université Victor Segalen, Bordeaux 2,Statistique Mathematique, UFR MI2S, B.P. 6933076 Bordeaux Cedex, France; tel: +33-(0)-5-57-57-10-70/(0)-5-57-57-14-25; fax: +33-(0)-5-56-98-57-36/+33-(0)-5-57-57-12-63e-mail: [email protected],[email protected] site: http://www.mass.u-bordeaux2.fr/MI2S/MMR2000/

5-7: Scandinavian Workshop on AlgorithmTheory, Bergen, NorwayInformation:e-mail: [email protected] site: http://www.ii.uib.no/swat2000

6-8: 6th Barcelona Logic Meeting, Barcelona,SpainInvited speakers: Jose Luis Balcazar (Catalunya),Pilar Dellunde (Barcelona), Peter Koepke(Bonn), Anand Pillay (Urbana-Champaign), YdeVenema (Amsterdam), Michael Zakharyaschev(Moscow)Scientific and organising committee: JoanBagaria (Barcelona), Enrique Casanovas(Barcelona), Rafel Farre (Catalunya), Josep MariaFont (Barcelona), Juan Carlos Martinez(Barcelona), Hiroakira Ono (Japan), MargaritaOtero (Madrid), Stevo Todorcevic (Paris)Information: e-mail: [email protected] web site: http://www.mat.ub.es/~logica/news.htmlor http://www.crm.es/

10-14: IUTAM Symposium on Free SurfaceFlows, Birmingham, UKInformation:web site: http://www.mat.bham.ac.uk/research/iutam.htm[For details, see EMS Newsletter 33]

10-14: Third European Congress ofMathematics, Barcelona, SpainInformation: contact Societat Catalana deMatemátiques, Carrer del Carme, 47, E-08001Barcelona;tel: (34 3) 270 16 26; fax (34 3) 270 11 80 e-mail: [email protected] site: http://www.iec.es/3ecm/[For details, see page 13]

13-14: Computational Challenges for theMillenium, Cambridge, UKInformation:

CONFERENCES


web site: http://www.ima.org.uk

17-20: IUTAM Symposium 2000/10 Diffractionand Scattering in Fluid Mechanics andElasticity, Manchester, UKInformation: contact Professor David Abrahams,Department of Mathematics, University ofManchester, Oxford Road, Manchester M13 9PL,UK, tel: +44-(0)-161-275-5901, fax: +44-(0)-161-275-5819 e-mail: [email protected] site: http://www.keele.ac.uk/depts/ma/iutam/[For details, see EMS Newsletter 33]

17-21: Ninth International Conference onFibonacci Numbers and their Applications,Luxembourg-City, LuxembourgInformation:e-mail: [email protected]: Colloquium on Lie Theory andApplications, Vigo, SpainInformation: contact I Colloquium on LieTheory and Applications, E. T. S. I.Telecomunicación, Universidad de Vigo, 36280Vigo, Spain; tel: +86-81-21-52/+86-81-24-45;fax: +86-81-21-16/+86-81-2- 01 e-mail: [email protected] web site: http://www.dma.uvigo.es/~clieta/[For details, see EMS Newsletter 33]

17-22: International Congress of MathematicalPhysics, London, UKInformation:web site: http://icmp2000.ma.ic.ac.uk/19-26: Third World Congress of Non-linearAnalysts (WCNA-2000), Catania, Italy23-31: ASL European Summer Meeting (LogicColloquium 2000), Paris, FranceInformation: e-mail: [email protected] site: http://lc2000.logique.jussieu.fr[For details, see EMS Newsletter 33]

24-3 August: EMS Summer School, New analyt-ic and geometric methods in inverse problems,Edinburgh, Scotland Organisers: Prof. Erkki Somersalo, Prof.Yaroslav V. Kurylev, Prof. Brian Sleeman Note: in collaboration with the InternationalCentre for Mathematical Sciences (ICMS;www.ma.hw.ac.uk/icms/) Information: contact Erkki Somersalo, HelsinkiUniversity of Technology, Finland e-mail: [email protected]

31-3 August: Third Conference of BalkanSociety of Geometers, Bucharest, RomaniaInformation: contact V. Balan, UniversityPolitehnica of Bucharest, DepartmentMathematics I, Splaiul Independentei 313, RO-77206, Bucharest, Romania; fax: (401) 411.53.65e-mail: [email protected] [For details, see EMS Newsletter 33]

2-9: Summer School on Mathematical Physics(emphasis on Quantum Field Theory),Sandbjerg Manor, DenmarkInformation:web site: http://www.maphysto.dk/events/

8-12: XVIII Nevanlinna Colloquium, Helsinki,FinlandInformation:e-mail: [email protected]

August 2000

web site: http://www.math.helsinki.fi/~analysis/NevanlinnaColloquium/[For details, see EMS Newsletter 33]

17-3 September: EMS Summer School inProbability Theory, Saint-Flour, Cantal, FranceProgramme: short courses of 10 lectures each,on the topics belowSpeakers: Sergio Albeverio (Germany), Dirichletforms and infinite-dimensional theory; WalterSchachermayer (Vienna), Mathematics andfinance; Michel Talagrand (France), Spin glassesOrganiser: Prof. Pierre Bernard Programme committee: Martin Barlow, GerardBenarous, Pierre Bernard, Lucien Birge, MichelEmery, Hans Follmer, Jean-Francois Le Gall,Michel Ledoux, David Nualart, Etienne Pardoux,Jean Picard, Alain-Sol Sznitman, Liming Wu Information: contact: P. Bernard, Laboratoire deMathématiques Appliquées, Univ. Blaise Pascal,F-63177 Aubière, tel/fax: +33-4 73-40-70-64e-mail: [email protected]

21-25: IMACS 2000, Lausanne, Switzerland[International Association for Mathematics andComputers World Congress]Information: contact Prof. Robert Owens,IMACS Congress 2000, DGM-IMHEF-LMF,Swiss Federal Institute of Technology, CH-1015Lausanne, Switzerland; tel: +41-21-693-35-89;fax: +41-21-693-36-46 e-mail: [email protected] site: http://imacs2000.epfl.ch[For details, see EMS Newsletter 32]

30-2 September: Innovations in HigherEducation 2000, Helsinki, FinlandInformation:e-mail: [email protected] site: http://www.helsinki.fi/inno2000

4-6: Mathematics of Surfaces, Cambridge, UKInformation:web site: http://www.ima.org.uk

4-8: FGI2000 French-German-ItalianConference on Optimisation, Montpellier,France Aim: to enable the exchange of results and ideasabout the state of the art in mathematical optimi-sation in a broad sense Topics: continuous and discrete (scalar and vec-tor) optimisation, calculus of variations, optimalcontrol, games, non-smooth analysis, criticalpoint theory, equilibria. Analytical as well asnumerical aspects are of interest, along withapplicationsScientific committee: H. Attouch (Montpellier),G. Buttazzo (Pisa), G. Di Pillo (Rome), F.Giannessi (Pisa), C. Lemaréchal (Grenoble), W.Oettli (Mannheim), J.-J. Strodiot (Namur), M.Théra (Limoges), R. Tichatschke (Trier), J. Zowe(Erlangen-Nuernberg) Organising committee Laboratoire d�Analyse, deCalcul Scientifique et Industriel etd�Optimisation de Montpellier (ACSIOM)Programme: invited lectures and contributedtalks Information: contact: Bernard Lemaire,Mathématiques, Université de Montpellier II,Place Eugène Bataillon, 34095 Montpellier cedex05e-mail: [email protected] web site: http://www.math.univ-montp2.fr/

September 2000

5-7: Quantitative Modelling in the Managementof Health Care, Salford, UK Participants: conference delegates will includethose involved in quantitative policy, evaluationand decision making in health care relating tothe British National Health Service, private sec-tor, and overseas experience. The first confer-ence in 1994 attracted medical practitionersworking in hospitals and general practice; healthservice managers; and operational research spe-cialists, economists, statisticians and mathemati-cians employed in health care and universitiesThemes: the conference will focus on practicalmethodologies in budgeting, financing, setting ofpriorities, and allocation of resources for the pro-vision of services, and the formulation and mea-surement of performance indicators. Papers cov-ering experience with established methodologiesand issues relating to their implementation arewelcome together with those describing newmethodologiesProgramme: keynote speeches, contributedpapers and an exhibition of softwareInvited speakers: (confirmed) Sandy Macara(BMA), Peter Millard (St George�s HospitalMedical School, London), Jonathan Rosenhead(London), Tom Treasure (St George�s HospitalMedical School, London)Organising committee: Rose Baker (Salford,chair), Sally Brailsford (Southampton), PeterMillard (St George�s Hospital Medical School),Patrick Rivett (Cumbria), Alison Round (North &East Devon Health Authority)Proceedings: selected papers to be publishedSite: University of Salford Call for papers: abstracts of 300-500 wordsshould be sent to Pamela Bye, Institute ofMathematics and its Applications, CatherineRichards House, 16 Nelson Street, Southend-on-Sea, Essex SS1 1EF, UK, by 1 May 2000Information: web site: http://www.ima.org.uk/mathematics/conferences.htm

5-16: Advanced Course on Algebraic QuantumGroups, Bellaterra, SpainSpeakers: Kenneth Brown (Glasgow), KennethGoodearl (Santa Barbara)Site: Centre de Recerca Matemàtica, Campus ofthe Universitat Autònoma de Barcelona,Bellaterra, SpainInformation:e-mail: [email protected] site: http://crm.es/quantum

