CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY

EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS STEEN MARKVORSEN Department of Mathematics Technical University of Denmark NEWSLETTER No. 42 Building 303 DK-2800 Kgs. Lyngby, Denmark December 2001 e-mail: [email protected] KRZYSZTOF CIESIELSKI Mathematics Institute EMS Agenda ...... 2 Jagiellonian University Reymonta 4 Editorial – Thomas Hintermann ...... 3 30-059 Kraków, Poland e-mail: [email protected] KATHLEEN QUINN Executive Committee Meeting – Berlin ...... 4 The Open University [address as above] e-mail: [email protected] EMS Council Elections ...... 8 SPECIALIST EDITORS INTERVIEWS Steen Markvorsen [address as above] New Members ...... 10 SOCIETIES Krzysztof Ciesielski [address as above] Anniversaries – Pierre de Fermat by Klaus Barner ...... 12 EDUCATION Tony Gardiner University of Birmingham Interview with Sergey P. Novikov ...... 17 Birmingham B15 2TT, UK e-mail: [email protected] Obituary – Jacques-Louis Lions ...... 21 MATHEMATICAL PROBLEMS Paul Jainta Werkvolkstr. 10 Ukrainian Mathematical Congress ...... 26 D-91126 Schwabach, Germany e-mail: [email protected] Forthcoming Conferences ...... 29 ANNIVERSARIES June Barrow-Green and Jeremy Gray Open University [address as above] Recent Books ...... 34 e-mail: [email protected] and [email protected] and Designed and printed by Armstrong Press Limited CONFERENCES Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK Kathleen Quinn [address as above] telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134 RECENT BOOKS Published by European Mathematical Society Ivan Netuka and Vladimir Sou³ek ISSN 1027 - 488X Mathematical Institute Charles University Sokolovská 83 The views expressed in this Newsletter are those of the authors and do not necessarily 18600 Prague, Czech Republic represent those of the EMS or the Editorial team. e-mail: [email protected] and [email protected] NOTICE FOR MATHEMATICAL SOCIETIES ADVERTISING OFFICER Labels for the next issue will be prepared during the second half of February 2002. Vivette Girault Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Laboratoire d’Analyse Numérique Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: Boite Courrier 187, Université Pierre [email protected] et Marie Curie, 4 Place Jussieu 75252 Paris Cedex 05, France INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, e-mail: [email protected] Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e- OPEN UNIVERSITY mail: ([email protected]). Please include the name and full address (with postal code), PRODUCTION TEAM telephone and fax number (with country code) and e-mail address. The annual subscription fee Liz Scarna, Kathleen Quinn (including mailing) is 65 euros; an invoice will be sent with a sample copy of the Newsletter.