10-17: Summer School on Geometry of Quiver-Representations and Preprojective Algebras,Isle of Thorn, UKTopics: degenerations of modules, theorem ofKac, moduli spaces, preprojective algebras, semi-invariants of quivers, Young tableaux andSchubert calculus Programme: the meeting is in two parts: in thefirst part the participants will lecture on intro-ductory topics; the second part is a workshopwhere specialists in the area will lecture on recentresultsOrganisers: W. W. Crawley-Boevey (Leeds), K.Erdmann (Oxford), Ch. Geiss (at present UNAM,Mexico)Support: provided by the TMR scheme of the ECInformation: contact Karin Erdmann,Mathematical Institute, University of Oxford,Oxford OX1 3LB, UK

CONFERENCES

EMS December 199934

e-mail: [email protected] web site: http://www.mathematik.uni-bielefeld.de/~sek/summerseries.html

11-15: Boundary Integral Methods: Theory andApplications, Bath, UKAim: to provide a forum for the exchange ofideas between academic and industrialresearchers in different disciplines whose com-mon interest is boundary integral methodsScope: as well as discussing recent developmentsin the theory and numerical analysis of boundaryintegral equations, the conference will strive toencompass applications of contemporary rele-vance such as direct and inverse (medium andhigh frequency) scattering, electromagnetics andmoving boundary problems in hydrodynamics.Continuing progress in key computational tech-niques such as multipole, wavelets and panelclustering, together with innovative algorithmdesign will be an additional themeSpeakers: W. C. Chew (Illinois), C. Constanda(Strathclyde), T. Hou (California), A. Kirsch(Karlsruhe), A. Rathsfeld (Berlin), S. A. Sauter(Leipzig), I. H. Sloan (Sydney), W. L. Wendland(Stuttgart), L. Wrobel (London)Organising committee: Ivan Graham (Chair)(Bath), Sia Amini (Salford), Simon Chandler-Wilde (Brunel), Ke Chen (Liverpool), PennyDavies (Strathclyde) Site: University of BathInformation: web site: http://www.ima.org.uk/mathematics/conferences.htm

12-15: Imaging and Digital Image Processing:Mathematical Methods, Algorithms andApplications, Leicester, UKAim: to provide a forum for discussing the math-ematical modelling of imaging systems, thedesign and implementation of specialised imageprocessing algorithms and novel applications ofimage processing software in industry and com-merceTopics: inverse problems in imaging, statisticalmethods in image processing, image compres-sion techniques, fuzzy systems theory, artificialneural networks, multi-fractals and wavelets,colour image processing, 3D imaging and imageprocessing, real-time image processing and sys-tems modellingInvited speakers: presentations on state of theart research will be given by a number of invitedspeakers who are internationally recognised fortheir contribution to the fieldOrganising committee: J. M. Blackledge(Leicester, chair), P. Andrews (Leicester), B.Carroll (GEC Marconi), M. McCormick(Leicester), N. Phillips (Leicester), M. Rycroft(Cambridge), P. Smith (Loughborough), Dr. H.Tassignon (Belgium), M. Turner (Leicester) Short course: a one-day short course,Introduction to Imaging and Digital ImageProcessing, will precede the conference on 12SeptemberSite: De Montfort University, LeicesterCall for papers: abstracts of 300-500 wordsshould be sent to Pamela Bye, Institute ofMathematics and its Applications, CatherineRichards House, 16 Nelson Street, Southend-on-Sea, Essex SS1 1EF, UK, by 31 January 2000.Notification to authors will be mid-March 2000.Final papers should be submitted by late-December 2000 for inclusion in the conferenceproceedings

Proceedings: to be published Information: web site: http://www.ima.org.uk/mathematics/conferences.htm

12-15: IWOTA-Portugal 2000 InternationalWorkshop on Operator Theory andApplications, Faro, PortugalMain topics: factorisation theory, factorisationand integrable systems, operator theoreticalmethods in diffraction theory, algebraic tech-niques in operator theory, related topics andapplications to mathematical physics Steering committee: T. Ando, H. Bart, H.Berovici, R. Dijksma, H. Dym, C. Foias, I.Gohberg, J. W. Helton, M. A. Kaashoek, H.Langer, R. Mennicken, L. Rodman, J. G.Stampfli Registration: use IWOTA web-page or e-mail toreceive second announcement Information: contact N.Manojlovic, U. C. E. H.,Universidade do Algarve, Campus de Gambelas,8000 Faro, Portugal, tel: +351-89-800914 ext7637, fax: +351-89-818560 e-mail: [email protected],web site: http://www.ualg.pt/cma/iwota/

18-22: International Data Analysis Conference,Innsbruck, AustriaScope: all aspects of data-analysis will be consid-ered, ranging from applied aspects to fundamen-tal questions on the description and analysis ofreal dataTopics: exploratory, fuzzy, statistical data analy-sisOrganizer: Prof. Reinhard Viertl Information:e-mail: [email protected] web site: http://www.statistik.tuwien.ac.at/ida2000/

18-23: International Congress on DifferentialGeometry, in Memory of Alfred Gray, Bilbao,SpainProgramme committee: Th. Banchoff, J. P.Bourguignon, E. Calabi, S. Donaldson, J. Eells, S.Gindikin, M. Gromov, O. Kowalski, M. Mezzino,S. Novikov, M. Pinsky, A. Ros, S. Salamon, L.Vanhecke, J. Wolf Organisers: M. Fernandez (chairman), L. C. deAndres, L. A. Cordero, A. Ferrandez, R. Iba-ez,M. de Leon, M. Macho-Stadler, A. MartinezNaveira, L. Ugarte Information: e-mail: [email protected] [email protected] web site: http://www.ehu.es/Gray

18-27: 8th Workshop on Stochastic and RelatedFields, G. Magusa, Famagusta, North Cyprus Speakers: include P. Malliavin, D. W. StroockProgramme committee: U. Capar, L.Decreusefond, A. S. Ustunel, M. Zakai Organisers: U. Capar, A. S. Ustunel Information: contact A. S. Ustunel, ENST, 46,rue Barrault, 75634 Paris Cedex 13, France,tel/fax: +33-1-45-81-31-19 e-mail: [email protected] web site: http://mozart.emu.edu.tr/workshop

19-22: Fractal Geometry: MathematicalTechniques, Algorithms and Applications,Leicester, UKAim: to provide a forum for discussing the math-ematical basis of fractal geometry, the computerimplementation of fractal algorithms and their

applications to modelling and analysing complexprocesses and patternsThemes: measure theory and fractal measures,multi-fractal measures, novel iteration functionsequences, statistically self-affine functions andLévy statistics, fractional dynamics, stochasticmodelling with fractals, inverse problems in frac-tal geometry, efficient algorithms for computingfractals, applications to time-series modelling(e.g. financial forecasting), applications to com-puter graphics (e.g. fractal surfaces), applicationsto simulation (e.g. L-systems), applications todata compression, applications to chaotic dynam-ical systems analysisInvited speakers: presentations on state of theart research will be given by a number of invitedspeakers who are internationally recognised fortheir contribution to the fieldOrganising committee: Prof. J. M. Blackledge(Leicester, chairman), Prof. K. Cevik(Fachhochschule Bielefeld), Dr. A. Evans(Leicester), Prof. M. Goman (Moscow), Dr. K.Hopcraft (Nottingham), Dr. S. Mikhailov(Moscow), Dr. M. Turner (Leicester) Proceedings: to be publishedShort course: a one-day short course,Introduction to Fractal Geometry and itsApplications, will precede the conference on 19September Site: De Montfort University, LeicesterCall for papers: abstracts of 300-500 wordsshould be sent to Pamela Bye, Institute ofMathematics and its Applications, CatherineRichards House, 16 Nelson Street, Southend-on-Sea, Essex SS1 1EF, UK, by 31 January 2000.Notification to authors will be mid-March 2000.Final papers should be submitted by late-December 2000 for inclusion in the conferenceproceedingsInformation: web site: http://www.ima.org.uk/mathematics/confractalgeometry.htm

18-20: Fifth International Conference onMathematics in Signal Processing, Coventry,UK Scope: signal processing constitutes an importantarea for the application of mathematical conceptsand techniques fuelled, for example, by recentdevelopments in mobile communications, multi-media systems and digital TV. The last IMA con-ference on this subject was held in December1996 and the intervening years have witnessedsignificant developments in many topics such asnon-linear/non-Gaussian signal processing,multi-rate signal processing, blind deconvolu-tion/signal separation and broadband systems Aim: the aim of this conference is to bringtogether mathematicians and engineers with aview to exploring recent developments and iden-tifying fruitful avenues for further research. It ishoped that the meeting will also help to attractmore mathematicians into this important andchallenging field Programme committee: Prof. J. G. McWhirter(chairman) (DERA, Malvern), Prof. O. R. Hinton(Newcastle) Site: University of Warwick Information: contact Mrs. Pamela Bye, Instituteof Mathematics and its Applications, CatherineRichards House, 16 Nelson Street, Southend-on-Sea, Essex SS1 1EF, UK, fax: +44-(0)-1702-354111, e-mail: [email protected]

December 2000

CONFERENCES


Books submitted for review should be sent to thefollowing address: Ivan Netuka, MÚUK,Sokolovská 83, 186 75 Praha 8, CzechRepublic.

D. Alpay, Algorithme de Schur, espaces ànoyau reproduisant et théorie des systèmes,Panoramas et Synthèses 6, SociétéMathématique de France, Paris, 1998, 189pp., ISBN 2-85629-067-1The aim of the book is to describe applica-tions of the theory of spaces with repro-ducing kernels in various fields of mathe-matics. Principal examples of such spacesare spaces of analytic functions of L. deBranges and J. Rovnyak. An importantproperty of reproducing kernels used inthe book is their positivity. The main partof the book contains a discussion of theSchur algorithm, the mathematical scatter-ing theory, function models in the theoryof operators and interpolation problemsfor holomorphic functions. Similar meth-ods are used in the last several chapters inmore general cases (e.g., for non-positivemetrics and non-stationary systems). Thebook contains an extended and detailedbibliography of the field (360 items). (vs)

T. Aubin, Some Nonlinear Problems inRiemannian Geometry, SpringerMonographs in Mathematics, Springer, Berlin,1998, 395 pp., DM168, ISBN 3-540-60752-8This is an extended and updated versionof the author�s earlier book �Non-linearAnalysis on Manifolds, Monge-AmpèreEquations, Grundlehren 252, Springer,1982�. Many important geometrical prob-lems are explained there, together withtheir history, up-to-date results and recentmethods of proofs. All presented prob-lems are related to non-linear partial dif-ferential equations arising in geometry andphysics.

The first part of the book is a nice intro-duction to Riemannian geometry, the the-ory of Sobolev spaces and the theory ofpartial differential equations onRiemannian manifolds. One interestingtopic treated in the book is the famousYamabe problem, which is described herein detail. Several proofs are presentedusing several different methods (variation-al, topological, etc.). Another topic dis-cussed extensively in the book is the prob-lem of prescribed scalar curvature (bothcases of positive and negative functions oncompact and non-compact manifolds aretreated). There is a nice overview of resultsand methods for the solution of the prob-lem. Solutions of the existence problemsfor a Kaehler-Einstein metric or a metricwith prescribed Ricci curvature can also befound in the book.

This book can be strongly recommend-ed to all those interested in contemporary

Riemannian geometry and non-linearPDE�s on manifolds. (jbu)

K. M. Ball and V. Milman, ConvexGeometric Analysis, Mathematical SciencesResearch Institute Publications 34, CambridgeUniversity Press, Cambridge, 1999, 236 pp.,£30, ISBN 0-521-64259-0This book collects articles on convexgeometry reflecting the research presentedin lectures or completed at theMathematical Sciences Research Institutewithin the framework of the programme�Convex Geometry and GeometricAnalysis� in 1996.

An incomplete list of topics and authorsfollows. J. Bourgain and G. Zhang give anegative answer to the generalisedBusemann-Petty problem. V. Milman andG. Schechtman prove an extension of theDvoretzky theorem. New results on poly-tope approximations are presented by W.T. Gowers and C. Schütt. A. Pajor esti-mates the metric entropy of theGrassmann manifold and M.Schmückenschlager defines curvature forgraphs. The inverse Brunn-Minkowskiinequality is improved by A. E. Litvak.Further new results on geometric function-al analysis are achieved by S. Alekser, A. E.Litvak and B. Maurey. Advanced probabil-ity techniques with application in optionpricing are developed by C. Borell. Thewhole collection provides a useful source ofinspiration for mathematicians working inconvex geometry and functional analysis.(jrat)

H.-J. Baues, Combinatorial Foundation ofHomology and Homotopy, SpringerMonographs in Mathematics, Springer, Berlin,1999, 362 pp., DM 159, ISBN 3-540-64984-0This book is devoted to a new categoricalformulation of homology and homotopytheories. Quite naturally, such anapproach leads to a general view of thesetheories, unifies many notions, presents adeeper understanding of the subject, andreveals new fields of investigation andapplications. In this book a theory is a cat-egory with an initial object and with finitesums, and a theory of coactions is a theory inwhich each object X is endowed with acogroup object X´ and a coactionX → X ∨ X´. The notion of a theory ofcoactions is of fundamental importance forthe constructions performed in the book.This is because each homotopy theory con-tains theories of coactions.

The book is divided into two parts,chapters A, B, C, D, and chapters I-VIII.The first part describes �classical� examplesof homology and homotopy theories, pre-sented in such a way that their commonand fundamental features come to light.The second part is then devoted to gener-

al categorical constructions. In principle,one might consider it possible to read onlythe second part, but practically this isimpossible, and in fact would make nosense. It seems that it is quite profitable toread both parts more or less simultaneous-ly. The book is not directly designed forbeginners in topology, but neverthelessthey can understand and learn from it.They can find here even the definition ofhomotopy groups � of course, in a moreabstract setting, but I think that it is natur-al for young mathematicians to start on ahigher level of abstraction than theirteachers started. For specialists in topologythe book presents a higher viewpoint and amore profound understanding of homolo-gy and homotopy theories and opens newperspectives. It can be strongly recom-mended. (jiva)

J. A. Beachy, Introductory Lectures onRings and Modules, London MathematicalSociety Student Texts 47, Cambridge UniversityPress, Cambridge, 1999, 238 pp., £15.95,ISBN 0-521-64340-6 and 0-521-64407-0The first three chapters of this text coverbasic results on (non-commutative) associa-tive rings and modules over them. Thefinal chapter consists of an introduction tothe representation theory of finite groups.All results are presented with full proofs,and are illustrated by a great variety ofexamples and exercises.

Among other things, the Gauss theoremon UFDs is presented in Section 1.4,Maschke�s theorem in Section 2.3, theKrull-Schmidt theorem for indecompos-able finite length modules in Section 2.5,the Wedderburn-Artin and Hopkins� theo-rems in Section 3.3, and the orthogonalityrelations for irreducible characters inSection 4.3. Moreover, each chapter endswith a section on more advanced relatedmaterial, such as Weyl algebras and Goldietheorems.

The text is aimed at advanced under-graduate or beginning graduate students,as a complement to Sharp�s book on com-mutative algebra (Volume 19 in the LMSstudent text series). Thus it was possible toskip over some of the basic notions of mod-ule theory that appear more frequently ina commutative setting, such as flat modulesand pure submodules. The text providesan excellent introduction to the Goodearl-Warfield text on non-commutative noe-therian rings (Volume 16 in the series).(jtrl)

N. L. Biggs, E. K. Lloyd and R. J. Wilson,Graph Theory 1736-1936, Clarendon Press,Oxford, 1998, 239 pp., ISBN 0-19-853916-9This is a new edition of the successful bookoriginally written in 1976. As the authorsclaim (and as the reviewer can certify), thisis a corrected and complemented (but for-tunately not expanded) edition which pre-sents the vivid origins of a popular field.

One cannot overlook that again the ref-erences are incomplete. For example, thefirst paper initiating a study of the SteinerTree Problem (V. Jarník and M. Kössler,About minimal graphs containing n givenpoints, Èas. Pì st. Mat. 63 (1934), 223-235)

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EMS December 199936

Recent booksRecent booksedited by Ivan Netuka and Vladimír Sou³ek

is omitted.This is a useful and general purpose

book. (jnes)

N. Bouleau, Philosophies des mathéma-tiques et de la modélisation, L�Harmattan,Paris, 1999, 363 pp., ISBN 2-7384-8125-6The author, an active mathematician in thefield of probability and mathematicalanalysis, and the head of an institute ofapplied mathematics, discusses a largespectrum of topics: philosophy of scienceand contemporary mathematics, theimpact of computer science and modellingto philosophy of mathematics, comparisonof the work of a computer with that of acreative mathematician, pure and appliedmathematics, teaching of mathematics, therole of abstraction in education, etc.

The introductory chapter brings a con-temporary view to a philosophical charac-terisation of mathematics and its faceunder the influence of the computer ageand the extensive use of modelling.The first part of the book summarises themost important moments and ideas in thedevelopment of philosophy of mathemat-ics (crises in foundation of mathematics,failure of Hilbert�s programme, mathemat-ics from a logical point of view, impact ofthe work of (among others) Bachelardi,Bourbaki, Carnap, Desanti, Feyerabend,Gödel, Heyting, Husserl, Lakatos,Lautman, Mill, Popper, Quine, Russell,etc.).

The second part deals with mathemat-ics: the nature of research, universality ofmathematical language, a role of simplifi-cations. The notion of �polysémie et dic-tionnaire� in mathematics is explained bymeans of several examples: geometricaltransformations, non-Euclidean geometry,intuitionistic logic, symbolic calculus, vari-ous aspects of potential theory, non-stan-dard analysis, etc. Creative processes,rigour and abstraction in mathematics areanalysed and pedagogical aspects are alsodiscussed.

The third part deals with the use ofmathematics � the author does not speakof applied mathematics, but coins the term�les mathématiques mixtes�: representationand communication by means of semi-arti-ficial ways of description. Various exam-ples of modelling are offered: car traffic,environment, finance, change of climate,symbolic description of dancing, etc. Thecentral notion here is that of a model andmodelling, which enables engineers to usemathematics directly, not necessarily in theframework of traditional disciplines. Theauthor also expresses his opinion on whatmathematics should be taught future engi-neers. The concluding chapter deals withmodernity and post-modernity in mathe-matics.