EMS December 2001 1 EMS NEWS EMS Committee EMS Agenda EXECUTIVE COMMITTEE PRESIDENT (1999–2002) 2002 Prof. ROLF JELTSCH 9-10 February Seminar for Applied Mathematics EMS Executive Committee Meeting in Brussels (Belgium), at the invitation ETH, CH-8092 Zürich, Switzerland e-mail: [email protected] of the Belgian Mathematical Society and the Université Libre de Bruxelles VICE-PRESIDENTS Prof. LUC LEMAIRE (1999–2002) 15 February Department of Mathematics Université Libre de Bruxelles Deadline for submission of material for the March issue of the EMS C.P. 218 – Campus Plaine Newsletter Bld du Triomphe Contact: Robin Wilson, e-mail: [email protected] B-1050 Bruxelles, Belgium e-mail: [email protected] Prof. BODIL BRANNER (2001–2004) 24-28 February Department of Mathematics Technical University of Denmark EMS Summer School in Eilat (Israel) Building 303 Title: Algebraic Geometry, Computations and Applications DK-2800 Kgs. Lyngby, Denmark Contact: Mina Teicher, e-mail: [email protected] e-mail: [email protected] SECRETARY (1999–2002) Prof. DAVID BRANNAN 1 March Department of Pure Mathematics Deadline for Proposals for 2003 EMS Lectures The Open University Walton Hall Contact: David Brannan, e-mail: [email protected] Milton Keynes MK7 6AA, UK e-mail: [email protected] TREASURER (1999–2002) 15 May Prof. OLLI MARTIO Deadline for submission of material for the June issue of the EMS Newsletter Department of Mathematics Contact: Robin Wilson, e-mail: [email protected] P.O. Box 4 FIN-00014 University of Helsinki Finland 19-31 May e-mail: [email protected] EMS Summer School in Craiova (Romania) ORDINARY MEMBERS Prof. VICTOR BUCHSTABER (2001–2004) Title: Mathematical and numerical methods in computational quantum chemistry Department of Mathematics and Mechanics Contact: Yvon Maday, e-mail: [email protected] Moscow State University 119899 Moscow, Russia e-mail: [email protected] 31 May Prof. DOINA CIORANESCU (1999–2002) Executive Committee meeting in Oslo (Norway) Laboratoire d’Analyse Numérique Université Paris VI 4 Place Jussieu 1-2 June 75252 Paris Cedex 05, France EMS Council Meeting, Oslo e-mail: [email protected] Prof. RENZO PICCININI (1999–2002) Dipartimento di Matematica e Applicazioni 3-8 June Università di Milano-Bicocca Via Bicocca degli Arcimboldi, 8 Abel Bicentennial Conference, Oslo 20126 Milano, Italy e-mail: [email protected] 28-29 September Prof. MARTA SANZ-SOLÉ (1997–2000) Facultat de Matematiques Executive Committee meeting in Stockholm (Sweden) Universitat de Barcelona Gran Via 585 E-08007 Barcelona, Spain 2003 e-mail: [email protected] 10-13 February Prof. MINA TEICHER (2001–2004) EMS-SMAI-SMF Meeting in Nice (France) Department of Mathematics and Computer Science Title: Mathématiques Appliquées - Applications des Mathématiques (Applied Bar-Ilan University Mathematics - Applications of Mathematics) Ramat-Gan 52900, Israel Contacts: Doina Cioranescu and Mireille Martin-Deschamps, e-mail: [email protected] EMS SECRETARIAT e-mail: [email protected] and [email protected] Ms. T. MÄKELÄINEN Department of Mathematics P.O. Box 4 2004 FIN-00014 University of Helsinki 25-27 June Finland EMS Council Meeting, Stockholm (Sweden) tel: (+358)-9-1912-2883 fax: (+358)-9-1912-3213 telex: 124690 27 June - 2 July e-mail: [email protected] 4th European Congress of Mathematics, Stockholm website: http://www.emis.de 2 EMS December 2001 EDITORIAL house, the EMS continues to offer a large and well-maintained collection of non- commercial journals and books on EMIS, EditorialEditorial the European Mathematics Information Service (www.emis.de). Thomas Hintermann Dr. Thomas Hintermann is at the Department of (Publishing Director, EMS Publishing Division) Applied Mathematics, ETH-Zentrum FLI C1, CH- 8092 Zürich, Switzerland; e-mail: [email protected] The idea for the EMS to engage in pub- the best option for long-term sustainabili- tel:+41 1 632 34 36, fax +41 1 632 11 04 lishing activities is probably almost as old ty. In other words, our publications will as the society itself. It resulted, most not be free, but available at the minimal notably, in the creation in 1999 of JEMS, the Journal of the European Mathematical The Citation Checker and Society, currently published on behalf of the EMS by Springer-Verlag, now a member of Cross Reference Link the Bertelsmann Springer group. Just Generator offered by about the same time, the first serious plans emerged to run a commercially operating Zentralblatt MATH publishing house. Among the available Bernd Wegner options, including taking over an indepen- dent publisher or combining the efforts of For quite a long time Zentralblatt member society publishers, the EMS even- MATH has offered the facility for tually decided to launch their own enter- exporting BIBTEX-files to users’ prise. Although this possibility had machines from the hit list obtained by already been hinted at in the EMS retrieving information from the Newsletter, the intention was first communi- Zentralblatt MATH database. This has cated to a large audience by the EMS turned out to be a useful tool for President, Rolf Jeltsch, during his speech authors preparing a list of references at the closing ceremony of the ECM in for their articles. Responding to fre- Barcelona in July 2000. In the interim, quent demand, Zentralblatt MATH now much energy has been spent on the legal provides an additional new service, in aspects of the undertaking, hopefully cul- order to allow you to check your arti- minating in the registration of the cle literature references conveniently European Mathematical Foundation, the and quickly, and to provide persistent governing body of the EMS publishing Thomas Hintermann links to individual Zentralblatt MATH house, with the Swiss chamber of com- database items. This tool is freely merce in late 2001. price possible under market conditions. available and will be soon extended to An increasing proportion of the mathe- Everything spent on them will be fully the Jahrbuch database. matical community is dissatisfied with the reinvested in the publishing house. With The search menu for the citation mathematical publishing industry. Above the purchase of a book or the subscription checker is available under the URL all, it is the pricing policy of some large of a journal you will support an endeavour http://www.emis.de/ZMATH/x-ref.html. and important commercial publishers that that has your interests in mind. No pay- Users will be requested to enter infor- is under debate, and there is a general feel- ments are made to shareholders, and any mation on the citation item in four ing that they hinder the dissemination of profits have to be used on aims set down in fields: last name of (first) author, sig- mathematical knowledge rather than fos- the statutes of the Foundation. nificant word in the title, volume num- ter it. Be that as it may, there is certainly We expect that the first publications of ber, first page. This will be sufficient no denying that at present the order of the the EMS to appear under their own name in nearly all cases to pinpoint the sin- day in every company is to meet short-term will be published at the beginning of 2004, gle item looked for – in particular, (short-sighted?) targets, most often at the possibly earlier. We intend to publish first- when all four fields are used. In the expense of everything else. Financial con- quality peer-reviewed journals, and books rather unlikely case that more than siderations are clearly given first priority, on all academic levels and from all fields of three items match the search criteria, and editorial matters and publishing mathematics, emphatically including the most recent three items are dis- aspects rank second. One of the aims of applied mathematics. Proposals are wel- played. If the requested item does not the EMS publishing house is to reverse that come and should be submitted to the belong to them, then the standard order. The needs of the community are address below. We appeal to all mathe- retrieval forms for Zentralblatt MATH foremost in our minds, admittedly with the maticians to support our effort by publish- may provide further help for those obligation to run an economically sound ing with us, and by endorsing the subscrip- who have a subscription to this service. operation. tion of our journals and the purchase of The search result will offer precise I do not share the view that scientific our books by the library of your home standardised bibliographic data, to be information should be entirely free. To institution. We promise to pay back your exported by the user into his own ref- quote John Ewing of the American confidence with the best possible service erencing system. The addition of the Mathematical Society, nothing is for free and quality. Zentralblatt MATH annotation number and the question is only who is paying. Although the EMF is legally a separate will add a unique identifier for the The collecting, editing and publishing of structure from the EMS, the statutes and article, which will be suitable as a per- scientific content will always entail labour by-laws of the foundation ensure the deci- sistent link to the electronic offer of that belongs in the hands of professionals, sive influence of the EMS, through the par- this publication and may serve as a rather than of scientists who should be able ticipation of committee members in the tool for reference linking going to a to devote themselves to research and board of trustees. Moreover, the editorial wider range than provided by DOI, for teaching. Such a sharing of responsibilities boards of our journals and book series will example. is effective and in the interest of us all. consist of mathematicians approved by, Bernd Wegner, TU Berlin, Fakultät II, Rather than depending on external fund- and sympathetic with, the aims of the EMS. Institut für Mathematik, 10623 Berlin, ing, on volunteers, and on direct or indi- You will be informed on the progress of Germany; e-mail: [email protected] rect support from University institutions, our plans in the EMS Newsletter. Apart berlin.de we believe that financial independence is from the creation of its own publishing EMS December 2001 3 EMS NEWS Services) project revealed that good progress had been achieved so far, and a first release of new software would come ExecutiveExecutive CommitteeCommittee MeetingMeeting out soon. A final report was received on the Berlin, 1-2 September 2001 Reference Levels for 16-year-olds project; the objective has been to identify some com- mon standards for levels of understanding Present: Rolf Jeltsch (President, in the costs of the Newsletter were quite high of mathematics across European countries Chair), David Brannan, Bodil Branner, because of the strength of sterling against at the particular age of 16. A short con- Victor Buchstaber, Doina Cioranescu, Luc the euro. ference on the project outcome had been Lemaire, Olli Martio, Renzo Piccinini, A list of new individual EMS members held in Luxembourg, and it was planned Marta Sanz-Sole and Mina Teicher; (by (see later in this Newsletter) was approved. to hold a briefing in Brussels for EU invitation) Carles Casacuberta, Tuulikki Commission staff. There was a lengthy Makelainen, David Salinger and Bernd Projects discussion of a possible similar project for Wegner; (by invitation to part of the meet- A report was received on the May meeting 18-year-olds. ing) Peter Deuflhard, Tony Gardiner, of the Zentralblatt für Mathematik Thomas Hintermann, Ari Laptev, Consultative Committee in the headquarters EMF/EMS Publishing House Christian Mehl and Rudolf Straesser. of FIZ-Karlsruhe. The financial situation The first meeting of the Board of Trustees The President thanked Bernd Wegner of Zentralblatt was improving. Bernd of the EMF (European Mathematical and Barbara Strazzabosco for the efficient Wegner was praised for his work for Foundation) had been held in Zürich in and pleasant local arrangements. Zentralblatt, particularly in relation to the July, and a report of its discussions was consortia arrangements. The pricing for received by the Committee. The EMF is a Officers’ Reports Zentralblatt for the year 2002 had now been not-for-profit trust that is the legal entity The President sent a personal card of con- agreed: there will be a slight increase in responsible for the work of the new dolences to the family of J.-L. Lions. A prices, with no lower price for the printed EMSph (European Mathematical Society conference dedicated to J.-L. Lions will be version only. It was noted that the Publishing House). Its Chair is Rolf Jeltsch, held at Collège de France, Paris, in July German government gives financial sup- with Olli Martio as Treasurer, David 2002. An Abel Prize has been established, with an endowment fund of 200,000,000 NOK, the annual yield covering the prize of 300,000 annually. A bid from the Swiss Mathematical Society to hold ICIAM 2007 in Zürich was successful. Rolf Jeltsch will be the local organiser, and the EMS will be actively involved. Colette Laborde has been appointed to the Education Committee, Chris Budd to the RPA (Raising the Public Awareness of Mathematics) Committee, and Kouli Kyriaki to the Committee on Women and Mathematics. The Euler International Mathematical Institute has been accepted as a member of ERCOM (European Research Centres in the Mathematical Sciences). There was a brief discussion of the new proposal for the 6th Framework Programme of the European Union, which will be voted on in 2002. Networks and Euroconferences are included as fundable; it might also be possible to support activi- ties in EU-Associated States (these do not include Russia) in this way. It was felt that the EMS might set up a small office in Brussels to coordinate its EU-related activ- ities. 35 people had attended an EMS Brainstorming Weekend on Applied Mathematics in Berlingen on 4-6 May 2001. Rolf Jeltsch proposed a meeting to be held in Berlingen in Spring 2002 to discuss publishing, meetings, EU funding for mathematics conferences and integrated initiatives. It was thought that societies tended to send high-quality people with port to Zentralblatt and that more interna- Brannan as Secretary and Eduard Zehnder real commitment to such meetings. tional financial help should be sought in (ETH) as the other trustee. The by-laws Several representatives of the EC would the future. The ownership of the and tax status of the EMF were discussed also attend. Zentralblatt title is shared between the at the Board meeting. The Treasurer reported that the Society’s EMS, FIZ, Springer and the Heidelberg EMF has appointed Thomas finances were under control. Expenditure Academy of Science Hintermann (formerly with Birkhäuser- in 2000 has been higher than average, due A report on the LIMES (Large Verlag, and with 12 years’ experience of to the Council meeting in Barcelona. The Infrastructure in Mathematics - Enhanced publishing mathematics) as the launch 4 EMS December 2001 EMS NEWS Managing Director of EMSph, and he took these journals, such a possibility will be Berlin, the latter represented by Bernd up his post on 1 September. In a wide- arranged on a separate server providing Wegner. ranging briefing to the Executive access control facilities; no charging will JSTOR offers more than 120 retro-digi- Committee, Thomas Hintermann noted take place on EMIS itself. tised journals in science. Between 10 and that the rationale for the EMSph had been Electronic content with charged access 20 of them offer a lot of mathematical con- the widespread dissatisfaction of mathe- will be made freely accessible in ElibM, tent. [JSTOR = Journal Storage. The maticians with the work and prices of after some period to be decided by each Scholarly Journal Archive: see many commercial publishers. In addition, individual dual journal. During the http://www.jstor.org or http://www.jstor.ac.uk]. a regular income from publishing would charged period, ElibM will provide free EMANI (Electronic Mathematics Archiving help to give the EMS financial stability. access to bibliographic data and abstracts. Initiative) is a cooperation between pub- His view was that there would always be a Distribution of the metadata to the mirrors lishers, editors and libraries, with the goal need for publishers, as it is not a good use will happen immediately after availability. of caring about the long-term archiving of mathematicians’ own time to divert it The papers themselves will be given to the and availability of electronic content in into such technical and time-consuming mirrors as soon as they are freely available. mathematics. The main contributors from matters. In relation to the archiving of electronic the publishers’ side are Birkhäuser and There was some daiscussion of the wide content, the authenticity of electronic ver- Springer-Verlag, but publications in ElibM range of models for collaboration that the sions of papers will be an important issue. may also take part in this initiative. A start EMSph might follow, depending on indi- The CEIC (Committee on Electronic on the archiving will be made by the vidual negotiations with each proposed Information and Communication) had Tsinghua University Library, the SUB partner. The EMSph would be active in been requested to develop a general rec- Göttingen and the Cornell University ommendation in the direction of fixing a Library. date after which a paper could not be fur- The Mathematical Heritage proposal ther altered without its becoming a sepa- rate publication. In future, PDF files will be requested as common standard for ElibM, to provide easier readability of the files. As a conse- quence of the large number of journals in ElibM, access facilities to the content need to be improved, giving an alternative to just clicking through contents. This will require more standardised delivery of metadata. Linking references with electronic or retro-digitised versions is an important quality issue for electronic publications. Carles Casaculberta The journals in ElibM are likely to move to such an enhancement, and electronic doc- publishing journals, individual books and ument identifiers will be needed for this. series of books. The DOI used by commercial publishers Marta Sanz-Solé for current electronic publications is a rel- EMIS atively expensive solution [DOI = Digital encourages mathematicians to make all There was a discussion led by Christian Object Identifier, see http://www.doi.org]; it their research papers available on the web. Mehl and Volker Mehrmann on the pre- will be possible to use the ZBL-annotation Martin Grötschel and Peter Michor both sent status of the left-hand side of EMIS. numbers for this. There is an initiative to have proposals in this direction. Arrangements were to be set up for ensur- produce a matching list between ZBL and There will be a satellite conference of ing that changes in the EMS committee MR annotations; for older items, the ICM 2002 on Electronic Information and memberships should appear on EMIS. Jahrbuch identifiers may be used. ZBL and Communication in Mathematics at Tsinghua The idea of setting up some sort of job the AMS have agreed to create a matching University in Beijing; the organisers will information site on EMIS had proved an list of identifiers for papers; this will be be Fengshan Bai and Bernd Wegner. impossible task; it was thought that an e- cheaper than DOI. ElibM and other projects in EMIS will be letter (weekly or monthly) could be a bet- EMIS has mirrors at SUB Göttingen and included among the subjects presented ter method for disseminating information, the Cornell University Library; they were there. Details of the conference can be and that this could be discussed at installed for looking after later archiving found on the ICM home page. Berlingen. Volker Mehrmann and of articles and books in EMIS. With more Christian Mehl were thanked warmly for than five years of electronic volumes avail- EMS Committees their work on EMIS. able for most journals in ELibM, archiving A new Chairman for the Committee on needs to be established in a more system- Developing Countries is being sought. It was ElibM atic way. This fits into a new initiative thought that the Committee might decide Three journals had been made available called EMANI (Electronic Mathematics to look afresh at its terms of reference. recently on ElibM: Advances in Geometry (de Archiving Initiative), where SUB The composition of the Committee for the Gruyter), CMAM (Byelorussia) and AMEN Göttingen and the Cornell University Support for Eastern and Central European (Taiwan). The installation of Annals of Library are partners, in which the TeX- Mathematicians was agreed as follows: Mathematics was in hand, due to the efforts source codes and the PDF files are the Andrzej Pelczar (Chair), Victor of Larry Siebenmann. The same privi- basis for archiving. This cooperation Buchstaber, Martin Fuchs, Michel leges were given as for the arXiv. There between libraries and journals will have to Hazewinkel, George Jaiani, Laszlo Marki, would be no longer be a five years’ delay. be established in every single case, journal Olli Martio and V.V. Sharko. The first years’ issues of JEMS would short- by journal, establishing a series of con- The topic of the Special Events ly be made freely accessible on EMIS. tracts. Committee’s Fifth Diderot Mathematical As announced previously, new develop- Retro-digitising will improve the avail- Forum (5DMF) on 22-23 November 2001, ments in the publication of commercial ability of electronic offers in mathematics. was to be Mathematics and mathematical journals and the dominating Most dual journals in ELibM have such Telecommunications, with special emphasis role of electronic versions may force the extended offers already, thanks to partici- on cellular phones. The cities and institu- dual journals in EMIS to charge for access pation in the ERAM-project. These activi- tions involved would be: Philips Research to the current electronic publications. For ties are guided by SUB Göttingen and TU (Eindhoven, Netherlands), Helsinki EMS December 2001 5 EMS NEWS University of Technology (Finland) and application to UNESCO-Roste was still 6.The EMS should further develop its École Polytechnique Federale de pending. Summer School Programme, and should Lausanne (Switzerland). The format The EAGER-ENI-EMS Summer School on continue to include topics in both pure would be as usual, with two days of meet- Computational Algebraic Geometry and and applied mathematics. ings (their length will depend on the site) Applications will be held in Eilat (Israel) on 7.The EMS should work towards the goals and three one-hour lectures (including 24-28 February 2002. The school includes that questions) shared between all three sites. an introduction on how to use computer (a) students majoring in mathematics The lectures would be given by Joachim algebra systems such as SINGULAR and should be exposed to applications of Hagenauer (Technical University, MACAULAY2 and packages such as mathematics in the sciences or in Munich) in Eindhoven, Yrjo Neuvo SCHUBERT (intersection theory) for other areas; (Nokia) in Helsinki, and Jacob Ziv research in algebraic geometry and its (b) high-school teachers should have (Technion Haifa) in Lausanne. applications. The programme consists of adequate education in applied math- Two other events, which could lead to lectures and practical exercise sessions in ematics and mathematical model- front of a computer. (EAGER is the ling. European Algebraic Geometry Education 8.The EMS should formulate a position and Research, and ENI is the Emmy with regard to the Bologna declaration Noether Research Institute for of 1999. Mathematics at Bar-Ilan University and 9.The EMS should continue to raise pub- the Minerva Foundation.) lic awareness of mathematics; the EMS The EMS Summer School on Computational should promote local initiatives, encour- Aspects of Fluid Mechanics will be held on 8- age collaboration with various organisa- 19 July 2002, in Brasov (Romania). tions, and collect and disseminate infor- Plans for Summer Schools in 2003-5 mation on initiatives of member soci- were also considered, as was the possibility eties in this area. of applying to the EU for funding for the The declaration was accepted as a positive 2003 summer schools. statement, which the EC will endeavour to The 2002 EMS Lecturer will be Professor follow, looking at practical methods of Tony Gardiner Gianni Dal Maso of the International implementation. The Berlingen School for Advanced Studies (SISSA) in Declaration will be an item on the agenda ‘special events’ that the EMS might take up Trieste (Italy). of the 2002 Council meeting. It was also as opportunities to celebrate the impact of It was agreed to add Antoine Bodin agreed that the President should ask the mathematics, are connected with the birth (Besançon) and Philippe Tilleuil (CREM) Applied Mathematics Committee to centenaries of John von Neumann (in to the membership of the EMS Education encourage nomination of a reasonable 2002) and A.N. Kolmogorov (in 2003). Committee. number of applied mathematicians as The Special Events Committee was Michele Emmer was added to the mem- Council delegates. encouraged to proceed with investigating bership of the Committee for Raising Public these projects. Awareness of Mathematics. Relations with Mathematical Saul Abarbanel (Israel) was elected to The Executive Committee decided to set Institutions/Organisations chair the Committee for Applied Mathematics up a General Meetings Committee, with Luc Peter Deuflhard reported that about 500 for 2002-5; his subject area is numerical Lemaire in the Chair (EU); the other participants (including 42 speakers) had hyperbolic PDEs. It was felt essential that members would be Renzo Piccinini (sum- all strands of applied mathematics should mer schools), Rolf Jeltsch, Jean-Pierre be represented in this EMS committee, Bourguignon (DMF), Ana Bela Cruzeiro that corporate members should be consult- (SPM), Michael Sorensen (Bernoulli ed on its membership, that no member Society) and Mina Teicher (EMS Executive had a right to specify a member of the Committee). Among other ideas, the committee, and that there should always committee should discuss EU 6th be adequate representation of applied Framework Programme funding for EMS mathematics and of this committee on the meetings, and the possibility that the EMS EC. hold regional meetings with member soci- It was agreed that the EMS Summer eties. Schools Committee should write guidelines for potential organisers of EMS summer Berlingen Declaration schools. These should indicate that there Sebastia Xambo had written an interesting are a limited number of speakers, that the report on the Berlingen meeting for the duration is at most 2 weeks, that it can be June EMS Newsletter. In short, the decla- for new postgraduates as well as for post- ration is as follows: doctoral mathematicians, and it should 1.The presence of applied mathematics in Peter Deuflhard outline the differences between a confer- EMS bodies and policy decision making ence and a summer school. should be significantly increased. registered for the Berlin EMS-SIAM confer- The St Petersburg Summer School, 9-22 2.The EMS Applied Mathematics ence in September 2001. The meeting con- July 2001, had been devoted to mathemat- Committee must be kept an active body sisted of 10 invited lectures, 151 talks, 37 ics and mathematical physics. The num- for the time being. Its mission statement mini-symposia and one Round Table, as ber of participants had been 78, and the should be adapted to the new role of the well as posters. Benoit Mandelbrot would school was considered a success. Financial committee. Its Chair should be invited give a lecture by TV from the USA. support had been received from the EMS, to the Executive Committee meetings. Funding had been received from the EU, UNESCO, NATO and the Russian 3.Pure and applied mathematics should the German Science Fund and the EMS, Foundation for Basic Research. Its be equitably represented in the publica- and an application to UNESCO was still Proceedings will be published by Kluwer tions of the EMS. pending; the sponsors of the meeting also and Springer. 4.Special interest groups should be creat- included Springer-Verlag. The moderator The Prague Summer School had 88 partic- ed gradually inside EMS. for the Round Table on Applied ipants. Financing had been obtained from 5.The EMS should consider increasing its Mathematics would be Martin Grötschel. the Czech Republic, ESF, AMIF, the activities by collaborating with interna- There was an interesting discussion on the International Visegrad Fund, and a guar- tional, national and regional societies in possibility of future joint meetings with antee of 2000 euro from the EMS; an organising meetings. SIAM and other bodies. 6 EMS December 2001 EMS NEWS Olli Martio had been elected as an EMS agreed to hold an Executive Committee mercial annual subscription price to representative on the Board of the Banach meeting in Stockholm in September 2002. libraries and departments of the Newsletter Centre for the Mathematical Sciences for 2001- European Congress of Mathematicians in of 60 euro to 65 euro in 2002. Discussions 4. It was agreed to re-elect Marta Sanz- 2008: Information for Possible Applicants would be held shortly in relation to review- Sole to a second term (2002-5) and to elect A call for outline bids for the 5ECM will be ing the prices of inserted material in the Rolf Jeltsch to a first term on the Board published on EMIS and in the EMS Newsletter mailings. (2002-5). Newsletter, with a deadline of 31 December The Publications Officer, Carles It was agreed that the EMS should 2002; if there are at least two bids, fuller Casacuberta, tabled the list of EMS books in become a member of CIMPA (Centre bids will be requested by 30 June 2003. In the Springer series: International de Mathématiques Pures et the summer of 2003 a site committee will be • N. J. Cutland: Loeb Measures in Practice: Appliquées). formed, to be followed by a recommenda- Recent Advances, Lecture Notes in Math. tion to the Executive Committee in the 1751 (EMS Sub-series), Springer-Verlag, Stockholm European Congress of autumn of 2003. The EMS Council will Berlin-Heidelberg, 2000 (1997 EMS Mathematicians (4ECM) in 2004 make the final decision in 2004, immediate- Lectures) The dates for the Congress will be 27 June ly before the 4ECM. • Diaz (ed.): Mathematics and Environment - 2 July 2004. A Letter of Understanding (2nd Diderot Mathematical Forum, 1997) between the Organising Committee and Membership matters plus a substantial list ‘in preparation’. It was agreed to recommend to Council the raising of class of the Israel Mathematical Future meetings of the Executive Union from Class 2 to Class 3. Committee The following indicative dates and locations Society elections in 2002 for future meetings were agreed: The Executive Committee discussed possi- • Spring 2002 in Brussels (Belgium), on 9- ble names for its nomination for officer 10 February; posts and Executive Committee member- • Summer 2002 in Oslo (Norway), on 31 ship for the period 2003-6. May 2002 (before the Council meeting); • Autumn 2002 in Stockholm (Sweden). EMS budgetary matters It was agreed to propose to Council in 2002 David A. Brannan that the corporate fee be raised from 340 to 360 euro.