This book can be recommended to any-body who is interested in general andphilosophical aspects of mathematics.Mathematicians surely appreciate that var-ious philosophical concepts are document-ed and explained by means of well-chosenexamples from mathematics. (in)

D. Bump, Automorphic Forms and

Representations, Cambridge Studies inAdvanced Mathematics 55, CambridgeUniversity Press, Cambridge, 1998, 574 pp.,£24.95, ISBN 0-521-65818-7This is a paperback edition of the bookpublished in 1997; for a review, see EMSNewsletter 29, September 1998, p.39) (vs)

J. H. Conway and N. J. A. Sloane, SpherePackings, Lattices and Groups, A Series ofComprehensive Studies in Mathematics 290,Springer, New York, 1999, 703 pp., DM139,ISBN 0-387-98585-9The third edition of this famous book con-tinues to pursue the question of determin-ing the most efficient way to pack a largenumber of equal spheres into n-dimen-sional Euclidean space. Related problems,such as the classification of lattices andquadratic forms, the covering and kissingnumbers and quantising problems, arealso examined, and connections with cod-ing theory, digital communication, grouptheory, data compression, n-dimensionalcrystallography and number theory arestudied. A supplementary biography since1988 containing over 800 items is of spe-cial interest. (jtu)

K. R. Coombes, B. R. Hunt, R. L.Lipsman, J. E. Osborn, and G. J. Stuck,The Mathematica Primer, CambridgeUniversity Press, Cambridge, 1998, 214 pp.,hardback £50, paperback £16.95, ISBN 0-521-63130-0 and 0-521-63715-5This book provides an introductory coursefor Mathematica, version 3, but even usersof an earlier version may learn a lot. Itcovers the most important parts of the sys-tem, the front end, numerical and symbol-ic calculations, graphics, and Web. Thebook consists of eight chapters: 1. Getting started (how to work with

Mathematica on different platforms), 2. Mathematica basics, 3. Mathematica notebooks, 4. Beyond basics, 5. Mathematica graphics, 6. Applications (illuminating a room,

mortgage payments, cryptography,Fibonacci numbers, Monte Carlo simu-lation, population dynamics, chemicalreactions, the 360° pendulum),

7. Mathematica and the Web, 8. Trouble-shooting (common problems,

common mistakes). At the end there are two appendices:Solutions to the practice sets and Glossaryof commands, options, built-in functionsand selected standard packages. The styleof explanation is learning by carefully cho-sen examples. Chapter 6, in particular,demonstrates the power of Mathematica invarious fields. The book is strongly recom-mended for beginners and also for inter-mediate or experienced users who may dis-cover new features of Mathematica. (jh)

R. Curtis and R. A. Wilson (eds.), TheAtlas of Finite Groups: Ten Years On,London Mathematical Society Lecture NoteSeries 249, Cambridge University Press,Cambridge, 1998, 293 pp., £27.95, ISBN 0-521-57587-7This book is the proceedings of a confer-

ence organised in Birmingham in July1995, to mark the tenth anniversary of theAtlas of Finite Groups. It contains twentyarticles by leading experts in the field.Besides research papers we note a histori-cal article on the development of the Atlasproject since 1970 by three of its authors,J. H. Conway, R. T. Curtis and R. A.Wilson. Of particular interest are also sur-vey papers on applications of charactertheory to surfaces by G. A. Jones, on recentadvances in the representation theory byG. Hiss, and on Zassenhaus conjectures onintegral group rings by W. Kimmerle. (jtu)

S. Donkin, The q-Schur Algebra, LondonMathematical Society, Lecture Note Series 253,Cambridge University Press, Cambridge, 1998,179 pp., £24.95, ISBN 0-521-64558-1These notes relate the representation the-ory of quantum linear groups Gq(n), of theq-Schur algebras Sq(n, r) and of the Heckealgebras H(r) defined by the symmetricgroup Sym(r). This generalizes the classi-cal theory which is recovered as the caseq = 1. There are two main tools employed.First, the Schur functor F from Sq(n, r)-mod to H(r)-mod: for r ≤ n, one hasH(r) ≈ eSq(n, r)e for an idempotent e, and Fis defined simply as the �descent�,F(V) = eV. Second, the identification ofSq(n, r)-mod with a full subcategory ofGq(n)-mod consisting of modules that arepolynomial of degree r.

Donkin�s approach is homologicalrather than combinatorial. Among otherthings, the character formula for irre-ducible Sq(n, r)-modules at q = 0 is provedin 2.2, and the Steinberg�s tensor producttheorem in 3.2. There is an explicit com-putation of tilting modules for the quan-tum GL2 in 3.4, and an explicit descriptionof the graded Grothendieck ring⊕d≥0 Grot(H(d)) in 4.4. In 4.8, the globaldimension of Sq(n, r) for r ≤ n is deter-mined.

The main part of the notes is written inarticle style. This is compensated for by along expository Chapter 0, and by anappendix on quasi-hereditary algebras.The book is an important addition to theliterature on the highly topical quantumversion of the classical representation the-ory. (jtrl)

H. M. Enzensberger, Zugbrücke ausserBetrieb, Drawbridge Up, A. K. Peters, Ltd.,Natick, 1999, 47 pp., £4, ISBN 1-56881-099-7This booklet is written by the distinguishedGerman poet and essayist Hans MagnusEnzensberger. His first book for children(and for other thinking beings) called�The Number Devil� (Metropolitan Books,N.Y. 1998 � translation from the German�Der Zahlenteufel: Ein Kopfkissenbuch füralle, die Angst vor der Mathematik haben�,Carl Hanser Verlag, München 1997) isquite well known. Professional mathemati-cians are accustomed to live surrounded bypeople who declare with an odd sort ofpride that they are mathematically illiter-ate. Enzensberger wishes to build a draw-bridge between these two groups andbelieves that progress in teaching is possi-

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ble and that mathematics can be madeexciting to young minds. Public attitudestoward mathematics can be improved asmathematics is a part of the culturalsphere. Drawbridge up is a �beautiful essayand a great delight for a mathematician toread� says David Mumford in the preface.(lbo)

G. Farin, NURBS: From ProjectiveGeometry to Practical Use, A. K. Peters, Ltd.,Natick, 1999, 267 pp., £30, ISBN 1-56881-084-9Today�s design technologies use sophisti-cated mathematical methods. Modellingcomplex objects such as ships, car bodies,or airplane fuselages has given rise to tech-niques known as Bézier curves and Coonsmethods. If we want to deal with the prob-lem of how we see things, the Euclideanviewpoint is no more advantageous. A newtool called NURBS (non-uniform rationalB-splines) appeared in 1975. A naturalsetting for it is projective geometry.

The book starts with a general outline ofprojective geometry. Conics are intro-duced through the classical projective def-inition, first as line conics and then aspoint conics. After Pascal�s andBrianchon�s theorems, the author presentsconics in parametric form, conic splinesand rational Bézier curves. Further chap-ters are devoted (e.g.) to rational cubics,NURBS curves and surfaces, rectangularpatches and Gregory patches. A chapteron Pythagorean curves is incorporated inthis second edition. The reader is assumedto know linear algebra, calculus and basiccomputer graphics. A significant featureof the book is a large collection of exercis-es, both practical and theoretical, at theend of each chapter. (lbo)

G. Farin and D. Hansford, The GeometryToolbox for Graphics and Modeling, A. K.Peters, Ltd., Natick, 1998, 288 pp., £34,ISBN 1-56881-074-1The subject of this book is an investigationof basic concepts of analytic geometry inthe plane and three-dimensional space. Itapproaches linear algebra from a geomet-ric viewpoint. Many figures and hand-drawn sketches help to explain linear ana-lytic geometry (dot and cross product,barycentric coordinates, affine maps,eigenvectors, etc.). Only the last chapter isdevoted to non-linear geometry, namely asan introduction to the theory of curves(parametric curves, Bézier curves, curva-ture and the Frenet frame). As an applica-tion, the authors mention curves used todesign cars (computer-aided geometricdesign). The theoretical level is kept to aminimum, and the emphasis of the book isnot on abstract proofs but rather on exam-ples and algorithms. The book can be rec-ommended to students, and can serve alsoas a general introduction to geometry andto applications of linear algebra (e.g.matrix theory) in geometry. (lbo)

H. O. Fattorini, Infinite DimensionalOptimization and Control Theory,Encyclopedia of Mathematics and itsApplications 62, Cambridge University Press,

Cambridge, 1999, 798 pp., £70, ISBN 0-521-45125-6This extensive monograph is a fundamen-tal contribution to optimal control theoryof evolution of finite- or infinite-dimen-sional systems, and summarises andextends the author�s many decades of last-ing intensive research in this area.

The first part (Chapters 1-4) deals with�finite-dimensional control problems�,optimisation problems governed by initial-value problems for systems of (possiblynon-linear) ordinary differential equa-tions. Chapter 1 �Calculus of variationsand control theory� contains motivatingexamples. Chapter 2 deals with �Optimalcontrol problems without target condi-tions�, starting from measure and integra-tion theory and functional analysis, andthen continuing with (non-)existence inclassical optimal control problems, spikevariations, minimum principle,Hamiltonian formalism, and linear-qua-dratic problems, including the feedbackRiccati equation. Then Chapters 3 and 4deal with (time-)optimal control problems,both on an abstract level and on the levelof concrete examples. Here Ekeland�svariational principle and the Kuhn-Tuckertheorem are the main tools used on theabstract level.

The second part (Chapters 5-11) isdevoted to �Infinite dimensional controlproblems�. Chapter 5, �Differential equa-tions in Banach spaces and semigroup the-ory� includes elements of functional analy-sis, the theory of the Lebesgue-Bochnerintegral, and (semi-)linear parabolic andhyperbolic partial differential equations asabstract Cauchy problems using the semi-group approach. Chapters 6 and 7 treatabstract minimisation problems in Hilbertand Banach spaces, with various applica-tions to linear or semi-linear hyperbolicand parabolic control problems, respec-tively, deriving always the minimum prin-ciple of Pontryagin�s type. Chapter 8 dealswith interpolations and domains of frac-tional power with application to Sobolev-Slobodeckii spaces and parabolic equa-tions, including Navier-Stokes equations.�Linear control systems� forms Chapter 9,including such special topics as bang-bangtheorems and controllability. Chapters 10and 11 address �Optimal control problemswith state constraints�, admitting (possiblyonly finitely additive) vector-valued mea-sures as the respective Lagrange multipli-ers. Suboptimal controls and their conver-gence are studied in detail.