Renzo Piccinni Changes to the EMS Statutes and By-laws Work had continued on possible changes to the EMS was agreed, subject to minor the Statutes and By-laws, to clarify and A common modifications. improve their operation. The Executive The composition of the Organising Committee discussed a draft, and agreed to Committee of the 4ECM was agreed as: Ari look again at a revised draft in February sense tip Laptev (President), Anders Lindquist, 2002. It was agreed to propose to Council From time to time, active mathemati- Christer Kiselman, Torsten Ekedahl, that academic institutions as institutional cians receive invitations to submit Mikael Passare, Ulf Persson and Kjell-Ove members should have a new fee category of papers to research journals or confer- Widman. A preliminary list of members of x (Rule 25), and that other institutional ences, to have their name included as the Scientific Committee was also discussed; members should continue to pay an annual a member of a journal editorial Lennart Carleson (Stockholm) will chair fee of 3x. board, to speak at a conference, to the committee, and the deputy chair will participate in a conference, to have be Bjorn Engquist. Bologna Declaration their name included as a member of The Executive Committee discussed Very little response had followed from the the organising committee of a confer- possible names to chair the Prize Committee. editorial on the Bologna declaration in the ence, and so on. Sometimes these It was suggested that at least one member June Newsletter or from member societies. invitations include a request for pay- of the EMS Executive Committee should This surprised the Executive Committee! ment of some sort (e.g. conference serve on the Prize Committee, to avoid fees, page charges, or whatever). problems developing. Nominations for Publications prize-winners from the mathematical com- The subscription price for the Journal of the The vast majority of such invitations munity would be sought. The point was EMS (JEMS) had remained constant until are of course entirely genuine and made that nominees should not benefit now, and needed to be reviewed. The welcome to the recipient! However, a from multiple nominations, in order to Executive Committee accepted 210 euro as small minority of such invitations avoid influence from pressure groups; the a basic price for the 2002 subscription to represent money-making schemes of only criterion that mattered should be the JEMS. The Publications Officer agreed to a type that might not be immediately merit of the proposed person. Work was check with Springer on any additional sub- obvious to the recipients, and that continuing on the guidelines for the Prize scriptions via the LINK scheme; and to urge might not be at all welcome to them if Committee; the 2002 meeting of the EMS Springer to include a credit card payment they understood what was going on. Council will decide on the final guidelines. option on its subscription renewal form. The internet is often used for such It was however agreed that the age limit The distribution of the EMS Newsletter is invitations, just as it is for a number for prize-winners should be 34 years, plus around 2500 copies of each issue. The of other doubtful financial schemes. a further 3 years in the case of a broken Executive Committee discussed the level of career. revenue from advertising in the Newsletter. If you receive an invitation to be A preliminary budget for the 4ECM was The Society’s General Purposes Committee involved in a journal or conference discussed; this incorporated a reduced fee had agreed to increase the Newsletter’s whose organiser’s reputability you do for early registration and a significant advertising rates from 1 January 2002 by not already know, it is wise to check reduction for EMS individual members. It around 6% over the figures that applied out the integrity of what is proposed was agreed to approach UNESCO and from 1999 to 2001, and to encourage more before agreeing to let your name be member societies of the EMS for funds to job advertisements in the Newsletter, as the used and before sending any money. support participation by Eastern cost to advertisers of around £100 is very European mathematicians. cheap. The General Purposes Committee David A. Brannan In the run-up to the 4ECM, it was had also agreed to increase the 2001 com- EMS December 2001 7 EMS NEWS ed about 25 books in these subjects, as well as a substantial number of research and expository papers. I am a great believer in the propagation and popularisation of EMSEMS CouncilCouncil electionselections mathematics, and try to achieve this through my books and in the 30-40 popu- lar lectures I give each year to various audi- ences. The following nominations for the EMS the current era of a united Europe, scien- Over the past three years, I have been Council were received by the deadline, 15 tific funding increasingly depends on the heavily involved with the activities of the November. As there were fewer nominations decisions of a supranational bureaucracy European Mathematical Society, as Editor- than vacancies, the following four persons have that is not easily accessible via national in-Chief of the EMS Newsletter, as a fre- been elected delegates of individual members for societies. quent attender of Executive Committee the years 2002-05. Maintaining and enlarging support for meetings, and as an invited speaker at the mathematics within Europe requires vigor- fourth Diderot mathematical forum. Marina Marchisio Torino (Italy), e-mail: ous lobbying efforts on the part of a body Statement: For the past three years I have [email protected] that can speak clearly and forcefully for the been Editor-in-Chief of the EMS Newsletter, Proposer: Alberto Conte; seconder: Giuseppe European mathematical community as a a role I hope to continue for some time to Anichini whole. The only credible candidate for come. I am running for the EMS Council Biography: I was born in Boves (Italy) on this important role is the EMS. It already because I wish to become more closely 20/12/1969. I studied at the University of proved its leadership, which I would like to involved with the activities of the Society, Torino, where I got my Doctorate in see broadened and strengthened. and because I believe that my knowledge Mathematics in March 1999 for a Thesis On the world level, I see the EMS as pro- of recent EMS events, acquired through on Unirational quartic hypersurfaces, under viding a useful and healthy balance to working on the Newsletter, could be of value the scientific supervision of Alberto Conte. other groups within the International to the Council. Since July 1999 I have been a Researcher Mathematical Union which can serve to (Ricercatore) in the Faculty of Sciences of further the interests of European mathe- Sebastià Xambó-Descamps, Barcelona the University of Torino. My research matics and mathematicians within that (Spain); e-mail: [email protected] field is algebraic geometry – in particular, body. rationality problems for higher-dimen- Finally, as a professional society, the sional algebraic varieties. Since 1996 I EMS must continue and expand its activi- have been acting as editorial secretary of ties in organising European Math. the Bollettino dell’Unione Matematica Congresses, in support of joint European Italiana. I have been a member of the mathematical conferences, scientific Council of the European Mathematical exchange, and the easy movement of Society for 1998-2001 as a representative mathematicians between the countries of of individual members. Europe. Statement: If I am re-elected, I shall contin- ue my action of the previous four years in Robin Wilson, Milton Keynes (UK), e-mail: favour of European Young Researchers, in [email protected] order to get more jobs for them in the uni- versities and research institutions.

Vitali Milman, Tel Aviv (Israel); e-mail: [email protected] Proposer: Dan Haran; seconder: Zeev Rudnick. Biography: Professor at Tel-Aviv University, 1973-. Incumbent, Argentinia Chair in Mathematics, Tel-Aviv University. Born: 1939. Education: Ph.D. 1965, Institute for Proposer: Manuel Castellet; seconder: Carles Low Temperature Physics, Kharkov; D.Sc. Casacuberta 1970, Institute for Low Temperature Biography: Full Professor of Information Physics, Kharkov. Fields of specialisation: and Coding Theories at the Technological Functional analysis; convexity; asymptotic University of Catalonia (Universitat geometric analysis. Publications: over 130 Politècnica de Catalunya) since 1993, and papers and 11 edited books. Invited Vice-Rector of Information and addresses: ICM1986, Berkeley (analysis sec- Documentation Systems April 1998-March tion); ICM1998, Berlin (analysis section); 2002. ECM1996, Budapest (plenary address); My main research interests at present are and over 150 colloquia and seminar lec- in the applications of algebraic geometry tures at major universities and talks at to fields such as enumerative geometry, international conferences. Editor of GAFA Proposer: David Brannan; seconder: Barbara error-correcting codes, computational (Geometric Analysis and Functional Analysis); Maenhaut. mathematics and mathematical physics. member of Editorial Board of Israel J. Biography: I am a senior lecturer in the Recently I coordinated the development of Math. President, Israel Math. Union pure mathematics department of the Open WIRIS (TM), a multilingual, web-accessible (2000-); Member, Board of Governors of University, UK, as well as being a Fellow of system, to cover a wide range of computa- Tel Aviv University (2001-); Member, Keble College, Oxford University. I am tional mathematics needs (which has been Board of Directors, Weizmann Scientific currently Visiting Professor in the History installed by the Catalan Ministry of Press of Israel (1983-92); Member, Board of Mathematics at Gresham College, Education to meet the computational of Directors, Institute of Industrial London, and have also held a number of needs of students and teachers of primary Mathematics, Beer Sheva (1992-95). visiting appointments in the USA. and secondary schools and includes facili- Statement: I view the EMS as potentially the My two main research areas are in graph ties for the production of digital teaching most important body representing and theory/combinatorics and the history of and learning materials). lobbying for mathematics in Europe. In mathematics, and I have written and edit- Born in 1945, married with two 8 EMS December 2001 EMS NEWS daughters, and first lecturer in the Andrzej Pelczar (2000-03), Institute of F-75252 Paris Cedex 05, France University of Barcelona since 1969, I spent Mathematics, Jagiellonian University, Robin Wilson (2002-05), Department of the terms 1977-78 and 1978-79 at the Reymonta 4, PL-30-059 Kraków, Poland Pure Mathematics, The Open University, University of Brandeis (Massachussetts, Zéev Rudnick (2000-03), School of Milton Keynes MK7 6AA, United Kingdom USA), where I learned algebraic geometry Mathematical Sciences, Tel Aviv Sebastià Xambó-Descamps (2002-05), from Teruishi Matsusaka, David Eisenbud University, Ramat Aviv 69978, Israel Department of Mathematics Apl. II, and Michael Harris. After receiving a Gérard Tronel (2000-03), Labo d’Analyse Technical University of Catalonia, ES- Master of Arts in Mathematics in 1978, I Numer., Univ. P. et M. Curie, 4 pl. Jussieu, 08028 Barcelona, Spain obtained my PhD in Barcelona in 1991. I was associate professor of geometry and topology in the University of Barcelona 1982-89 and full professor of algebra in Computational the Universidad Complutense of Madrid 1989-93. Statement: President of the Catalan Mathematical Society, of the Institute of Catalan Studies, since February 1995 (and Algebraic Geometry leaving office not later than December 2002); I was the president of the Executive and Organising Committees of the 3rd European Congress of Mathematics in Barcelona, 10-14 July 2000. My motivation and Applications for such undertakings as these, stems from the desire to contribute in as an effective way as possible to the development of a really comprehensive European space for mathematics where everybody can deliver the best of themselves. EAGER - ENI - EMS The full list of delegates of individual mem- bers for 2002-03 is as follows: Summer School, Giuseppe Anichini (1996-99-03), Dipto di Matematica Appl., G. Sansone, Via S. Marta 3, I-50139 Firenze, Italy Eilat, Israel Vasile Berinde (2000-03), Department of Mathematics, Univ. of Baia Mare, Victoriei 76, RO-4800 Baia Mare, Romania 24th-28th February 2002 Giorgio Bolondi (1996-99-03), Dipartimento di Matematica-Politecnico, The SUMMER SCHOOL is an introduction to the use of computer algebra systems, such as Piazza Leonardo 32, I-20133 Milano, Italy SINGULAR and MACAULAY2, and packages, such as SCHUBERT (intersection theory), for Alberto Conte (2000-03), Corso Francia, research in Algebraic Geometry and applications. The programme consists of lectures and practical exercise sessions on the computer. The topics to be considered include: 17, IT-10138 Torino, Italy computer algebra systems, Groebner bases and syzygies, ideal and radical member- C. T. J. Dodson (2000-03), Department of ship, manipulating ideals and modules, Hilbert polynomials and Hilbert functions, elimi- Mathematics, UMIST, PO Box 88, nation, computations in local rings and Milnor numbers, homological algebra (construc- Manchester M60 1QD, UK tive module theory, Ext and Tor, sheaf cohomology, Beilinson monads), primary decom- Jean-Pierre Françoise (2000-03), Dept. position, normalization, rings of invariants, parametrization, deformations, intersection Math., Univ. Paris 6, 4 Place Jussieu, Case theory, applications to special varieties, computer vision, and coding theory. 172, F-75252 Paris Cedex 05, France Course Director: Prof. Wolfram Decker (Saarbrücken, Germany). Salvador S. Gomis (2000-03), Depto Guest lecturer: Dr. Jeremy Kaminski (Bar-Ilan, Israel). Analisis Matematico/Mat. Aplicada, Universidad de Alicante, Campus de San Participants will need to bring laptops. The level will be appropriate for graduate stu- Vicente, ES-03080 Alicante, Spain dents. There will be limited financial support for local expenses. Laurent Guillopé (2000-03), Dép. Math., Organisers: Prof. Mina Teicher and Prof. Boris Kunyavski of the Emmy Noether Institute. Fac. Sciences & Techniques, Université de (Conference Secretary: Ms Chen Fireman) email: [email protected] Nantes, 2 rue de la Houssinière, BP 92208, http://www.cs.biu.ac.il/~eni/ann1-2002.html F-44322 Nantes Cedex 03, France Klaus Habetha (1996-99-03), Rektor, RWTH Aachen, D-52056 Aachen, Germany Willi Jäger (2000-03), Inst. für Angewandte Math., Universität Heidelberg, Im Neuenheimer Feld 294, D- 69120 Heidelberg, Germany Tapani Kuusalo (1996-99-03), Department of Mathematics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40351 Jyväskylä, Finland Marina R. Marchisio (1998-01-05), Via Primula 20, I-12012 Boves (CN), Italy László Márki (1996-99-03), Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364 Budapest, Hungary Vitali Milman (1998-01-05), School of Mathematics, Tel-Aviv University, Ramat- Aviv, Israel EMS December 2001 9 EMS NEWS Novick-Cohen, Amy Carro Rosell, Maria Jesus Olevskii, Alexander Cerda i Martin, Joan New EMS members Reisner, Shlomo Cifuentes Muniz, Patricio We welcome the following new individual members to the Roitman, Moshe Curto Dias, Josep European Mathematical Society. Rom-Kedar, Vered Fernandez Garcia, Guillermo Rosset, Shmuel Galindo Pastor, Carlos Schuss, Zeev Giraldo Carbajo, Antonio Sever, Michael Gomez Torrecillas, Jose Australia Periaux, Jacques Shoikhet, David Hernandez Penalver, Gregorio Urbas, John Rhin, Georges Shustin, Eugenii Lopez Gonzalez, Luis Maria Roos, Guy Shvartsman, Ludmila Martin del Rey, Angel Belgium Timmel, Jean-Francois Sodin, Mikhail Martinez Pastor, Ana Bair, Jacques Trotman, David Srebro, Uri Ojeda Aciego, Manuel Bellemans, J. Ursat, Xavier Tkachenko, Vadim Ortega Titos, Miguel Borrey, Sabine Vergne, Michele Tsirelson, Boris Padron Fernandez, Edith Botterman, Stefaan Waldschmidt, Michel Weir, Yitzhak Pedregal Tercero, Pablo De Maesschalck, P. Weiss, Benjamin Perez Riera, Mario Dehaye, Paul Olivier Germany Pison Casares, Pilar Devillers, Alice Alefeld, Götz E. Italy Richard, Philippe R. Fiorini, Samuel Cleve, Ludger Balossini, Mario Romance del Rio, Miguel Geivaerts, Marcel Frommer, Andreas Capalbo, Antonio Sanchis Lopez, Manuel Kuijken, Elisabeth Fuegenschuh, Armin Casiraghi, Sergio Sastre Rosa, Maria Asuncion Luyckx, Deirdre Haase, Peggy Cesarano, Clemente Soria de Diego, Javier Stulens, Koen Heinlein, Peter Chiaretti, Mauro Mielants, Wim Holzleitner, Ludwig Cichero, Anna Sweden Quarta, Lucas Hubski, Martha Cipollone, Roberto Andersson, Karl Gustav Rigo, Michel Kawohl, Bernhard Citrini, Claudio de Gosson, M. Roisin, Jean-Roger Nakamura, Shu Gilbert Conti, David Essén, Matts Plastria, Frank Smoczyk, Knut Di Lorenzo, Emilia Hansson, Örjan Sebille, Michel Werner, Dirk Eschgfaeller, Josef Passare, Mikael Simar, Léopold Fiorito, Giovanni Pefferly Jr, R. J. Stienon, Mathieu Greece Furi, Massimo Stulens, Koen Dassios, George Furnari, Giuseppe Switzerland Teugels, Jef Mavridis, N. Gaeta, G. Bissegger, Elena Toint, Philippe Vlamos, Panayiotis Gonella, Corrado Buchmann, Fabian Martin Van Camp, Ellen Gori, Franco Frauenfelder, Philipp Warrinnier, Alfred Guatemala Machi, Antonio Imhof, Jean-Pierre Zhang, Yinhuo Moreira Galicia, Manuel Micelli, Giuseppe Iozzi, Alessandra Moscucci, Manuela Ishikawa, Masaharu Brazil Hong Kong Paveri Fontana, Stefano Jainz, Michael Barbosa, Rommel Hu, K. Y. Pennisi, Mario Joosten, Robert Ferreira, Jorge Pizzimenti, Pasquale Francesco Kuensch, Hans Rudolf Ireland Puccio, Luigia Loher, Damian Canada Hutchinson, Kevin Rivara, Luigi Matache, Ana-Maria Fillmore, Peter Romito, Marco Motamen, Simin Lakhany, A. Israel Ruf, Bernhard Ortega, Juan Pablo Thomas, R. S. D. Abarbanel, Saul Salvetti, Mario Reimann, H. M. Adin, Ron Savare, Giuseppe Savelieva, Marina Czech Republic Agranovsky, Mark Sibillo, Marilena Schmidlin, Gregor Ephremidze, Lasha Alesker, Semyon Smit Ghinelli, Dina Struwe, M. Alkalai, Nurit Volcic, Aljosa Todor, Radu-Alexandru Croatia Amram, Meirav Zanchetta, Nadir Torrilhon, Manuel Ivansic, Ivan Arad, Zvi Toselli, Andrea Beck, Jonathan Luxembourg Troxler, Andreas Denmark Bercovier, Michel Bausch, Raymond Wihler, Thomas Bennedsen, Helge Berezina, Miriam Zimmermann, Susanne Booss, Bernhelm Besser, Amnon Norway Brons, Morten Chillag, David Reichelt, Yngvar Turkey Carstensen, Angela Cwikel, Michael Akinci, Karen Christiansen, Edmund Dax, Achiya Poland Claudius, Michael Dula, Giora Ciesielski, Krzysztof United Kingdom Conradsen, Knud Elin, Mark Czerwinska-Lenkowska, Teresa Byott, Nigel Haugaard, Kristian Enden, Giora Pisarek, Jerzy Deitmar, Anton Hoffmann-Jorgensen, Jorgen Farber, Michael Radzikowska, Eugenia Gardiner, A. D. Hogsbro-Thygesen, Uffe Gelaki, Shlomo Rogula, Dominik Hasson, R. Kiming, Ian Gilat, David Sztyren, Malgorzata Jarvis, T. M. Kjargaard Pedersen, Gert Gitik, Moti Keeling, H. Kjeldsen, Tinne Gohberg, Israel Portugal Lillington, John Newman Lynggaard, Joergen Gordon, Yehoram Guerreiro, Antonio A. Pantilie, R. Madsen, Tom Haran, Dan Pereira, Antonio M. R. Rubidge, N. W. Sinclair, Robert Horwitz, Lawrence Paul Santos, Carlos A. Stewart, J. Skovsmose, Ole Juhasz, Arye Wiltshire, Ronald Sørensen, Michael Krasnov, Yakov Romania Wilson, P. L. Thusgaard Ruhoff, Peder Kaminski, Jeremy Yermiyahu Radulescu, Vicentiu Wotherspoon, Craig Iain Kaplan, Gil France Karp, Lavi Russia United States Boivin, Daniel Kheifets, Alexander Yagola, Anatoly Edwards, Robert D. Bodin, Antoine Krushkal, Samuel Linnell, P. A. Borrelli, Vincent Lawrence, Ruth South Africa Martens, Johan Cerf, Jean Leborgne, Daniel Kalinde, Albert Norton, Julia Chavent, Guy Leizarowitz, Arie Nworah, Kingsley I. Chéniot, Denis Lerer, Leonid (Arie) South Korea Saloff Coste, Laurent Cont, Rama Levy, Azriel Kim, A. C. Coupet, Bernard Levy, Eliahu Ukraine Duval, Yves Margolis, Stuart W. Spain Suvorov, Serghey G. Elskens, Yves Megrelishvili, Jonathan Arias Cano, Cristina Jambu, Michel Merzbach, Eli Bonilla, Luis L. Uzbekistan Mardin, Arif Moran, Gadi Cal Casals, Fernando Aripov, Mersaid

10 EMS December 2001 EMS NEWS

EurEuropeanopean CongrCongressess ofof MathematicsMathematics Call for Bids for the 5ECM Outline bids from possible organisers of the 2008 Congress are now invited, and should reach the EMS Secretariat by 31 December 2002. The address of the Secretariat is Mrs Tuulikki Mäkeläinen, Department of Mathematics, University of Helsinki, P.O. Box 4, FI-00014 Helsinki, Finland (Tel: +358-9-1912-2883; Fax: +358-9-1912-3213; e-mail: tuulikki.make- [email protected]). The information below may be helpful to possible organisers. Informal discussions are welcomed, and may be addressed to the Secretary David Brannan (e-mail: [email protected]) or any other member of the Executive Committee.

General information on ECMs European Congresses of Mathematics are organised every four years. The first Congress was held in Paris in 1992, the second in Budapest in 1996, and the third in Barcelona in 2000. In 2004 the Congress will be held in Stockholm. The next free slot for a Congress is the year 2008. The Congress must be in Europe. Experience of previous Congresses suggests that the attendance might be expected to be around 1000 mathematicians. The duration has so far been 5 days. 10 EMS Prizes are awarded to young outstanding European mathematicians at the opening ceremony. The Congress programme should aim to present various new aspects of pure and applied mathematics to a wide audience, to offer a forum for discussion of the relationship between mathematics and society in Europe, and to enhance cooperation among mathematicians from all European countries. The standard format of previous ECMs has been: - about 10 plenary lectures; - section lectures for a more specialised audience, normally with several held simultaneously; - mini-symposia; - film and mathematical software sessions; - poster sessions; - round tables. An exhibition space for mathematical societies, booksellers, etc. is required. No official language is specified and no inter- pretation is needed. The Proceedings of the previous ECMs have been published by Birkhäuser-Verlag.

Decision process for 5ECM (i) Bids are invited via this notice in the EMS Newsletter in 2001, and via letters to the EMS member societies sent out in 2001 by the EMS Secretariat; the deadline for bids is 31 December 2002. These bids need only be outline bids giving a clear idea of the proposal and possible sources of financial and local support. (ii) Early in 2003 the Executive Committee of the EMS ('EC') will consider the bids received. It will invite one or more of the bids to be set out in greater detail so that it can decide which bids are sufficiently serious options to be considered further. The deadline for such 'worked up' bids is 30 June 2003. (iii)The EC will then create a short-list of sites that appear to offer the best possibilities for a successful Congress. (iv) The EC will then appoint a Site Committee to visit the short-listed sites between July and December 2003 to check a range of items in connection with the development of the Congress. For example: - Size and number of auditoriums; location and equipment - Room for exhibitors - Hotel rooms and dormitories; location, prices, number in different categories and transportation to lectures - Restaurants close to Congress site, number and prices - Accessibility and cost of travel from various parts of Europe - Financing of the Congress; support to participants from less favoured countries, in particular - Financing for the EMS Prizes - Experience in organising large conferences - Timing of the Congress - Social events - Plans to make publicity for Mathematics on the occasion of the Congress (v) In 2004 the EC will make a recommendation for the site to the EMS Council on the basis of the bid documents and the Site Committee report. The Council will reach its decision prior to 4ECM in 2004.

Relations between the EC and the Organising Committee of 5ECM After the Council decision, the local organisers will be asked to present a draft budget and an outline of the programme of the Congress. The actual Congress organisation is the responsibility of the local organisers. At least two committees must be appointed - namely, the Scientific Committee and the Prize Committee. The Scientific Committee is charged with the responsibility for conceiving the scientific programme and selecting the speakers. The Prize Committee is charged with the responsibility of nominating the EMS Prizewinners. For each of these committees the Chairs are suggested by the local organisers and agreed after consultation with the EC. In turn, the members of the committees are suggested by the Chairs, and are approved after consultation with the EC. The local organisers are responsible for seeking financial support for the Congress and for the meetings of its committees. However the EMS commit to provide some financial support for the travel of Eastern European mathematicians to the ECM, and would also assist and advice in seeking sources of funds, in particular from the EU. The EMS and the local organisers should be partners in the effort to find funding support for the prizes. The level of the registration fees is of great importance to the success of an ECM. The EC asks that it should be involved before a final decision on the level of fees is made; members of the EMS normally receive a reduction of some 20% on the reg- istration fees. The EC would wish to be informed of progress at its regular meetings. The EC would be pleased to offer advice to the local organisers on matters such as the scientific programme, budgetary developments, registration, accommodation, publications, web site, etc. Publicity for the ECM via the EMS Newsletter and the EMIS site is strongly recommended. Marta Sanz-Solé and David Brannan

EMS December 2001 11 ANNIVERSARIES PPierrierree dede FFermatermat (1601?(1601? -- 1665)1665) His life beside mathematics Klaus Barner

Fermat’s outwardly uneventful life is soon told. André Weil [13]