The third part (Chapters 12-14) dealswith �Relaxed controls� which come intoconsideration if an original optimal con-trol problem lacks solutions. A unique the-ory of �Spaces of relaxed controls� formsChapter 12. Classical Young measures(i.e., parametrised probability Radon mea-sures) are only a particular case arising ifcontrols range a metrisable compact. Innon-compact cases, a generalisation to cer-tain finitely-additive probability measuresis made. Chapter 13 applies relaxed con-trols to finite-dimensional evolution sys-tems. Original controls range a compactset so that the relaxed controls are classical

Young measures here, except the last sec-tion where unbounded Rk-valued controlsare admitted, too. Finally, Chapter 14develops a relaxation theory both forabstract infinite dimensional systems andfor concrete semi-linear parabolic orhyperbolic partial differential equations,where often the controls range naturally anon-compact set, so that the generalised(i.e., finitely-additive) Young measuresappear.

Bibliographical comments accompanyeach part. This outstanding monographwill be a great source both for experts andfor graduate students interested in calculusof variations, non-linear programming,optimisation theory, optimal control, andrelaxation theory. (trou)

D. Fowler, The Mathematics of Plato�sAcademy, Clarendon Press, Oxford, 1999,441 pp., £60, ISBN 0-19-850258-3�The Mathematics of Plato�s Academy� is anupdated second edition of a well-knownbook devoted to early Greek mathematics.The book is divided into three parts:Interpretation, Evidence and Later develop-ments.

The first part (Chapters 1-5) presents anew interpretation of some mathematicalideas and topics found in the works ofPlato, Aristotle, Euclid, Archimedes, etc.The author shows that the methods, algo-rithms and procedures derived from theirworks had a great influence on the devel-opment of early Greek mathematics.Chapter 5 has been rewritten, while otherchapters have many smaller additions,modifications and corrections.

The second part (Chapters 6-7)describes the evidence forour knowledgeof Plato�s Academy, describing the trans-mission of Greek texts to our time andlooking at the treatment of numbers andfractions.

The third part (Chapters 8-11)describes the development of continuedfractions since the seventeenth century.Chapter 10 (Appendix) introduces newmaterial that can be considered as a mod-ern interpretation of Greek mathematicsand the mathematical topics of Plato�sAcademy. The new brief autobiographicalEpilogue, the new significantly expandedBibliography, the Index of cited passages,the Index of names and the General indexhave been added to this second edition.(mbec)

J. Glynn and T. Gray, The Beginner�sGuide to Mathematica® Version 3,Cambridge University Press, Cambridge, 1997,347 pp., ISBN 0-521-62202-6 and 0-521-62734-6 This book serves both as a tutorial and as areference book. It is written as seventyshort chapters in Question and Answerform. It covers a variety of problems likethe front end, symbolic and numerical cal-culation, typesetting, packages, graphics,Internet environment, and programming.A lot of information contained in the bookmay be found in the Mathematica helptopics, and the style of presentationenables the Mathematica user (both the

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EMS December 199938

beginner and the advanced user) to getimportant pieces of information veryquickly. The book is strongly recommend-ed not only to all Mathematica users butalso to those who would like to learn howto use the full capability of Mathematica.(jh)

W. M. Goldman, Complex HyperbolicGeometry, Oxford Mathematical Monographs,Clarendon Press, Oxford, 1999, 316 pp., £65,ISBN 0-19-853793-XThis book is a very good introduction tothe geometry of a complex hyperbolicspace and its boundary. It is accessibleeven for undergraduate students. Theauthor�s motivation was the need to have awell and systematically organised introduc-tory text on this subject - namely, it wasdesirable to unify and �normalise� exposi-tions which appeared mostly in variousjournals. Anyhow, this book seems to bethe first one that presents such a systemat-ic treatment. The author himself considershis book as a �user�s guide� to complexhyperbolic geometry. His exposition usesminimal possible technical tools. He triesto avoid references to general theoremsexceeding the framework of the complexhyperbolic geometry, and prefers to deriveresults by concrete considerations andcomputations; this is exactly the point thatwill surely be appreciated by an under-graduate reader. His idea is to introducethe reader into geometry via concreteexamples, and complex hyperbolic geome-try suits this purpose well.

In order to motivate the reader, theauthor starts with a chapter that reviewsthe complex 1-dimensional geometries.They are presented in such a manner thatthey suggest generalisations to higherdimensions. The next chapter deals withthe relevant linear algebra and necessarynotions from differential geometry. Thenwe come to the main parts of the book.The author presents the complex n-dimen-sional hyperbolic space first in the form ofthe unit ball model (in Cn) and then in theform of the paraboloid (or Siegel domain)model. We remark explicitly that theauthor also devotes systematic attention tothe geometry of the boundary of the com-plex hyperbolic space. It is here where theHeisenberg geometry appears. He pre-sents old results (usually in more modernand elegant way) as well as quite recentones. There are many interesting exercis-es that substantially enrich the main text,and many nice pictures. The bibliographycontains 175 items and goes up to 1998.(jiva)

J. Harris and I. Morrison, Moduli ofcurves, Graduate Texts in Mathematics 187,Springer, New York, 1998, 366 pp., DM118,ISBN 0-387-98438-0 and 0-387-98429-1The main topic of this book is a descrip-tion of the properties of moduli spaces ofalgebraic curves. This subject has grownrapidly in the last few years. In the firstpart, there is a short summary of basic factsconcerning moduli and parameter spacesof curves, Hilbert schemas, the space Mgand its geometric and topological proper-

ties. There is also an interesting chaptercontaining a description of Witten�s con-jectures and the Kontsevich theorem.Deformation theory, stable reduction andthe Grothendieck-Riemann-Roch aredescribed in the second part of the book.The rest of the book contains a selection ofcontemporary results on the geometry ofmoduli spaces.

These theories are presented here in avery nice form, with examples and manyexercises. The authors� preference hasbeen to focus on examples and applica-tions rather than on theoretical founda-tions. This method seems to be veryappropriate for this topic. The book endswith a rich bibliography. (jbu)

A. B. Kharazishvili, Applications of PointSet Theory in Real Analysis, Mathematicsand Its Applications 429, Kluwer AcademicPublishers, Dordrecht, 1998, 236 pp., £66,ISBN 0-7923-4979-2The main goal of this book is to demon-strate the usefulness of set-theoreticalmethods in various questions of real analy-sis and classical measure theory. The bookis devoted to some results from classicalpoint-set theory and their applications tocertain problems in mathematical analysisof the real line.

The author concentrates on the follow-ing topics:(a) similarities and differences betweenmeasure and category: many non-trivialexamples and facts are presented in thebook;(b) set-theoretic, topological and algebraicaspects of the measure extension problem:in particular, there are applications ofErshov�s measure extension theorem to theclassical property of Luzin and to theuniqueness property of invariant mea-sures;(c) various constructions of Lebesgue non-measurable sets and of sets without theBaire property: some connections betweenthese constructions and infinite combina-torics (namely, the Ulam matrix) and thegeneral theory of commutative groups areindicated;(d) various singular objects in mathemati-cal analysis from the point of view of theKuratowski-Ulam theorem: in particular, itis established that the classical principle ofcondensation of singularities followsdirectly from the above-mentioned theo-rem;(e) geometrical properties of certain sub-sets of an abstract space E, equipped with agroup G of its transformations: first, theso-called G-thick sets, G-scattered sets, G-thin sets, G-negligible sets and absolutelyG-negligible sets, and several relationshipsbetween these properties, the theory ofinvariant (quasi-invariant) measures andthe general theory of G-equidecomposabil-ity of sets are thoroughly considered;(f) some set-theoretical aspects of the theo-ry of differential equations, concerning theexistence and uniqueness of solutions ofsuch equations.

The material presented in this book isessentially self-contained and is accessibleto a wide audience of mathematicians. It

will appeal to specialists in set theory,mathematical analysis, measure theory andgeneral topology. It is also recommendedas a textbook for postgraduate students.(pp)

Y. Kitaoka, Arithmetic of Quadratic Forms,Cambridge Tracts in Mathematics 106,Cambridge University Press, Cambridge, 1999,270 pp., £18.95, ISBN 0-521-40475-4 and0-521-64996-XThe aim of this book is to provide an intro-duction to the arithmetic theory of qua-dratic forms. The book starts from thebasics and proceeds to many recent results.It covers several aspects of the subjectincluding lattice theory, Siegel�s formula,and tensor products of positively definitequadratic forms. Quadratic forms aremainly considered over the rationals or thering of rational integers and their comple-tions.

The reader is required to have only anelementary knowledge of algebraic num-ber fields. This makes the book ideal forgraduate students and researchers fromother fields interested in quadratic forms.(jtu)

P. Koosis, Introduction to Hp spaces,Second Edition. Cambridge Tracts inMathematics 115, Cambridge University Press,Cambridge, 1998, 287 pp., £45, ISBN 0-521-45521-9The first edition of this book was publishedin 1980. There is a Russian translationthat is accompanied by two appendices onJones interpolation formula and weakcompletness of the factor L1/H1(0), writtenby V. P. Havin; these appendices arereproduced in the new edition. There arealso some other changes, but they do notalter the spirit of the first edition.

The contents of the book can be dividedinto two parts. The first part, consisting ofChapters I-VI is devoted to basic informa-tion on the Hilbert transform and theHardy spaces Hp for the disk and theupper half-plane. Here the author usesthe so-called �complex function methods�,but some key results (such as the Rieszbrothers� theorem on analytic measuresand the M. Riesz theorem on Lp bounded-ness of the Hilbert transform) have severalproofs.

The second part contains deeperresults. The duals of Hp and Hp-bestapproximation of Lp-functions are investi-gated in Chapter VII. The characterisa-tion of ReH1 based on the Hardy-Littlewood maximal functions is discussedin Chapter VIII. Interpolation results forHp-functions (Carleson and Shapiro-Shields theorems) and for bounded har-monic functions (Garnett theorem) areproved in Chapter IX. Chapter X is devot-ed to functions of bounded mean oscilla-tion (two proofs of the Fefferman repre-sentation of the dual of ReH1(0) are pre-sented); the main changes with respect tothe first edition are in this chapter. TheWolff�s proof of the Carleson corona theo-rem is given in the last chapter.