The 400th birthday of Pierre de Fermat, the great seventeenth-century French mathematician, was celebrated in 2001. However, this is probably based on a fallacy (see [2]): Fermat was probably born in 1607, or in the first days of January 1608, in Beaumont-de-Lomagne. He was the son of the rich wholesaler and manufacturer Dominique Fermat, and his mother, Claire De Long, his father’s second wife, came from a noble family of jurists (see [11]). Thus, strictly speaking, the celebrations and conferences with respect to Fermat’s 400th birthday are premature. But we won’t spoil the fun - we’ll join the celebrations of Fermat’s birthday, and report on his little-known private and professional life. In the second half of the fifteenth century, the Fermat family apparently emigrated from Catalonia to Beaumont- de-Lomagne, a fortified village with a market, about 55 kilometers to the north- west of Toulouse. There, in the sixteenth century, Pierre Fermat’s grandfather Anthoine run an ironmongery that earned him a modest fortune which he bequeathed to his two sons Dominique (from his first marriage, Fermat’s father) and Pierre (from his third marriage, Fermat’s godfather). Both sons increased their father’s inheritance to the best of their abilities. Dominique was particularly successful. A merchant who ran a leather wholesale trade with Italy, Spain and England, he also had a flourishing lime factory and gained considerable prosperity. He invested his profits in numerous farms and other plots of land, which he leased on the basis of metayage Fermat Memorial with the sculpture by Falguière in front of the covered market of contracts. Beaumont Through his marriage with a office had to be up for sale, and the reputation far beyond France attracted noblewoman, Claire de Long, reflecting support of members of the particular students from all parts of Europe - above his increased standing, he gained access parliament was needed, requiring all from Scotland, the Netherlands and for his sons Pierre and Clément to the substantial favouritism. At the end there Switzerland, as well as from German noblesse de robe. His family’s social would be an entrance examination in law countries where students of Lutheran promotion was planned well in advance: which not everyone passed. denomination formed a high proportion. for, the only way to achieve it was to buy Pierre de Fermat spent his schooldays In the sixteenth century Orléans had made the office of a parliamentary councillor with the Frères Mineurs Cordeliers in his a name for itself as a stronghold of (conseiller) at one of the Supreme Courts of home town. These were Franciscans who humanistic jurisprudence. In this, a Justice (cours de parlement) in the French had settled in Beaumont around 1515 and critical-philological return to the classical provinces, just as in Toulouse or founded a demanding grammar school in origins and sources of Roman law Bordeaux. This custom, already disputed which classical Greek was taught, in (particularly Justinian) played a central during the Ancient Régime but completely addition to Latin, Italian and Catalan. part. A reliable mastery of Latin and legal, had been introduced by the French This was unusual for the time in a small classical Greek was indispensable for these Crown in the sixteenth century because of place with only 3000 inhabitants. For studies, and the classical languages were lack of money. The prerequisite for this Pierre, who left school in 1623 at the age of especially cultivated by the faculty of the was not only a respectable fortune. One 16, his good command of classical artes liberales of Orléans. A baccalaureate had also to gain appropriate qualifications: languages was a crucial precondition for from Orléans undoubtedly gained a young three years of study of law, leading to a his study in Orléans. jurist a considerable reputation. baccalaureus (juris civilis), and four years of His choice of this place for study was well Around August 1626, Pierre de Fermat practical experience as a lawyer at one of founded. The town on the Loire had an passed his examinations in Orléans, and the Supreme Courts. Further, a suitable old and famous faculty of civil law whose duly received his certificate for successfully 12 EMS December 2001 ANNIVERSARIES passing the examination of baccalaureus their living from their estates, which they today’s standards. The idea of separating juris civilis. In the following month leased. Fermat, who had inherited from the powers of legislature, executive and Dominique Fermat wrote his last will and his father six farms and numerous other judiciary, which had been elaborated by testament. Giving a compensation to his pastures, gardens and vineyards, was no John Locke and Charles de Montesquieu younger son Clément, and fixing the exception in this respect. Only very and politically realised much later, was still dowries of his daughters Louise and Marie, wealthy landowners could afford the completely unknown in the seventeenth he chose his elder son Pierre as sole heir. luxury of purchasing an office of that kind. century. The parlements performed the Pierre Fermat proceeded to Bordeaux The ‘profit’ consisted of the advancement tasks of law-making, administration and and was sworn in as a lawyer by the Grand’ into the noblesse de robe, the social jurisdiction, so far as they had been Chambre of the parlement de Bordeaux in reputation and privileges that went with it, transmitted to them by the Crown for the October 1626. Being called to the Bar of and the participation into political power. provinces administered by them. one of the French provincial parliaments, After Fermat had asked for the king’s The parliament de Toulouse was opened he had to set up in practice as a lawyer, consent and passed the prescribed for the first time in 1303. From the start, because this was by royal law a entrance examination of the parlement de its area of responsibility included the precondition for recognition as a conseiller Toulouse, he was sworn into office by the complete south-east of the kingdom. by the Minister of Justice. After his natural Grand’ Chambre on 14 May 1631. From this Following the Parisian model, it had a choice of Orléans as a place of study, his moment onward, he enjoyed all the rights Grand’ Chambre, the original chamber from selection of Bordeaux for practising as a and privileges of a conseiller’s office - the which all other chambers developed for lawyer was surprising; for many different income from his office, and the right to use procedural reasons: the chambre criminelle reasons Toulouse was a more obvious (also known as la Tournelle) and two choice. It is likely that Fermat’s choice of chambres des enquêtes. The Tournelle dealt in Bordeaux is connected with his the final instance with all offenders mathematical leanings. threatened with corporal punishment, and In Bordeaux, there was a small circle of no clergyman was allowed to be a member lovers of mathematics, of whom the names of it; this chamber regularly delighted the D’Espagnet, Philon and Prades are known citizens of Toulouse with its public from Fermat’s correspondence; Étienne executions. Each year two conseillers were D’Espagnet, whose father had been first exchanged between the Grand’ Chambre president of the parliament of Bordeaux and Tournelle, so that they were considered and a friend of Viète, owned Viète’s works as one chamber divided in two. In the two which were very difficult to obtain at that chambres des enquêtes civil actions were time. Here Fermat, who was just 20, decided in writing in the final instance. started his mathematical career. But who The chairman of the Grand’ Chambre and advised him to settle as a lawyer in head of the whole parliament was the Bordeaux? It was probably Jean premier président. He was the only Beaugrand, who cultivated scientific magistrate who had not purchased his relations with the gentlemen in Bordeaux. office, being appointed by the king. His Fermat may have made his acquaintance in deputies in the Grand’ Chambre were the August 1626 in Orléans. At any rate, it is chairmen of the other chambers and the significant that Beaugrand followed présidents à mortier (two or three per Fermat’s mathematical career with chamber) who had also bought their particular interest, and he always proudly Two recent Fermat stamps prestigious offices, at three times the price reported on Fermat’s achievements during of the ordinary conseillers. They regularly his journeys to Italy and elsewhere. the title éculier and put ‘de’ before his led the sittings of their chambers in Beaugrand obviously felt that he had name. rotation. ‘discovered’ Fermat. The close chronological linking between An ordinary conseiller, as Fermat When Dominique Fermat died on 20 Fermat’s appointment as conseiller au remained all his life, could also play a June 1628, Pierre became a wealthy man, parlement and his marriage with Louyse de central role if he was appointed the and had only another two years to spend as Long, the daughter of Clément de Long, rapporteur of a case by the chamber. an avocat in Bordeaux. If the opportunity conseiller au parlement de Toulouse, is Additional income came with a rapporteur’s then arose for him to buy a conseiller’s office interesting. The marriage contract was role in a court case, and a hardworking (in Toulouse, preferably), the first stage of concluded on 18 February 1631, and on 30 rapporteur could raise his income the family plan would be achieved. This March, de Long paid his future son-in-law significantly. Fermat was one of the most opportunity arose at the end of 1630, 2865 livres as a down payment on the hard-working rapporteurs of the during a severe plague epidemic that promised dowry of 12000 livres. The parliament; for example, in a ten-week carried off numerous conseillers au church wedding took place on 1 June in period in the Tournelle from November parlement in Toulouse. On 29 December the Cathétrale St-Etienne of Toulouse. 1657 to January 1658, he wrote no fewer 1630, Fermat concluded an advance The de Longs, remote relatives of than 34 rapports/arrêts. Fermat drew up his contract with Ysabeau de la Roche, widow Fermat’s mother, lived in Toulouse in the first arrêt on 6 December 1632 in the of Pierre de Carrière, conseiller au parlement rue Saint-Remesy, and also possessed a chambre des requêtes, his first rapport in the de Toulouse and commissaire aux requêtes, house in Beaumont-de-Lomagne Grand’ Chambre on 9 December 1654, and regarding the purchase of the deceased’s adjoining the premises of the Fermat his last arrêt in the chambre de l’Edit on 9 office. family. In that house Clément de Long January 1665, three days before his death. The purchase price of 43500 livres, with used to spend his parliamentary vacations. The four chambers mentioned above an initial payment of 3000 livres on taking Pierre and Louyse must have known each formed the proper cour of the parlement de up the office, represented a usual, but other from childhood, and their marriage Toulouse. The chambre des requêtes in which enormous, sum. A farmer could earn seems to have been settled by the families Fermat took up his office of conseiller and about 100 livres per year, a parish priest long ago, provided that Pierre made it to commissaire in 1631, did not belong to the some 300 livres, and a busy conseiller up to conseiller au parlement. Contemporaries proper cour of the parlement and was at the 1500 livres on which he then had to pay praise the beauty, beguiling charm and lower end of the parliament’s hierarchy. tax. From an economic point of view such charity of the young woman who bore Its members heard preliminary civil cases, a purchase was a miserable deal, Pierre five children, Clément-Samuel, leaving the final judgements to one of the particularly since by royal law the conseillers Jean, Claire, Catherine and Louise. chambres des enquêtes. were not allowed to carry on a trade or The French provincial parliaments of A commissariat aux requêtes was generally a practise a craft; nearly all of them earned the Ancient Régime were not parliaments by position for a beginner, allowing him to EMS December 2001 13 ANNIVERSARIES become acquainted with the practice of the first time for the chambre de l’Edit, and citizens’ meetings - his name turns up in parliament, but it gave no advancement. Fermat was selected by the king on 16 July. the minutes for many years - helping them For this purpose, the conseiller had to sell He spent the session of 1638-9 with his with particularly difficult items on the his office in the chambre des requêtes and family in Castres. agenda. The Fermat family also showed its purchase an office in the proper cour of the From 1646, Fermat’s letters to his close attachment to Beaumont with charity parliament. Fermat duly gave up his erudite collegues became sparse, and for and donations and by becoming commissariat des requêtes on 4 December several years his mathematical godparents on numerous occasions. Very 1637, and acquired an office in the cour of corrrespondence almost stopped often Fermat had less time there for his beloved ‘geometry’ than he had hoped. The Huguenot stronghold Castres, seat of the chambre de l’Edit de Nantes, was a particularly strong attraction for Fermat. Again and again he tried, not always successfully, to be proposed by the Grand’ Chambre for the delegation to Castres and to be confirmed by the king. Between 1632 and 1665, of the 45 conseillers au parlement de Toulouse delegated to Castres whose term was renewed by the king for a further year, seven were renewed twice, four three times, and only Fermat four times: in 1644-6, 1648-50, 1655-7 and 1663-5. But what attracted Fermat so strongly to this town on the banks of the river Agout? Three reasons can be given. First, a certain sympathy for the Reformed Church, which can already be observed in his parents and grandparents. Secondly, Fermat’s exceptional capability as a mediator between conflicting interests, inherited from his father Dominique, which could not show to better advantage Coats of arms on one of Picharrot’s towers. In the lower row are those of four consuls of than at a chamber where reconciliation Beaumont, elected for the year 1617. Third from left is the coat of arms of the Fermat family between the representatives of the two the deceased Pierre de Raynaldy. He was completely. Why was this? Deteriorating religions had regularly to be sought. The registered at the court of the parliament mental ability? (Fermat was just forty years third, and perhaps strongest, reason was on 16 January 1638, and held this office old.) Mersenne’s death on 1 September the intellectual atmosphere of Castres until his death. 1648? (His place was soon taken over by which, while the seat of the chambre de During Fermat’s time as a commissaire Carcavi.) We have rather to look for l’Edit, saw a golden age of culture that it aux requêtes he made the acquaintance of reasons among the strains of Fermat’s never achieved again, before or since. his long-time friend Pierre de Carcavi, who professional life; these were connected Historians of Toulouse lament the in 1632 became his colleague at the with social and political disturbances: intellectual fall of that town in almost all parlement de Toulouse. Carcavi moved to peasants’ revolts in the south of France areas of art and science at that time, Paris in 1636 and mediated for Fermat arising from brutal methods of tax particularly with regard to the university, with Marin Mersenne and his Parisian collections, the rebellion of the Fronde but note as an exception and gloire de circle. Fermat’s long-standing against Mazarin, and the war against Toulouse the great scholar Pierre de correspondence with these gentlemen Spain. At the beginning of the 1650s, the Fermat. started a few days after Carcavi’s arrival at last great French plague epidemic broke In Castres, in 1648, the Protestant Paris and lasted (with an interruption) out, followed by famine. Academy was founded with 20 initial until shortly before his death. Fermat’s We are rightly used to seeing Fermat as members who came exclusively from the famous dispute with Descartes occurred at the great mathematician and humanist Reformed Church. Most of these the time of his move from the chambre des scholar. But according to his conception gentlemen were conseillers or avocats of the requêtes to the first chambre des enquêtes. of himself, he was first and foremost a chambre de l’Edit. Among them were the The chambre de l’Edit de Nantes belonged judge. At the parliament of Toulouse he poets Samuel Izarn, Hercule de Lacger to the parlement de Toulouse. This chamber had a seat for life. Even though he could and Jacques de Ranchin, the theologians was created in 1598 by Henri IV, with live off his possessions in Beaumont-de- Raymond Gaches and André Martel, the equal representation by members of the Lomagne, he regarded his job as conseiller philosopher Pierre Bayle, the medic, Reformed Church and the Roman au parlement de Toulouse as his proper life’s chemist and philosopher Pierre Borel, the Catholic Church, and had its seat from work, and his career in this institution was physicist and translator Pierre Saporta, 1632 to 1670 in Castres, 75 kilometres to more important to him than his reputation and the historiographer Paul Pellisson, but the east of Toulouse. In this chamber, all as a mathematician. Only when his no mathematician. cases of conflict, and all criminal cases in professional activities allowed him enough Bayle and Pellisson enjoyed national which adherents of both religions were leisure, such as when parliament was not in reputation, and Saporta and de Ranchin involved, were settled. It consisted of two session during the numerous religious were Fermat’s friends. The latter read presidents, one from each Church, as well festivals, could he devote himself to his poems of Pierre and Samuel Fermat at as ten magistrates of each denomination. hobby of mathematics. meetings of the Academy; to him Fermat The judges, members of the Reformed Fermat spent the great parliamentary dedicated his critical commentary on the Church, were local and had purchased recesses in September and October à la work of the Greek historian Polyainos, their offices. Each year, eight of the campagne in Beaumont-de-Lomagne, thereby demonstrating a knowledge of Catholic judges were elected by the king where at harvest time he received his share Greek philology. In 1664 Fermat saw one from a list of twelve conseillers au parlement of the yields from the leased farms, as of Polyainos’s rare works printed, de Toulouse that had been compiled by the agreed by contract. He gave advice on prepared by Saporta; it concerns a short Grand’ Chambre. On 29 May 1638, the legal questions to the inhabitants of his text in which Fermat interprets a passage Grand’ Chambre nominated Fermat for the home town, and regularly took part in the from a letter of Synesios of Kyrene. Time 14 EMS December 2001 ANNIVERSARIES and time again, Fermat felt drawn to differences, stood up for justice and confiscate the forbidden dye-stuff. This Castres; his youngest daughter Louise was humanity without shrinking from wasn’t a pleasant task for a ‘gentle, born there in 1645, and when Fermat died confrontations with the mighty, such as the retiring, even shy man’ ([7, Vol. 1, p.22]). there in 1665 his younger son Jean was first president Gaspard de Fieubet. Frequently Fermat was assigned to a small canon. In 1648 and 1651 Fermat committed group of conseillers who travelled far to His strong interest in a delegation to himself to a rather hopeless fight against meet bishops, ministers and other Castres did not prevent Fermat from pressing ahead with his professional rise to the Grand’ Chambre. By 1647 he was already the longest serving conseiller in the first chambre des enquêtes and he frequently took over the presidency when the présidents à mortier were both absent. His move from the first chambre des enquêtes to the Tournelle coincided with the outbreak of the Toulouse plague epidemic of August 1652 to July 1653. About 4000 citizens died - about ten per cent of the town’s population - and Fermat himself almost fell victim to the plague. In May 1653 the philosopher Bernard Medon, conseiller au présidial de Toulouse and a friend of Fermat, wrote to the Dutch writer Nicolas Heinsius the Elder of Fermat’s death (Fato functus est maximus Fermatius), only to withdraw this news in his next Epitaph from the former Fermat-mausoleum in the monastary of the Augustins, letter: Priori monueram te de morte Fermatii, Toulouse. Year of creation: 1665 vivit adhuc, nec desperatur de ejus salute, quamvis paulo ante conclamata. Fermat was the illegal and brutal methods with which dignitaries, or escorted them a long one of those who became ill with the the tax collectors (partisans) recovered the distance when they had taken their leave of bubonic plague and survived, but his taille from the farmers. On this occasion Toulouse. In such cases Fermat’s health was weakened from this time Fermat uncovered the partisans’ deceitful reputation as a scholar and good onwards. practice of backdating the tax receipts, conversationalist was the reason for his Soon after the outbreak of the plague thereby withholding for themselves selection. Fermat progressed to the Tournelle, revenues that were due to the king. In Certainly Fermat was political, but he according to the principle of seniority, and 1651, at the time of the Fronde, he was a lacked two important qualities: from there a move to the Grand’ Chambre member of the delegation for the unscrupulousness and ambition for power. was routine. In November 1654 he parliament of Toulouse which successfully But his abilities as a jurist have also been became a member of the highest chamber demanded (after negotiation for several doubted by Mahoney (see [7, Vol. 2, p.20]) of the parliament, and on 9 December he months) that the delegates of the Estates of who wrote: ‘The most candid appraisal of read his first rapport there. In November Languedoc (who took the side of the Fermat’s abilities as a jurist, and one that 1655 he was back in Castres, but returned Fronde) should return to a legal state of runs counter to the usual adulation, comes to Toulouse in November 1657, again to affairs loyal to the king. And on 30 July from a secret report of Claude Bezins de the Tournelle. 1652, through a courageous visit to the Bésons, intendant of Languedoc, to Throughout his life Fermat was a loyal camp of the royal army, he prevented his Minister Colbert in 1663. Speaking of the servant of the Crown. Born during the home town of Beaumont-de-Lomagne conseillers and their relations to the suspect regency of Henry IV, he was a fourteen- (which had been plundered by the soldiers First President, Gaspar de Fieubet, Bezin year-old boy when the young king Louis of the Fronde) from being taken by storm said of Fermat: "Fermat, a man of great XIII spent the night of 24 November 1621 and completely destroyed by the king’s erudition, has contact with men of learning in his father Dominique’s house in soldiers. After the defeat of the Fronde, everywhere. But he is rather preoccupied; Beaumont-de-Lomagne, while on a Fermat achieved through tough he does not report cases well and is journey from Toulouse to Lectoure. But negotiation the outcome that Beaumont confused. He is not among the friends of Fermat’s impression of his king did not should receive reparation payments of the First President".’ Mahoney then drew remain unsullied. In 1632 he witnessed 16266 livres. In 1654 Fermat put through negative conclusions with regard to the arrival in Toulouse of Louis XIII, with the Grand’ Chambre a fairer distribution of Fermat’s judicial qualities that have since Cardinal Richelieu and 5000 soldiers. The the income from the charges between the been adopted without question by other king forced the Toulouse Grand’ Chambre Tournelle and the Grand’ Chambre; in this authors. If he had investigated more and the Tournelle to condemn to death the way, Fermat made himself unpopular with carefully, such incorrect judgements would popular and highly regarded Duke Henri the clerics in the Grand’ Chambre. not have occurred to him. II de Montmorency because of rebellion Another stereotype is the claim that In 1965, the legal historian Henri Gilles against the king. The awkward task of Fermat never ventured farther than of Toulouse showed, in a careful rapporteur in this case fell to the oldest Bordeaux (see [13, p.39]). As we have investigation which Mahoney obviously did conseiller of the Tournelle, Fermat’s father- already seen, he studied law in Orléans not read, that Fermat always cultivated a in-law Clément de Long, in whose house from 1623 to 1626. He may also have very clear style and that the language of his Fermat lived at that time with his wife visited Paris as a student. Certainly, his arrêts and reports stands comparison with Louyse. duties as a conseiller forced him to the style of those written by his colleagues A stereotype that goes back to Mahoney undertake longer journeys; for example, in (see [6]). I have convinced myself that (see [7, 8]), and has been adopted by more November 1646 the Grand’ Chambre Gilles is right. A disparaging judgement recent authors, is that Fermat was a banned the dyers of Nîmes from buying by the intendant Claude Bazins de Bessons mediocre conseiller and judge who tried to high-quality indigo from the Middle East is easily explained: in September 1663 the avoid all social, political and religious instead of the woad produced around minister Jean-Baptiste Colbert demanded conflicts. Nothing is further from the Toulouse. When the dyers disobeyed the from the intendants individual judgements truth. Fermat was no jurist who composed ban, Fermat was sent to Nîmes, about 300 of all conseillers and other royal officials at legal treatises, but was an outstanding kilometers to the east of Toulouse, to the parliaments. The intendants complied practitioner who, tolerant of religious present the parliament’s decision and with this request so reluctantly that Colbert EMS December 2001 15 ANNIVERSARIES asked some intendants for greater in form of a wicked slander: that it was January 1665 aged 57 years, after thoroughness. Had Mahoney read the Fermat who condemned the priest to be receiving the holy sacraments and with an whole report of 24 December 1663, and burned alive (see [12, p.808f] and [8, alertness of mind to the end. On the next not only an isolated citation in the p.360]). day he was laid to rest in the chapel of the Jacobins in Castres. The date of Fermat’s birth is disputed, and there is also confusion about where his mortal remains found their last resting place. Is it the chapel of the Jacobins in Castres which was demolished soon after Fermat’s decease? Or is it the family mausoleum in the church of the Augustins in Toulouse, to which Samuel and Jean Fermat had their father’s body moved? After examining all arguments (see [10, 4]) I believe that Fermat’s body was transferred to Toulouse in the year of his death. But there is no proof. The family mausoleum was destroyed during the French Revolution and only Fermat’s epitaph, currently restored, has survived.

References 1. K. Barner, Eine traurige Episode im Leben Fermats, Mathematische Schriften Kassel, Preprint No.21/00. 2. K. Barner, How old did Fermat become? NTM, International Journal for History and Ethics of Natural Sciences, Technology and Medicine (New series) 8 (4) (October 2001). 3. H. Blaquière & M. Caillet (eds.), Un mathématicien de génie: Pierre de Fermat 1601- 1665, Catalogue de l’exposition organisée par la Bibliothèque Municipale de Toulouse, Lycée Pierre-de-Fermat, Toulouse, 1957. 4. P. Chabbert, Fermat à Castres, Revue d’Histoire des Sciences 20 (1967), 337-48. 5. G.B. Depping, Correspondance administrative sous le règne de Louis XIV, tome II, Imp. Nationale, Paris, 1851. 6. H. Gilles, Fermat magistrat. Pierre de The house where Fermat was born. Its present shape was given to the property in the 18th Fermat, Toulouse et sa région, Actes du century. In the background at the top is a 15th-century tower that belongs to the premises. XXIe congrès d’études régionales tenu à Toulouse les 15 et 16 mai 1965, Fédération accompanying text for an exhibition Perhaps because of this event, or because des Sociétés Académiques et Savantes de catalogue (see [3, p.33]), he would have of his visibly deteriorating health, Fermat Languedoc-Pyrénées-Gascogne, Toulouse, realised how superficial the judgements seems to have thought about relinquishing 1966, 35-53. turned out to be (see [5, p.111ff]). his office of Conseiller in the Grand’ 7. M.S. Mahoney, The Mathematical Career of De Bessons resided in Montpellier and Chambre. In a letter of 25 July 1660 to the Pierre de Fermat (1601-1665), 2 vols., had to travel to Toulouse to make ailing Pascal, he proposed that the two Princeton University Press, 1973, 1974. investigations and write his report. There men should meet half-way between 8. R. Rashed, C. Houzel & G. Christol (eds.), he first informed himself about the Clermont-Ferrand and Toulouse because Oeuvres de Pierre Fermat, Vol. I, La conseillers. By that time Fermat was not in his health was hardly better than Pascal’s théorie des nombres, Albert Blanchard, Toulouse, but rather in Beaumont or [10, Vol. II, p.450]). If the latter expected Paris, 1999. Castres. Therefore de Bessons, turned on Fermat to travel the whole distance of 300 9. P. Salies, Sur quelques points d’histoire behalf of Fermat to the king’s man, the kilometres, then Pascal would run the risk toulousaine, Mémoires de l’Academie des first president Fieubet, Fermat’s enemy. de me voir chez vous et d’y avoir deux malades Sciences, Inscriptions et Belles-Lettres de That no fair judgement resulted is not en même temps. Toulouse, 14ème série, 1 (1960), 181-99. surprising. On 4 March 1660, Fermat wrote his last 10. P. Tannery, Paul & C. Henry (eds.), Much more interesting is the reason for will and testament, with his elder son Oeuvres complètes de Fermat, Vols. I-IV, the aversion between Fermat and Fieubet. Samuel as his sole heir. He amplified this Gauthier-Villars, Paris, 1891-1912. The judicial murder of a priest, Jean testament on 13 September 1664, in a 11. L. Taupiac, Fermat: sa vie privée avec Montralon, was stage-managed by Fieubet codicil in which he made settlements in pièces justificatives, Bulletin de la Société on 26 January 1658 (see [1]). This case favour of his wife Louyse: Samuel was to Archéologique de Tarn et Garonne 1879, had a Jansenist background, and Fermat pay his mother 32000 livres from the Forestié, Montauban, 1880. was involved in it as rapporteur and inheritance, an imposing sum which she 12. J. Wallis, Commercium Epistolicum, Opera examining judge. Montralon, of whose could make good use of. Louyse outlived Mathematica II, 757-860, Oxford, 1693. proved innocence Fermat was convinced, her husband by more than 25 years. In the 13. A. Weil, Number Theory, An approach through was hanged next day and his body was preamble of this codicil Fermat speaks history, From Hammurapi to Legendre, burned. Fermat was so incensed and rather openly of his coming end ([4, Birkhäuser, Boston, 1983. shocked that he could not work as a judge p.347]): Je soubsigné éstam incommodé d’une for a month. On 6 February 1658, Sir maladie qui pourroit avoir de mauvaises suittes. Fachbereich Mathematik-Informatik, Kenelm Digby, a notorious liar, reported In October 1664 Fermat set off for Castres Universität Kassel, D-34109 Kassel, Germany on this case to John Wallis in Oxford, but for the last time, and died there on 12 e-mail: [email protected] 16 EMS December 2001 INTERVIEW InterviewInterview withwith SerSergeygey PP.. NovikovNovikov

Interviewer: Victor M. Buchstaber (Moscow)

Since 1996 Professor Novikov has been a the third of them, the youngest of the and mathematical community as carriers Distinguished University Professor in the three sons. All the sons became physicists of honour. University of Maryland-College Park, USA. and mathematicians, while the daughters Aleksei Andreevich Lyapunov, a pupil of He also keeps strong ties with Russia, occupying chose other professions. My elder brother, my father, a well-known mathematician part-time positions in Moscow; he is a principal Leonid Keldysh, is one of the and a distant relative of an even more researcher in the Landau Institute for internationally known theorists in solid- famous mathematician, organised a DNO Theoretical Physics and Head of the Geometry (a children’s scientific society), where his and Topology groups in the Steklov children, my brother Andrei and I, Mathematical Institute and in MSU. Vladimir (Dima) Arnold and other Novikov is a Fields Medallist (1970). The children in our family’s circle, became Soviet Authorities did not allow him to attend acquainted with the elements of science. the awards ceremony in Nice as a punishment A. Lyapunov especially took a great for the letters he wrote supporting people who interest in some branches of biology that were arrested and sent to mental hospitals. were prohibited at that time. Novikov is a member of several academies, Traditionally, high school students with including the Russian Academy, the US a talent for mathematics participated in National Academy and other European university circles and in Olympiads. I was academies. He is an honorary member of the successful in Olympiads at ages 13 and 14 London Mathematical Society, and Doctor and decided that I could probably become honoris causa of the Universities of Athens and a mathematician. However, I had no Tel Aviv. His works were rewarded through calling for mathematics and so postponed several prizes in the former USSR. During the S.P. Novikov's mother L.V. Keldysh with my choice of profession until university. I period 1985-96, he was President of the P.S. Alexandrov decided to wait to see whether some other Moscow Mathematical Society, succeeding A. profession would attract me. It seemed to N. Kolmogorov state physics and in condensed matter me that our family already had a lot of This interview is in two parts – the second part physics. My other brother, Andrei mathematicians. will appear in the March 2002 issue. Novikov, was an expert in algebraic I did not choose mathematics as my number theory, but unfortunately died profession until I was 17, and I entered the What role did your famous family of prematurely. Mathematics Division of the Moscow State Novikovs and Keldyshs play in your Additionally my mother’s brother, University (MGU), the Department of becoming a scientist? Mstislav Keldysh, was a very talented Mechanics and Mathematics. My family played a great role. My father, mathematician in the theory of functions Petr Sergeevich Novikov, was a famous of a complex variable and in differential There are many legends about the famous mathematician. All mathematicians know equations. An especially fundamental MGU Department of Mechanics and his work on the theory of algorithms and contribution was made by him to applied Mathematics in the 1950s and 1960. Could combinatorial group theory, including the branches of aerodynamics. He was a well- you elaborate on the story, please? insolubility of the word problem and the known person in Soviet society, the chief I learned from my family that one could solution of the Burnside problem for theorist-adviser of the government and an grow into a scientist at voluntary torsion groups. In the 1930s he was one of organiser of computational work related to educational seminars by solving non- the best experts in the so-called jets and space between 1940 and 1960. All standard problems and studying things information on the work of such people missed from the obligatory programmes. was officially restricted and not reflected in I began to visit such a seminar during my the world press. For a long time he was first year. It was supervised by President of the Academy of Sciences of V. Uspenskii, a pupil of A. N. Kolmogorov the USSR. My mother’s father, in mathematical logic, who was at that time Vsevolod Keldysh, was one of the leading a young employee at MSU. At this seminar building engineers in the USSR; he was we studied the complete cycle of mentioned in Nikita Khrushchev’s elementary problems in set theory, the memoirs. foundations of the theory of functions of a By the way, Natalia Brusilova, the real variable, and the algebra of logic. mother of Vsevolod Keldysh (my great- Soon Sasha (Alexander) Olevskii, my grandmother), was an aunt of the famous fellow participant at the seminar, became Russian general who defeated the well known for his papers on the theory of Austrians during the First World War (the functions of a real variable. S.P. Novikov's father P.S. Novikov in 1947 Brusilov breakthrough, 1916). The dodgy During my second year, when I was 18, I ‘descriptive set theory’ and in the 1940s in Bolshevik leaders Lenin and Trotsky used had to choose a research supervisor for the mathematical logic. He also started in the his military talents in their General Staff first time and work with him for a year. 1930s a new branch of mathematical during the civil war. Only after that, in the third year, was a physics: the reconstruction of a Among the close friends of my parents student finally allowed to choose his homogeneous bounded domain from its were leading Soviet physicists and specialisation. This rule was in use during gravitational potential at infinity. My mathematicians of their generation: Kolmogorov’s Deanship of the mother, Lyudmila Vsevolodovna Keldysh, I. Tamm, a Nobel prizewinner and teacher Department of Mechanics and was also a prominent mathematician – a of A. Sakharov, M. Leontovich and Mathematics. full professor, and an expert in set theory A. Andronov, applied physicists who Unlike many of my friends, I chose and geometric topology. played an important role in the country algebraic topology. I was probably The family had five children, and I was and who were known in the Soviet physical attracted by an announcement concerning EMS December 2001 17 INTERVIEW a seminar by M. Postnikov, V. Boltyanskii, Bizarre homological calculations with area. In particular, in collaboration with and A. Shvarts. This announcement special Hopf algebras formed a quite my student A. Mishchenko, in 1967 we aroused the petulance of P. Aleksandrov, remarkable area that was then absolutely began to apply formal groups in topology. the chief Moscow topologist, because set- unknown, outside a narrow circle of This idea was soon picked up by D. Quillen theoretic topology was placed in an algebraic topologists. Many years later, (1969), who made an important unfavourable light. when the importance of Hopf algebras contribution. In collaboration with my In this seminar I began by choosing became known to everyone, people even student, V. Buchstaber, we introduced the M. Postnikov as my research supervisor forgot who first discovered these objects: it idea of a multi-valued formal group and attended the brilliant lectures of was actually Armand Borel (rather than (1971). Later, the theory of these objects A. Shvarts, then a postgraduate, in which Hopf) in 1954, but for a rather narrower and their topological applications were the modern achievements of topology were purpose, the homology of Lie groups and considerably developed by V. Buchstaber. presented following the perfectly written H-spaces. In collaboration with my students works of J.-P. Serre. Hopf algebras of a new ‘Steenrod’ type V. Buchstaber, S. Gusein-Zade and During the second and third years I were discovered by John Milnor in 1957. I. Krichever, we started another mastered a large collection of modern In Adams’ works, they began to give deep investigation in which formal groups were topological ideas, with a group of friends results for the problem of Hopf invariants. intensively used to study finite and that included D. Anosov. When I began I was the first (as well as J. Milnor) to apply compact transformation groups; this gave my fourth year, my research supervisor this technique in cobordism theory, an alternative approach to the Atiyah-Bott- M. Postnikov left Moscow for China for extremely successfully. At that time, in Hirzebruch analytic methods. These almost the entire academic year, and topology, refined algebraic manipulations researches were decades ahead of their A. Shvarts did not get work at MSU as a became tightly mixed up with the time. punishment for the above announcement. geometry of function spaces, involving the We organised a seminar without research theory of manifolds and using However, as is well-known, you also supervisors: D. Anosov, D. Fuks, fundamental ideas of transversality, returned to this topic later? G. Tyurina and A. Vinogradov were among cobordism and the calculus of variations. Yes. In the last decade you and I have had the participants. In that year (1958-59) I My first works were published in 1959- occasion to return to this area in completed my first scientific research. 60 and became well known. The connection with the theory of quantum techniques of Hopf algebras and new groups and other algebraic problems. The Tell us about the atmosphere at the homological constructions were applied to store of algebraic ideas originating from Department of Mechanics and Mathematics the calculation of homotopy groups of complex cobordism theory is still far from at that time and on its formative influence spheres and of cobordism groups. The exhausted. on you as a scientist. most significant results were my theorems At the Department of Mechanics and on the evaluation of cobordism rings, and Let’s return to the Department of Mathematics there was a creative spirit, the very ideas of cobordism were greatly Mechanics and Mathematics in the early and an anxiety on the part of the students extended. 1960s. to start scientific activity as soon as By 1960, after all this work, I began to Having completed my first work I became possible. feel like a mature scientist and decided to actively interested in what was happening Completing my third year at the age of turn my efforts to a new area, differential around me in the Department of 20, I encountered the following situation at topology. Mechanics and Mathematics, and outside the Department of Mechanics and topology. Dima Anosov drew my attention Mathematics: those who had chosen areas I well remember the great impression to the geometry and topology of dynamical related to the theory of functions of a real produced by your report at the 1966 systems, and I began to study this area. In variable were already authors of well- known scientific works. Some of them, members of the Kolmogorov seminar, had even written famous works. In algebraic topology the situation was quite different: Moscow was not then at the centre of this area. Especially after the departure of Shvarts, I had to find my way to science without help from research supervisors.