This book is written chiefly for graduatestudents with a working knowledge of real

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and complex function theory, and containsmany valuable comments on ideas andtechniques of proofs. The use of differenttypographical forms also helps to clarifycomplicated proofs. (jmil)

M. Kracht, M. de Rijke, H. Wansing andM. Zakharyaschev (eds.), Advances inModal Logic 1, CSLI Publications, Stanford,1998, 392 pp., £15.95, ISBN 1-575-86102-X and 1-575-86103-8The first conference in the Advances inModal Logic (AiML) conference series washeld at the Free University of Berlin inOctober 1996. AiML is also a forum,established in 1995, for scientists workingin various areas of modal logic and itsapplications. The book contains 21 papersin the field. The book covers a large spec-trum of topics, offering results on themathematics of modal logic, proof-theoret-ical properties, theoretical and appliedcomputer science, applications in knowl-edge representation, philosophy and lin-guistics. We find here contributions onterminological modal logic, hybrid lan-guages, topological next-time logic, mini-mal knowledge states in non-monotonicmodal logics and relations between modelsand parallel computations. The papersmotivate the field and review basic notionsand facts. A subject index is included. Thebook can be seen as a good and represen-tative source of information concerningresearch in the subject. It is accessible toadvanced students in non-classical logic.(jmlc)

K. Leichtweiss, Affine Geometry ofConvex Bodies, Johann Ambrosius BarthVerlag, Heidelberg, 1998, 310 pp., DM148,ISBN 3-335-00514-7The author presents a systematicequiaffine theory of convex bodies, andstresses connections and differences fromthe convex geometry in Euclidean spaces.Special attention is paid to the definitionof the affine surface area and to a compar-ison of the author�s definition with otherones. Some generalisations of classicalinequalities from convex geometry (such asthe isoperimetric inequality) to the affinecase are also presented. (jrat)

B. R. Mandelbrot, Fractals and Scaling inFinance, Springer-Verlag, New York, 1997,551 pp., ISBN 0-387-98363-5This book presents an alternativeapproach to the analysis of financial data,or more generally, to any data set possess-ing features like financial time series.Approximately half of the book consists ofthe author�s contributions to various prob-lems from the last 40 years in the form ofpreprints from journals (together with con-tributions of other authors related to thetopic), while the remaining half is com-pletely new. The key concept in the bookis scaling.

The first two chapters are devoted bothto non-mathematical and mathematicalpresentations. The third chapter dealswith personal incomes and firm sizes. Thefourth chapter describes and illustrates theMandelbrot 1963 model of price variation.

The fifth chapter consists of some com-ments beyond the Mandelbrot 1963model.

This book is recommended to anymathematician and/or financial analystwho wishes to learn more about the varietyof alternative models and to avoid usingjust the classical methods. (jh)

P. Marage and G. Wallenborn (eds), TheSolvay Councils and the Birth of ModernPhysics, Historical Studies, Science Networks22, Birkhäuser, Basel, 1999, 224 pp.,DM118, ISBN 3-7643-5705-3 and 0-8176-5705-3The Solvay Councils, held in Brussels since1911 following an initiative of the Belgianindustrialist E. Solvay, played an essentialrole in forming the paradigm of modernphysics. Organised as a series of meetingsof the most distinguished physicists of thattime, the Councils provided ground for theconstitution of new physics beyond �classi-cal� mechanics and field theory, of thequantum theory of matter and radiation.Reports of the Councils, at least of thosebefore the Second World War, can be readas a detective story on how the contempo-rary knowledge of atoms, atomic nuclei,and subatomic particles came into beingthrough a brilliant stroke of experimentsand seemingly bizarre hypotheses, ofteninspired by vivid discussions at theCouncils. The book �tells the story� of theCouncils, together with short explanationsof the necessary physical background, sothat it is useful not only for physicists (whowill find here historical facts that are oftenoversimplified in physics textbooks), butalso for scientists of non-physical areas andthe broad public seeking reliable informa-tion on the birth of quantum mechanics.The text is based on the Brussels 1995exhibition and conference devoted to theSolvay Councils, and contains (besides adescription of the most important Councilsbefore the Second World War) contribu-tions dealing with the role of some person-alities in the science of that period and thehistorical and sociological background. Itis worth mentioning that the book containsexcellent and not commonly known pho-tographs of the most influential Councilparticipants. The book is recommended toall who are interested in the fascinatingdevelopment of physics in the 20th centu-ry. (pc)

K. Matsuzaki and M. Taniguchi,Hyperbolic Manifolds and KleinianGroups, Oxford Mathematical Monographs,Clarendon Press, Oxford, 1998, 253 pp., £60,ISBN 0-198-50062-9This book is a revised and enlarged trans-lation of a book by the same authors whichappeared in 1993 in Japanese. It is devot-ed to the study of hyperbolic 3-manifoldsand Kleinian groups, which since 1980have attracted much attention. The bookstarts from the very beginning of hyperbol-ic geometry and leads the reader up tocontemporary research. Its prerequisitesare rather modest. Practically, it requiresonly basic knowledge of geometry, algebraand analysis, and some familiarity with

hyperbolic plane geometry and hyperbolicsurfaces. But for the reader�s convenience,and also as motivation, the authors includeChapter 0, a summary about hyperbolicsurfaces and Fuchsian groups. Then, fromChapter 1, the reader is presented with allthe necessary details. This means thateven 3-dimensional hyperbolic space isintroduced and three of its models arecarefully studied. Then hyperbolic 3-man-ifolds are defined and the Kleinian groupsappear as the universal covering transfor-mation groups of their universal covering,3-dimensional hyperbolic space. Chapters2, 3 and 4 deal directly with the Kleiniangroups. Special attention is devoted togeometrically finite and finitely generatedKleinian groups. But even Chapter 5, �Thesphere at infinity�, studies the actions ofKleinian groups on this sphere anddescribes how the hyperbolic geometry ismirrored by this sphere. Chapter 6 isabout the ends of hyperbolic manifoldsand the final chapter studies algebraic andgeometric convergence of Kleinian groups.A short appendix is devoted to theThurston uniformisation theorem.

The presentation of the whole theory isvery nice; we find here many concreteexamples and interesting remarks. Simply,the book reads well, and will be interestingand accessible for mathematicians fromseveral branches of mathematics. The lit-erature has 108 items and goes up to 1997.(jiva)

G. Navarro, Characters and Blocks ofFinite Groups, London Mathematical SocietyLecture Note Series 250, Cambridge UniversityPress, Cambridge, 1998, 287 pp., £24.95,ISBN 0-521-59513-4This book presents an account of the theo-ry of Brauer (alias modular) characters andblocks for finite groups. The motivatingresult for the first part of the book is theZ*-theorem of G. Glauberman which is oneof the main applications of modular repre-sentation theory to finite groups. The firstchapters develop the theory and includethe main theorems of R. Brauer. Afterproving the Z*-theorem, the author con-centrates on p-solvable groups and, finally,on the groups with Sylow p-group of orderp and description of their p-blocks.

This book can be used by both graduatestudents and researchers interested inmodular representation theory of finitegroups. Its style is accessible and includessome recent results. At the end of eachchapter is a set of open problems. (rb)

J. A. Nohel and D. H. Sattinger (eds.),Selected Papers of Norman Levinson, 2vols., Contemporary Mathematicians,Birkhäuser, Boston, 1998, 1152 pp., DM976,ISBN 3-764-33862-8 and 3-764-33979-9This selection reflects Levinson�s contribu-tion to complex, harmonic and stochasticanalysis, to differential and integral equa-tions, and to analytic number theory. Hislist of publications contains 124 items, ofwhich 76 are reproduced in this collection.

Each section contains a complete list ofpapers covering the topic of the sectionand commentaries written by B. Conrey, B.

RECENT BOOKS

EMS December 199940

Levitan, J. Moser, J. Nohel, M. Pinsky, A.Radakrishnan, R. Redheffer, D. Sattinger,H. Sussman and E. Zeidler. Photos fromvarious periods of his life can be found inboth volumes. Finally, personal tributes byH. McKean, W. T. Martin, B. Konstant andhis wife Zipporah (Fagi) complete the pic-ture about his life and personality, helpingthose of us who never had an opportunityto meet him.

The first volume is devoted to the fol-lowing topics: stability and asymptoticbehaviour of solutions of ordinary differ-ential equations, non-linear oscillationsand dynamical systems, inverse problemsfor Sturm-Liouville and Schrödinger oper-ators, eigenfunction expansions and spec-tral theory for ordinary differential equa-tions, singular perturbations of ordinaryand partial differential equations, ellipticpartial differential equations and integralequations.

The second volume treats harmonic andcomplex analysis, stochastic analysis, ele-mentary number theory and the primenumber theorem, the Riemann zeta-func-tion and miscellaneous topics. (�por)

B. Novák (ed.), Life and Work of Vojtì chJarník, Society of Czech Mathematicians andPhysicists, Prometheus, Praha, 1999, 197 pp.,ISBN 80-7196-156-6Vojtì ch Jarník (1897-1970) was one ofleading personalities of Czechoslovakmathematics of the 20th century. His pre-cise style of writing, both in his famousseries of books on analysis and in his ownresearch work, heavily influenced manygenerations of mathematicians inCzechoslovakia.

Besides biographical articles, personalrecollections and articles on his pedagogi-cal activities, the book contains a descrip-tion of Jarník�s research contribution todiophantine approximations (by M.Dodson), geometry of numbers (by P.Gruber), combinatorial optimisation (by B.Korte and J. Ne�etøil), real analysis (by D.Preiss) and lattice theory (by B. Novák).These contributions show the continuingimpact of Jarník�s ideas in number theoryand real analysis up to the present time.The last 85 pages contain 7 selected papersof Jarník, including his pioneering paperon Hausdorff measure and diophantineapproximations and his bibliography. (vs)

G. Pisier, The Volume of Convex Bodiesand Banach Space Geometry, CambridgeTracts in Mathematics 94, CambridgeUniversity Press, Cambridge, 1999, 250 pp.,£17.95, ISBN 0-521-36465-5 and 0-521-66635-XThe classical Dvoretzky�s Theorem relatesthe analytic properties of Banach spaces tothe geometry of its finite dimensional sub-spaces. This book presents some recentresults of a similar nature. The basic toolsare various (classical and recent) inequali-ties for volumes of convex bodies in finite-dimensional Euclidean spaces, such as the(inverse) Brunn-Minkowski inequality orthe (inverse) Santaló inequality. Besidesthe classical methods of convex geometry,the techniques of Gaussian processes and

approximation theory are used.Consequently, important results areobtained for the geometry of (infinite-dimensional) Banach spaces. The presen-tation is self-contained and, due to itsinterdisciplinary character, should attractthe attention of a wide group of mathe-maticians. (jrat)

B. Polster, A Geometrical Picture Book,Universitext, Springer, New York, 1998, 291pp., DM98, ISBN 0-387-98437-2Pictures are what this book is all about.They illustrate various kinds of geometry,such as incidence structures, affine andprojective planes and spaces, linear spaces,designs, circle planes, generalised poly-gons, etc.

The book is divided into two parts. Thefirst part presents pictures of finite geome-tries with small numbers of points, the sec-ond part contains pictures of topologicalgeometries, mainly those that live on sur-faces. Each chapter contains definitions, aminimum of theory, and references to text-books and survey articles. The book isaddressed at advanced undergraduatesand graduate students. (lbo)

A. D. Polyanin and A. V. Manzhirov,Handbook of Integral Equations, CRCPress, Boca Raton, 1998, 787 pp., DM228,ISBN 0-8493-2876-4In this book, more than 2100 integralequations with solutions are given. Newexact solutions to many linear and non-lin-ear equations are included. Special atten-tion is paid to equations of general formthat depend on arbitrary functions. Otherequations contain one or more free para-metrs. The number of equations describedin the book is of an order of magnitudegreater than in other available books.Equations considered here appear in vari-ous fields of mechanics and theoreticalphysics (elasticity, plasticity, hydrodynam-ics, heat and mass transfer, electrodynam-ics, etc.). The second part contains exactand approximate analytical and numericalmethods for solving linear and non-linearintegral equations.

The handbook has no analogue in theliterature and is intended for a wide audi-ence of researchers, college and universityteachers, engineers, and students in thevarious fields of mathematics, mechanics,physics, chemistry, and queueing theory.(mbr)

J. Rappaz and M. Picasso, Introduction àl�analyse numérique, Presses Polytechniques etUniversitaires Romandes, Lausanne, 1998,256 pp., sFr62, ISBN 2-880-74363-XThis book is aimed at undergraduate engi-neering and science students who need areadable textbook on numerical mathe-matics. It presents a comprehensivedescription of the fundamental tools fornumerical solutions of ordinary and partialdifferential equations. The text is centredaround those topics that form the essen-tials of the finite-difference and finite-ele-ment method: polynomial interpolation,numerical differentiation and integration,solution of linear and non-linear algebraic

equations. The authors use a practicalapproach based upon solving model ellip-tic, parabolic, hyperbolic and convection-diffusion problems, and all ideas are intro-duced from this viewpoint. The text con-tains solved exercises as a bridge from thetheory to the applications. (jfel)

Y. B. Rudyak, On Thom Spectra,Orientability, and Cobordism, SpringerMonographs in Mathematics, Springer-Verlag,Berlin, 1998, 587 pp., DM198, ISBN 3-540-62043-5This is a fundamental monograph on thetopics in the title, written by an author whohas substantially contributed to the subject.It contains a relatively large amount ofmaterial, even in comparison with olderbooks on these subjects. (This can bealready seen from the number of pages.) Agreat deal of material cannot be found inany other monograph. The main topicshere are spectra and (co)homology theo-ries, with special emphasis on the (co)bor-dism theories. We note that two chaptersare devoted to the (co)bordism with singu-larities, and that there is a chapter aboutthe phantom maps and a chapter aboutorientability with respect to cohomologytheories.

The book is indispensable for researchworkers in algebraic topology. The pre-sentation of the material is very nice andthorough, and this makes the book conve-nient for students with preliminary knowl-edge of algebraic topology. The book isnot self-contained, because this wouldenlarge its size still further. But wheneverthe author decides not to introduce anotion or present a proof, he gives an ade-quate reference. The beginner will espe-cially appreciate the author�s historicalremarks that help one understand the ori-gins and spirit of the theory. But evenfrom a formal point of view the author triesto make the reading as easy as possible.The list of notations is carefully arrangedinto several groups, which enables quickorientation. The references extend to 18pages. (jiva)

G. Sambin and J. Smith, Twenty-FiveYears of Constructive Type Theory, OxfordLogic Guides 36, Clarendon Press, Oxford,1998, 283 pp., ISBN 0-19-850127-7Beginning in 1970, Per Martin-Løf hasdeveloped a constructive foundation ofmathematics which he called intuitionistictype theory. On the occasion of the 25thanniversary, a special conference on thesubject took place and it was decided topublish the proceedings without restrictingcontributions to participants of the confer-ence. Thus, among others, it contains oneof the first preprints of Martin-Løf (1971)on the subject. It is published here for thefirst time.

Type theory has increasing applicationsto a variety of fields like constructive math-ematics, logic, computer science, linguis-tics etc. Fourteen remaining papers in theproceedings cover many of these applica-tions. The book presents a good survey ofthe current state of the subject. (ak)

RECENT BOOKS


A. Scott, Nonlinear Science: Emergenceand Dynamics of Coherent Structures,Oxford Applied and Engineering Mathematics1, Oxford University Press, Oxford, 1999, 474pp., £39.95, ISBN 0-19-850107-2Originally prepared as notes for coursespresented to advanced undergraduates atthe Technical University of Denmark, thisbook is designed as an introduction to thestudy of non-linear partial and difference-differential equations.

It starts with a description of the histor-ical development of non-linear models.The reader is supposed to have a basicknowledge of physical notions and of thelinear theory (Fourier transform, stability,scattering theory), although the latter isbriefly reviewed in an introductory chap-ter. In the main part of the book are pre-sented classical soliton equations(Korteveg-de Vries, sine-Gordon, non-lin-ear Schrödinger), non-linear diffusionequations (Fisher, Hodgkin-Huxley, Fitz-Hugh-Nagumo), non-linear lattices (herethe spatial variable takes its values in a lat-tice of points), and their exact solutions(travelling waves, solitons) are discussed.The Bäcklund transform and the inversescattering method are explained by meansof examples, as well as being generally for-mulated. A discussion of perturbationsand quantum lattice solitons is also includ-ed. The final chapter is a personal view onfuture directions of research in applied sci-ence. The presentation in the book isbased on concrete equations and the for-mulas are often derived from physical intu-ition. There are no definitions and theo-rems. Much attention is paid to the physi-cal, biological or chemical context. (efa)

N. N. Tarkhanov, The Analysis ofSolutions of Elliptic Equations, Mathematicsand its Applications 406, Kluwer AcademicPublishers, Dordrecht, 1997, 479 pp., £146,ISBN 0-7932-4531-1This book includes a broad analysis of gen-eral elliptic systems of differential equa-tions. It starts with singularities of solu-tions and their removability. Severalresults illustrate the role of adequatecapacities, as well as the Hausdorff mea-sures and Minkowski�s content, in estimat-ing the size of singular sets. Parallels withthe development of the theory of functionsof complex variables are underlined. TheLaurent series for solutions of homoge-neous elliptic systems and an investigationof appropriate expansions of solutions mayserve as an example; another such topic isthe theory of uniform approximation byholomorphic functions, which stimulatedthe study of questions concerning uniformapproximation by solutions of general sys-tems of differential equations. While theproblem of uniform approximation has along history, investigation of the meanapproximation has begun comparativelyrecently. There is also a chapter thatincludes a discussion of how approxima-tion within BMO may be seen as interme-diate between the approximation theoriesin uniform and in Sobolev norms. Otherthemes treated in the book include solv-ability of the Cauchy problem and the sta-

bility theory, its role in the theory of quasi-conformal mappings, and special classes ofsolutions of first-order elliptic systems.The reader is expected to have a goodknowledge of basic functional analysis, dis-tribution theory, function theory and par-tial differential equations (pseudo-differ-ential operators). This comprehensive text(479 pp.) provides rich material that maybe used in specialised seminars. (jokr)

M. Yamaguti, M. Hata and J. Kigami,Mathematics of Fractals, Translations ofMathematical Monographs 167, AmericanMathematical Society, Providence, RhodeIsland, 1997, 78 pp., £19.50, ISBN 0-821-80537-1The translation of the Japanese originalstarts with the basic concepts concerningfractals (dimension, Hausdorff measuresand dimension, etc.). The self-similarity isdescribed with many nice examples andrelations to nowhere-differentiable func-tions and the Takagi function are present-ed. Some problems concerning waveletsare also treated. The final chapter is con-cerned with some equations of mathemati-cal physics (Laplace�s equation, Gauss-Green formula, Poisson equation,Dirichlet problem, etc.) on sets having afractal character. The book is a goodintroduction to the topic. Interestingapplications are presented. (ss)

List of reviewers for 1999The Editor would like to thank the follow-ing for their reviews this year:J. Andì l, R. Bashir, J. Beèváø, L. Beran,L. Bican, L. Boèek, M. Brzezina, J. Bure�,M. Èadek, P. Èejnar, K. Cuda, A. Drápal,E. Fa�angová, M. Feistauer, J. Felcman,D. Hlubinka, P. Holický, J. Hurt,M. Hu�ek, J. Jelínek, O. John,J. Jureèková, T. Kepka, M. Klazar,O. Kowalski, A. Kuèera, J. Král, M. Lichá,M. Loebl, J. Luke�, J. Malý, J. Milota,J. Mlèek, K. Najzar, M. Nìmcová-Beèváøová, J. Ne�etøil, I. Netuka,S. Porubský, P. Pyrih, J. Rataj, M. Rokyta,T. Roubíèek, �. Schwabik, J. Slovák,J. Souèek, V. Souèek, J. �tìpán, J. Trlifaj,V. Trnková, J. Troják, J. Tùma, P. Valtr,J. Van�ura, J. Veselý, M. Zahradník,L. Zajíèek, J. Zichová, V. Zizler, J. �emliè-ka.