How were your first works written? Among them was the well-known Milnor-Novikov theorem on the complex cobordism ring. How does one begin? The most difficult task is to produce one’s first scientific work, especially if one has no supervisor such as Kolmogorov who can quickly introduce S.P. Novikov with some of his students in Edinburgh in 1998: from left B. Dubrovin, one to the very centre of mathematics and P. Akhmetev, V. Buchstaber, S.P. Novikov, S. Tsarev, A. Veselov, I. Krichever, O. indicate problems that are both deep and Mokhov, I. Taimanov. James Clerk Maxwell is lurking in the background. accessible. My approach to this problem was as International Congress of Mathematicians the late 1950s, I. Gelfand suggested that S. follows: one must take some new in Moscow. It was related to your earliest Dynin should consult me about algebraic outstanding work that has not yet been work, and the Adams-Novikov Spectral topology in connection with the index studied in detail by the community and try Sequence and Landweber-Novikov algebras problem for elliptic operators, and this with great effort to study it in depth. If you had developed from your first interests. helped him to produce good results for are successful, then you will be at home Yes. Some years after I returned to this which he was awarded the prize of the with methods almost all the experts in your topic, in 1966-68, I reconsidered the Moscow Mathematical Society. The index area are out of touch with. In this case you methods of algebraic topology from the problem was already becoming will soon succeed in doing something new. viewpoint of the theory of complex fashionable, and so I began to master This I did, by studying the remarkable cobordism. The interaction of partial differential equations and works of Frank Adams and Rene Thom in homological algebra with the geometry of functional analysis with the help of my 1958. manifolds adds a special elegance to this friends, especially Boris Mityagin. 18 EMS December 2001 INTERVIEW In 1962 the famous work of Atiyah and began to rise. These meetings were of to continuous homeomorphisms of Singer appeared, which increased the great importance for me since they showed manifolds) occupied a special place in public’s interest in topology. Smale’s me the frontiers of differential topology. topology. Incidentally, as Milnor-Kervaire discoveries in 1961 significantly increased After my meeting with Smale at the Steklov showed in 1962, the complete Pontryagin the role of topology in explaining Mathematical Institute, where I was a class regarded as an integral cohomology postgraduate, my local superiors began to class is not invariant under PL- regard me as a serious scientist. homeomorphisms. The topological Very soon, in the autumn of 1961, I invariance is established only for the managed to make a decisive breakthrough integrals of these classes over those cycles in the classification problem for simply that can be expressed via a Riemannian connected manifolds with dimension metric. greater than 5. This result was I managed to prove this conjecture in acknowledged as the best mathematical 1965 by using a sophisticated technique work in the Academy of Sciences of the based on all the achievements of algebraic USSR for that year. and differential topology. The idea Specifying the homotopy invariants of a consisted of a construction that is, in a simply connected manifold and the sense, similar to the so-called étale integrals of the Pontryagin classes over the topology of Grothendieck. Working with cycles, you can determine the manifold simply connected manifolds, I artificially uniquely up to finitely many possibilities. introduced toric neighbourhoods of cycles The description of this finite set is rather and constructed differential topology in delicate, and I shall not dwell on it here: their coverings. Notably, in subsequent the set can be completely evaluated in works (by Kirby and others) where other terms of homotopy groups of the Thom known problems in topology of continuous space of the normal bundle describing homeomorphisms were solved, the special cobordisms of normal maps of presence of toric constructions was manifolds of degree 1. These maps are obligatory. Thus, all integrals of analogous to the birational smooth maps Pontryagin classes over cycles turn out to S.P. Novikov in 1974 in algebraic geometry. They have a be topologically invariant. remarkable topological property, which is As a rule, they are not homotopy complicated dynamical systems, and the the basis of the method. This technique invariant. For simply connected manifolds works of Grothendieck, Hirzebruch, Atiyah was discovered independently by Browder there is only one homotopy invariant and Milnor brought topology and in 1962 while solving another problem. expression in Pontryagin classes, namely algebraic geometry together. The evaluations in concrete examples the Hirzebruch formula for the so-called After this, I began to study different led me to interesting conclusions. For ‘signature’ of the manifold – the important areas of mathematics, actively attending instance, it follows from one of these homotopy invariant characteristic of seminars by I. Gelfand, V. Arnold, calculations that the group of cobordism discovered in the early 50’s by I. Shafarevich, M. Vishik and others. In diffeomorphisms of the 8-dimensional R.Thom and V.Rokhlin.. Its importance in turn, they asked me for help with modern sphere (to be more exact, the connected topology, in algebraic geometry, and in the topology. component of this group) cannot be index theory of elliptic operators is well This was precisely the atmosphere of the contracted to the orthogonal subgroup. known. I observed that, if the fundamental Department of Mechanics and The PL-classification of manifolds also group is non-trivial, then there are non- Mathematics at that time, to help each follows from these methods. As far as trivial cohomology classes with the other to master new ideas and the methods continuous homeomorphisms are following property: if we multiply this class of different areas in the simplest and best concerned, the problem must be discussed by the Pontryagin-Hirzebruch polynomial way, and to explain ideas to one another separately. and integrate over the entire manifold, transparently, without artificial then the result is homotopy invariant; for complexities. We now come to your famous theorem on the example, products of one-dimensional At that time, the Department of topological invariance of Pontryagin cohomology classes have this property. Mechanics and Mathematics of MSU classes and to the Novikov conjecture on In the course of my proof of topological represented all branches of pure and higher signatures. invariance of the Pontryagin classes, I applied mathematics. I do not know of any Continuous homeomorphisms differ needed to establish some special cases of similar scientific group assembled substantially from smooth and piecewise- the above statement. Around 1967 my anywhere in the West after the Second linear ones. For instance, the property of conjecture concerning products of one- World War. a map to be a diffeomorphism is stable in dimensional cohomology classes was the C1 topology: any map that is sufficiently completely proved by a number of authors What about your results on the C1-close to a diffeomorphism is also a (V. Rokhlin, G. Kasparov, W-C. Hsiang classification of manifolds? What is diffeomorphism. This is not true for and T. Farrell). In 1970 I formulated the Browder-Novikov theory? continuous homeomorphisms of general conjecture, that this property I was greatly impressed by Milnor’s manifolds: perturbing a homeomorphism holds for any Eilenberg-MacLane cocycle remarkable discovery of smooth structures in the C0 topology, one can obtain that sits on the fundamental group – that on the 7-dimensional sphere, together something very complicated but is, it arises from homological algebra. The with the classification theory of manifolds homotopic to the identity map. corresponding integral (over the entire that are homotopy spheres. During the While establishing the topological manifold) of the product of this class with academic year 1960-61 I studied the invariance of various quantities (homology the Pontryagin-Hirzebruch class is writings of Whitney, Pontryagin, Thom and cohomology, Stiefel-Whitney classes, referred to as a higher signature. My and Milnor, all of which are written with etc.), the methods of classical algebraic conjecture also includes the hypothesis great clarity. The completeness of the topology led to a stronger theorem, that that the higher signatures exhaust all proofs in these papers was achieved with these quantities are in fact homotopy homotopically invariant expressions of the no detriment to understanding and invariants. This property is stable. curvature tensor. without any artificial formalisation. For simply connected manifolds, the For the past 30 years, this conjecture has In the summer of 1961 I met the ‘stars’ integrals of Pontryagin classes over the been studied in many works in which of world topology: Milnor, Hirzebruch and cycles are certainly not homotopy homological algebra has become mixed Smale, who came to the USSR for various invariant. For this reason, the problem of with the theory of infinite-dimensional conferences as the iron curtain gradually their topological invariance (with respect representations and functional analysis. EMS December 2001 19 INTERVIEW The conjecture has been proved for In 1982 I became interested in a under small perturbations of the direction hyperbolic groups, for discrete subgroups fundamental geometric picture arising in of the magnetic field. This picture holds of Lie groups, and in some other special the theory of metals. Each crystalline for a set of full measure (in the two- cases. metal has a ‘Fermi surface’, a level surface dimensional sphere) of directions of the In the late 1960’s and the early 1970’s, I of a Morse function on a three- magnetic field. For those particular developed ideas for a special algebraic dimensional torus corresponding to the directions for which this picture fails, the analogue of symplectic geometry (which I dual lattice; this torus is called the ‘quasi- situation can be incomparably more called a Hamiltonian formalism over rings with involution); I thought that the explanation of higher signatures and of other deep properties of multiply connected manifolds had a symplectic origin. However, research by topologists into the problem of higher signatures used a different approach. In 1971 I. Gelfand went into my algebraic ideas: they impressed him greatly. In particular, he told me of his observation that the so-called von Neumann theory of self-adjoint extensions of symmetric operators is simply the choice of a Lagrangian subspace in a Hilbert space with symplectic structure. Many years later, in 1997, I used this idea in my work involving scattering theory on graphs.