All of the above are on the staff of theCharles University, Faculty of Mathematicsand Physics, Prague, except:M. Èadek and J. Slovák (MasarykUniversity, Faculty of Natural Sciences,Brno), J. Král, �. Schwabik and J. Van�ura(Mathematical Institute, Czech Academy ofSciences), �. Porubský (TechnicalUniversity, Prague).

Editor�s note: We regret that the ProblemCorner, due for publication in this issue,has had to be held over to the March issue.

EditorialsRolf Jeltsch (EMS President) 31-3Luc Lemaire (EMS Vice-President) 32-3Andrzej Pelczar (EMS Vice-President) 33-3David Brannan (EMS Secretary) 34-3

Introducing . . .the Committee 31-5, 32-5the Editorial team 33-5, 34-7

EMS NewsExecutive Committee Meetings (Barcelonaand Zurich) 32-6, 34-83rd European Congress of Mathematics 31-7,

34-12World Mathematical Year 31-15, 34-11EMS Summer Schools: Call for proposals

32-11Fourth Diderot Mathematical Forum:Mathematics and Music 33-4Felix Klein Prize 34-10

Feature articlesJohn Fauvel: Caring for the mathematicalpast 31-10Ian Stewart: Making the magical maze 32-7

Short articlesMathematics in Eastern Europe (PeterMichor) 31.16Obituary of André Weil (Jeremy Gray) 31-22Oxford Doctorate for Andrew Wiles 33-7A Universal Mathematical Resource Locator?(Alain Damlamian) 33-12

InterviewsRobert M. Mattheij 31-13Helmut Neunzert 32-10Tim Gowers 33-8Jan van Maanen 34-16Olaus Nevanlinna 34-18Ian Frigaard 34-19

SocietiesThe Union of Bulgarian Mathematicians

31-20London Mathematical Society: De MorganHouse 31-21Finnish Mathematical Society 32-16Polish Mathematical Society 32-17Swiss Mathematical Society 33-18Edinburgh Mathematical Society 33-20Luxembourg Mathematical Society 34-26Kharkov Mathematical Society 34-26

1999 anniversariesMaria Agnesi (June Barrow-Green) 31-18Hilbert�s Grundlagen der Geometrie (JeremyGray) 31-19Felix Klein & Sophus Lie (Jeremy Gray) 32-12Wolfgang Krull (Jeremy Gray) 32-13Caspar Wessel (Bodil Branner) 33-13E. C. Titchmarsh (Robin Wilson) 33-16Laplace�s & Poincare�s Mécanique céleste(June Barrow-Green) 34-20Otto Neugebauer (Jeremy Gray) 34-22Oscar Zariski (Jeremy Gray) 34-23

Conferences Oberwolfach programme 2000 31-23Forthcoming conferences (Kathleen Quinn)

31-25, 32-23, 33-22, 34-29ICIAM in Edinburgh (Rolf Jeltsch) 33-10SIAM/EMS Joint Conference onComputational Science (Gil Strang) 33-11

Book reviewsRecent books (Ivan Netuka & VladimírSoucek) 31-31, 32-29, 33-26, 34-35Book review by Sir Michael Atiyah 32-28

EMS Newsletter Index for 1999

RECENT BOOKS

EMS December 199942

This is a new venture. We list below informa-tion about some appointments, awards anddeaths that have occurred during 1999. Sincethis list is inevitably incomplete (containingmainly UK items) we invite you to send appro-priate information from other countries to theEditor [[email protected]] or to yourCountry representative (see page 15) for inclu-sion in the next issue. Please also send items forinclusion in the 2000 Personal Columns.

Sir Michael Atiyah and Ioan James havebeen elected to Honorary Fellowships atNew College, Oxford University.

David Brannan has been re-elected Deanof Mathematics at the Open University,UK.

Terry Griggs and Mike Grannell havebeen appointed Research Fellows. BarbaraMaenhaut (Queensland), Toby O�Neil(Edinburgh), Kathleen Quinn and StevenVickers (London) have been appointedLecturers in Mathematics.

Christopher Campbell, Sarah Rees andAnvar Shukurov have been promoted toReaderships at Newcastle University, andA.M. Constantin, M.A. Dritschel andG. Sarson have been appointed to lecture-ships.

Philip Candelas (Texas) has been appoint-ed Rouse Ball Professor of Mathematics,Oxford University, succeeding RogerPenrose.

S. J. Chapman has been appointed to theChair of Mathematics and its Applications,Oxford University, from 1 July 1999.

Boris Zilber (Kemerovo) has beenappointed to the Chair of MathematicalLogic, Oxford University, from 1 October1999.

David Draper has been promoted toProfessor of Statistics at the University ofBath.

Noel Lloyd, Professor of Mathematics atthe University of Wales (Aberystwyth) hasbeen appointed Registrar and secretary ofthe University.

Terence Lyons (London) has beenappointed to the Wallis Chair ofMathematics, Oxford University, from 2April 2000, succeeding Simon Donaldson.

Roger Penrose has been appointedGresham Professor of Geometry, inLondon, succeeding Ian Stewart.

Appointments

Robin Wilson has been appointed aFellow by Special Election at KebleCollege, Oxford University.

Sir Michael Atiyah has been awarded anHonorary Doctorate at Heriot-WattUniversity, Edinburgh.

Alan Baker (Cambridge) has been award-ed an Honorary Doctorate in Strasbourg.

John Ball (Oxford) has been awarded aTheodore von Kármán Prize by the Societyfor Industrial and Applied Mathematics(SIAM).

Arrigo Bonisoli (Potenza) and MarcoBuratti (Penigia) have been awarded theHall Medal by the Institute ofCombinatorics and its Applications.

Martin Bridson (Oxford), Gero Friesecke(Oxford), Nicholas Higham (Manchester)and Imre Leader (London) have beenawarded Senior Whitehead Prizes by theLondon Mathematical Society.

David Burns (London) has been awardedthe Junior Berwick Prize by the LondonMathematical Society.

David Crighton (Cambridge) has beenawarded an Honorary Doctorate atUMIST, Manchester.

Simon Donaldson (London) has beenawarded the 1999 Polya Prize by theLondon Mathematical Society.

George A. Elliott (Copenhagen andToronto) has received the John L. SyngeAward for applied mathematics.

Ali Fröhlich (Cambridge) has been award-ed an Honorary Doctorate at theUniversity of Bristol.

Tim Gowers (Cambridge), JohnOckendon (Oxford), William Stirling(Durham) and John Toland (Bath) havebeen elected Fellows of the Royal Societyof London.

Stephen Hawking (Cambridge) hasreceived the Albert Medal from the RoyalSociety of Arts.

Anthony Hilton (Reading) has beenawarded the 1999 Euler Medal by theInstitute of Combinatorics and itsApplications for distinguished research incombinatorics.

Robert Hiorns (Oxford) has been elected

Awards

an Honorary Fellow of the Institute ofMathematics and its Applications.

Helge Kristian Jenssen (Trondheim) hasbeen awarded the Esso Young ResearcherPrize for the best NTNU (Trondheim )Ph.D. thesis.

Christine Keltel-Kreidt (Berlin) has beenawarded an Honorary Doctorate at theUniversity of Chichester.

Adam McBride (Strathclyde) received theOrder of the British Empire for services tomathematics in schools.

Sir Roger Penrose (Oxford) has beenawarded an Emeritus fellowship by theLeverhulme Trust.

Mike Powell (Cambridge) has been award-ed the Senior Whitehead Prize by theLondon Mathematical Society.

John Rognes (Oslo) has been awarded the1999 Dals Research Prize for research inK-theory.

Tomás Roubí³ek (Prague) has beenawarded the prize of the Minister ofEducation of the Czech Republic.

Caroline Series (Warwick) has been award-ed an EPSRC Senior Research Fellowship.

Jaromír �im�a (Prague) has been awardedthe Prize of the Czech Academy of Sciencesfor the popularisation of mathematics.

John Tate (Austin, Texas) has been electedan Honorary Member of the LondonMathematical Society.

Andrew Wiles has been awarded anHonorary Doctorate at Oxford University.

We regret to announce the deaths of:Ernest Albasiny (18 July)Jiøi Be³vár (25 January)Roland Clark (28 July)Sir Wilfred Cockcroft (27 September)Walter Deuber (16 July) Albert Green (12 August)Jack Howlett (5 May)Johann Leicht (14 May)Sir William McCrea (25 April)Josef Novák (20 August)Vlastimil Pták (9 May)Werner Raffke (11 May)Gian-Carlo Rota (19 April)Zbyñek Sidák (12 November)Christine Shiu (16 October)Helmut Titze (30 March)Jürgen Weishaupt (29 July)

Deaths

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