Did you work in the topology of low- S.P. Novikov and M.F. Atiyah in Edinburgh in 1998 dimensional manifolds? Is it true that your classical theorem on the theory of foliations momentum space’. The only electrons of complicated. According to my conjecture, is purely topological? importance for electrical conductivity at these particular directions form a set In 1963, under the influence of friends low temperatures are free electrons close whose fractal dimension is less than 1. working in dynamical systems (especially to the Fermi surface. In a magnetic field, Behind this picture lie beautiful and V. Arnold), I developed the qualitative electrons begin to move along the Fermi deep theorems of three-dimensional theory of codimension-1 foliations on surface. The trajectories of their motion topology. The observable triple of integers manifolds, and managed to find deep on the universal covering R3 look like the is in fact a two-dimensional homology class results for two-dimensional foliations of intersections of the Fermi surface by of the three-dimensional torus, called the three-dimensional manifolds. In planes perpendicular to the magnetic ‘support of the open trajectories’. For particular, I proved the well-known field. This dynamical system on the Fermi these physical systems, it turns out that the conjecture that every non-singular surface can be extremely complicated if competition between topological complete foliation of the three-dimensional sphere the image of the fundamental group covers integrability and stochasticity is won by S3 has a compact leaf; in fact, I proved that the entire lattice. To this end, the genus of integrable systems for the overwhelming a foliation on S3 always contains a tube – the Fermi surface must be not less than 3. majority of magnetic fields. Only a set of that is, a two-dimensional torus filled with It is interesting that some metals (gold, small fractal dimension are stochastic a special Reeb foliation. The complete set copper, lead and platinum) satisfy this systems, and the investigation of this of these Reeb components is necessarily condition. complicated set requires deeper analytical knotted. We still do not know which knots Many years ago, the well-known Soviet and numerical tools and exceeds the limits (linkages) can serve as a complete set of physicist I. Liftshitz and his school of standard differential topology. Reeb components of a non-singular (M. Azbel’, M. Kaganov, V. Peschanskii foliation on S3. and others) formulated the principle of Your research in metal physics has involved I gave a topological classification of ‘geometric strong magnetic field limit’, both topology and non-linear dynamics. analytic foliations in the solid torus in which states that all essential properties of What has been your experience in terms of tree-like sequences of conjugacy electrical conductivity in strong magnetic interacting with both mathematicians and classes in braid groups. Using braids, fields are determined by the above theoretical physicists? Zieschang and I showed in 1963 that a dynamical system on the Fermi surface. In When working with physicists, I have non-singular foliation exists on any three- normal metals, this description works for aimed to find points of contact between dimensional manifold. I also managed to magnetic fields that do not exceed 103T science and the ideas and methods of find the first non-trivial topological (107 Gauss). What is the geometry and modern mathematics that had not condition on a three-dimensional manifold topology of this dynamical system? Is this previously been used outside pure admitting an Anosov system with system useful or not? These problems mathematics. continuous or discrete time; for example, have been investigated at my seminar for I was not interested in providing for discrete time the manifold must be many years since 1982. The work of my rigorous mathematical justification for homeomorphic to a 3-torus. The Anosov students A. Zorich, I. Dynnikov and results already obtained by physicists. I foliations arising here are not smooth in S. Tsarev helped to overcome the main managed to find applications of topology general, and so direct topological methods topological difficulties in 1984-1993. and non-linear dynamics, of analysis on are necessary. This work originally had a However, my student A. Ya. Mal’tsev and Riemann surfaces (algebraic geometry), gap (indicated by Anosov) which was filled I have recently established that the and of some non-standard aspects of by my student A. Brakhman in 1968. topological facts can be combined in an Riemannian geometry, in some areas of extremely successful way so as to lead to theoretical and mathematical physics You have recently considered topological physical conclusions. It turns out that the where nobody expected such applications. problems arising from the physics of metals. conductivity in a strong magnetic field Moreover, I have helped some prominent What is the ‘Novikov problem’ concerning either vanishes or has a very special form physicists, A. Polyakov, I. Dzyaloshinskii, the motion of electrons along a Fermi characterised by a triple of ‘topological G. Volovik and others, to apply topology in surface, and how is it connected with real integers’. These three numbers are the theory of Yang-Mills fields and physics? topologically stable, being preserved condensed matters physics. 20 EMS December 2001 OBITUARY France, he held the Chair in Mathematical Analysis of Systems and of their Control, for twenty-five years. His series of lectures, Jacques-LouisJacques-Louis LionsLions (1928-2001)(1928-2001) which in the tradition of the Collège had to be renewed each year, were always Philippe G. Ciarlet (Paris) attended by vast audiences, attracting not only his own students but also the students of his students! Jacques-Louis Lions was born in the heart After defending his thesis in 1954, The Seminar in Applied Mathematics of Provence in the charming city of Grasse, Jacques-Louis Lions began his career ‘en that he organised there until 1998, first much renowned for its perfume industry province’ (outside the Paris region) as was with Jean Leray and then with Haïm and its historical centre. then customary, at the University of Brezis, soon became an ‘institution within In spite of his young age, he had the Nancy, where he held a professorship from an institution’. Indeed, countless applied courage and determination to join the 1954 to 1962. mathematicians, from Paris and its vicinity French Résistance at the end of 1943, as a Far from keeping him fully occupied, his and French and foreign colleagues visiting soldier in the FFI (French Forces of the remarkable mathematical achievements Paris, gathered each Friday afternoon to Interior). There he met Andrée, his wife during that period left him enough time to hear prestigious lecturers, such as Stuart and life-long companion. envision the immense opportunities Antman, John Ball, Felix Browder, Ciprian Their son Pierre-Louis, who was born in offered by scientific computing, which was Foias, Gu Chao-hao, Li Ta-tsien, Klaus 1956, would also be distinguished by then coming of age, with the manifold Kirchgässner, Peter Lax, Andrew Majda, industrial applications that would Louis Nirenberg, Olga Oleinik, Sergei henceforth become amenable. This Sobolev, Tosio Kato, Mark Vishik, and constant quest for applications, that would many others. guide him all his life and become one of From 1966 to 1986, Jacques-Louis Lions the most exceptional aspects of his career, was also part-time professor at the École materialised in 1958 when he became Polytechnique, where he created a course scientific consultant for the SEMA (Society in numerical analysis from scratch, that for Economics and Applied Mathematics), soon became a legend! Following the rule a society headed by Robert Lattès, who had at the École Polytechnique, he also wrote entered the École Normale Supérieure one lecture notes whose contents were year after him. While such inclinations are revolutionary for the time, at least in common nowadays, it required lots of France. Indeed these notes constituted a courage to follow them at that time. The kind of encyclopaedia in which, with his applications of mathematics did not then natural gift for teaching, Jacques-Louis arouse the enthusiasm that they now Lions described and analysed practically generate! all that was then known about the After Nancy, Jacques-Louis Lions was numerical analysis of partial differential named professor at the University of Paris, equations. Introductions to numerical where he very quickly created a weekly optimisation and numerical linear algebra seminar on ‘Numerical Analysis’, a were also presented in two separate discipline that was practically unheard of chapters written by his first two doctoral in France at that time. This seminar first students, Jean Céa and Pierre-Arnaud met in the basement of the Institut Henri Raviart. A mystery remains about the first Poincaré, then in a dusty room of the versions of these lecture notes: they were Institut Blaise Pascal, which was situated in affectionately referred to as ‘the the rue du Maroc in the North of Paris. Diplodocus’, even though no-one When the University of Paris split into (including their author) ever seemed to Photo: Collège de France (J.-P. Martin) thirteen distinct universities, he chose the understand why! sixth one, which was later to be named the But all of these essentially academic mathematical talent. This gift earned him Université Pierre et Marie Curie. Two of activities that would normally occupy all of the highest mathematical distinction, the his major initiatives there were to found one’s time did not take up all of his. Far Fields Medal, awarded to him during the the Laboratoire d’Analyse Numérique from it! From 1980 to 1984, he was also 1994 International Congress of (after thirty years on the Jussieu campus, President of INRIA (National Institute for Mathematicians in Zürich. His parents this department was relocated in 1999 in Research in Computer Science and had the great joy of being present on this the rue du Chevaleret, near Place d’Italie) Automatics), normally a full-time position! unique occasion. and to create a DEA (Diplome d’Etudes His leadership was of profound and lasting At the early age of nineteen, Jacques- Approfondies, a set of advanced courses influence at INRIA. During his first weeks Louis Lions passed the entrance exam to that a doctoral student has to pass before at the head of this institute, he used his the highly coveted École Normale beginning a dissertation), specialising in incredible talents as an organiser to Supérieure de la rue d’Ulm. There he met Numerical Analysis. This DEA, from rejuvenate the organisation and objectives Bernard Malgrange, among others, and at which a considerable number of applied – in particular, by introducing the notion the end of their studies they both decided mathematicians now holding positions in of a project, gathering a clearly identified to opt for a university career in universities, at CNRS, or in industry, have team around a well-defined objective on a mathematics (a rather uncommon choice graduated over the years, was always highly specific theme. at a time when most ‘Normaliens’ would regarded. The degree is now one of the During his four-year term as president, rather teach the famed ‘classes de most successful components of the he strongly advocated the creation of start- Mathématiques Spéciales’ in the lycées). ‘Jussieu-Chevaleret Doctoral School of up companies by researchers from the They were then awarded a grant by CNRS Mathematical Sciences’, headed by Yvon institute and he initialised its (the National Centre for Scientific Maday. decentralisation through the creation of Research) to prepare their doctoral In 1973, at the early age of forty-five, similar institutes at Sophia-Antipolis and dissertations, and went to Nancy to work Jacques-Louis Lions had the highly Rennes. Through his personal prestige, under the guidance of a prestigious thesis unusual honour of being named professor the teams he was able to gather, and the advisor, Laurent Schwartz, who had just at the celebrated Collège de France and numerous first-class international received the Fields Medal for his theory of simultaneously elected to the French conferences that he organised there, he distributions in 1950. Academy of Sciences. At the Collège de greatly contributed to the fame of INRIA. EMS December 2001 21 OBITUARY From 1984 to 1992, he held another during his presidency were not limited to up numerical analysis departments at the high-level, and also normally full-time, Committee 2000. His efforts were also Universities of Malaga, Sevilla, Santiago de official position as President of CNES decisive in promoting the need for a Compostela, Lisboa, and at the (National Centre for Space Studies), where profound reform in the status of the Universidad Complutense de Madrid, he continued and developed the action of Academy; the principles of this reform modelled after the one he had created in his predecessor Hubert Curien, who had have now been accepted. He also played a Paris. In the same vein, he was the main just been named Minister of Research and major role in the creation of an Academy speaker in a 1997 European video- Technology. There he used not only his of Technology, always desired but never conference on ‘Mathematics and the eminent intellectual capacities but also his previously achieved. This academy was Environment’, organised in Madrid by eventually created on 12 December 2000. Jesus Ildefonso Diaz. He also chaired the As exemplified by his presidencies at Prize Committee that awarded the ten INRIA and CNES, Lions was an ‘Prizes for Young Mathematicians’, during exceptionally successful promoter of ever- the Third European Congress of closer ties between academic research, too Mathematics, held in Barcelona in 2000. often seen as disconnected from the real For many years, he also chaired the world, and the more pragmatic industrial Scientific Committee of the Istituto di research. In this spirit, he headed Analisi Numerica del CNR of the scientific committees in major public utility University of Pavia, headed for several companies, such as Météorologie decades by Enrico Magenes and then by Nationale, Gaz de France, France Telecom Franco Brezzi. and Electricité de France, and he held Together with Paul Germain, he high level advisory positions in major represented France at the 1975 meeting companies, such as Pechiney, Dassault on ‘Functional Analysis and Mechanics’ of Aviation, or Elf. the IUTAM (International Union for Jacques-Louis Lions’s influence Theoretical and Applied Mechanics), held extended far beyond frontiers. Since the in Luminy, where the other representatives beginning of his career, he was an were Klaus Kirchgässner from West talents for intelligent persuasion to indefatigable traveller who, in addition to Germany, Sir James Lighthill from the convince the French authorities that the the traditional venues in Europe and the United Kingdom, and William Prager directions that he advocated were well Americas, very quickly added more from the United States. founded. In this way, he played a major unusual ones to his list of destinations. For His intelligent proselytising was not role in the conception of the French- instance, as early as 1957 he set out for a limited to Europe, however. In China, for American ‘Topex-Poseidon’ space three-month visit to the Tata Institute of instance, he was one of the driving forces program for oceanography. Topex- Fundamental Research in Bombay – at the behind the creation in 1997 of the LIAMA Poseidon is also the name of the satellite time a genuinely adventurous trip! He (French-Chinese Laboratory of Computer that made it possible at last to understand enjoyed the splendour of the ancient Taj Science, Automatics, and Applied ‘El Niño’, a major event in climatology. Mahal Hotel and the hospitality of Mathematics), an offspring of INRIA and His influence was likewise a decisive factor Kollagunta Gopalaiyer Ramanathan, with Academia Sinica, housed ever since by the in the French-Russian negotiations that whom he contributed to the creation of an Institute of Automatics of the Academy of ultimately allowed Jean-Loup Chrétien applied branch of the Tata Institute on the Sciences in Beijing. He likewise played a and Michel Tognini to participate in campus of the Indian Institute of Sciences major role in the creation in 1998 of the manned space missions. in Bangalore, twenty years later. ISFMA (Chinese-French Institute of For many years his presence at the In 1966 he began an extended series of Applied Mathematics), splendidly housed Monday afternoon seances of the French visits to the former Soviet Union. by the Department of Mathematics of Academy of Sciences were rare. But he Frequently invited by the USSR Academy Fudan University in Shanghai, thanks to eventually gave new life to this noble of Sciences or by the Novosibirsk Institute the tireless efforts of its Director Li Ta- ‘Compagnie’ (as it is traditionally known for Computation, he initiated many tsien. among its members) when he became scientific exchanges with eminent soviet From 1991 to 1995 Jacques-Louis Lions President in January 1997 for the mathematicians such as Guri Marchuk, was President of the IMU (International customary two years. Immediately after Olga Oleinik, Lev Semenovitch Mathematical Union). During a meeting Lions took office, President Jacques Chirac Pontryagin, Ilia Vekua, Mark Visik and of this organisation in Rio de Janeiro, on 6 gave him the mission of supervising the Nicolay Nicolayevich Yanenko. One of his May 1992, he proposed that the year 2000 drafting of a document concerning the merits during this period, and not the be named ‘World Mathematical Year’. state of the art world-wide in each of the least, was to contribute greatly to the This proposal, which was later supported following areas: access to knowledge for all dissemination in the West of Soviet by UNESCO, turned out to be a genuine and electronic processing of information; research in applied mathematics. One success story that significantly contributed knowledge of our planet and ways of life; particular trip that left him with a lasting to the improvement of the image of and understanding life systems and impression was the journey that he mathematics among the general public improving health-care for all. He undertook in 1975 to Beijing, where he and helped to encourage mathematical immediately began to work on this was received with great ceremony. He was research in developing countries. ambitious undertaking by creating and particularly impressed there by the He likewise was a constant supporter of heading a ‘Committee 2000’, under his mathematical talents of Feng Kang, who the initiatives of the Third World Academy ongoing close supervision, whose task was had just independently rediscovered the of Sciences (TWAS), either directly or to analyse the three areas and make finite element method. He was also through colleagues from his group. proposals. Remarkably, in spite of the impressed by Feng Kang’s impetuosity Particularly noteworthy in this respect scope of this project, he was able to meet when he spoke about the Gang of Four! were his undertakings for the progress of the 2000 deadline he had set himself, and However, his international ventures were mathematical research in Africa. personally handed President Chirac the not limited to traditional scientific The mathematical works of Jacques- requested document during a ceremony at exchanges, as his talents as a lecturer, Louis Lions are immense. Alone, or in the Elysée Palace on 25 January 2000. He thesis adviser, and organiser produced collaboration, he wrote more than twenty even succeeded in having all the Members many disciples throughout the countries books, most of which have become classics and Corresponding Members of the he visited. As early as the 1960s, for (often translated into several foreign Academy invited for the occasion, a first instance, he was the adviser of Antonio languages), as well as more than five indeed! Valle, the first in a long series of students hundred papers. The different themes of However, Jacques-Louis Lions’s actions from Spain and Portugal, who in turn set his work are briefly described below, in 22 EMS December 2001 OBITUARY approximately chronological order. substance of another well-known book, by Jacques-Louis Lions and Robert He had, and will continue to have for a Inequalities in mechanics and physics (1972), Dautray. This work, which comprises long time, a considerable influence on that he wrote with Georges Duvaut. almost four thousand pages, is justly mathematics and its applications, not only He was equally interested in the regarded as the modern counterpart of the through his own work, but also through numerical simulation of these problems, at celebrated Courant-Hilbert work. that of the School he created and His on-going interest in problems with constantly kept in touch with. Over the small parameters led him to write Singular years this School, which numbered some perturbations in boundary value problems and fifty initial students and scores of students in optimal control (1973), in which he laid of students, etc., has acquired widespread down the foundations of the asymptotic fame, not only in university circles, but also analysis of such problems. The methods in industry – an accurate indication that and notions that he then introduced and the directions of research he envisioned analysed, such as a priori estimates, stiff and promoted were highly relevant. problems, boundary layers, multiple scales, If a single title were to be attached to and so on, were subsequently recognised as Jacques-Louis Lions’s mathematical works, fundamental for many applications; for it might be with a fair degree of accuracy instance, they later played a major role in that of ‘Partial differential equations in all the mathematical modelling of elastic their aspects: existence, uniqueness, structures and ‘multi-structures’ made of regularity, control, homogenisation, plates, rods or shells. numerical analysis, etc., and the Another field where small parameters applications they model, such as fluid and a time when it was realised that the arise naturally is in the modelling of solid mechanics, oceanography, applicability of finite difference methods composite materials – of constant use in climatology, etc.’. had reached its limits; for instance, these the aerospace industry, for instance. Their Jacques-Louis Lions produced his first methods do not perform well when the asymptotic analysis, a special case of what mathematical works in 1951. At the same problems to be approximated have rapidly became known as ‘homogenisation theory’, time, two major books were published, one varying coefficients or are posed on was abundantly developed and illustrated by Laurent Schwartz on the theory of domains with complicated geometries. On by applications in another seminal work, distributions and one by Sergei Sobolev on the other hand, the finite element method, Asymptotic analysis for periodic structures their applications to mathematical physics, already familiar to engineers when (1978), which he wrote with Alain as well as a founding paper by John von handling these types of difficulties, Bensoussan and George Papanicolaou. In Neumann and Robert Richtmyer on the remained essentially unknown to this book, a substantial number of numerical approximation of non-linear mathematicians. essentially empirical formulas used in the hyperbolic problems arising in With remarkable intuition, Jacques- modelling of periodic structures were hydrodynamics. Louis Lions immediately foresaw that it is rigorously justified for the first time, Inspired by these works, Lions’s first preferable to discretise the variational, or thanks notably to the compensated objectives were to undertake a systematic weak, formulations of partial differential compactness method of his students study of linear and non-linear boundary equation problems, rather than the partial Francois Murat and Luc Tartar and to the value problems – notably, by constantly differential equations themselves. oscillating test-functions method of Luc using the theory of distributions, and then Accordingly, he quickly pointed out to his Tartar. finding ways to numerically approximate group of colleagues and students the need In 1958, a fundamental work by Lev their solutions. for studying and analysing Galerkin Semenovitch Pontryagin on the optimal In 1954, he began a series of methods in general, and finite element control of systems governed by ordinary collaborations and lasting friendships with methods in particular. A productive differential equations (the objective was to eminent Italian mathematicians, such as period ensued, to which he himself control the trajectories of artificial Enrico Magenes, Guido Stampacchia, contributed with another classic, Numerical satellites) immediately attracted his Ennio de Giorgi and Giovanni Prodi analysis of variational inequalities (1976), co- attention. Through the contacts he (brother of the current President of the authored with Roland Glowinski and already had at that time with the European Union). One such collaboration Raymond Trémolières. engineering community, he quickly resulted in an exhaustive analysis of His 1969 book Some methods for solving became convinced that the next step was to boundary value problems posed in non-linear boundary value problems was a extend optimal control to distributed fractional Sobolev spaces, due in particular major contribution to the theory of non- systems – systems whose state is governed to the theory of interpolation between linear partial differential equations, which by partial differential equations. The Banach spaces that he initiated with Jack even today remains a substantial source of inclination that he then developed for the Peetre in 1961. This analysis is the object inspiration – it is unfortunate that this optimal control of such systems was always of the celebrated three-volume treatise book was never translated into English. In to remain at the centre of his mathematical Non-homogeneous boundary value problems this work, Lions introduced and interests. and applications (1968-70) that he wrote systematically analysed the so-called A pioneer, as always, he began by laying with Enrico Magenes. From 1965 to 1967, compactness methods, which play a key down the foundations of a general theory he developed with Guido Stampacchia the role in the existence theory for the Navier- in yet another celebrated book, Optimal foundations of the theory of variational Stokes and von Kármán equations, the control of systems governed by partial inequalities, as they appear (for instance) monotony methods he had developed with differential equations (1968), in which he in unilateral problems in elasticity. Jean Leray, and the regularisation and notably introduced an infinite-dimensional His inclination towards applications led penalty methods, which can for instance be version of the Riccati equation. him to propose a particularly elegant proof applied to the Schrödinger or Korteweg-de In two books co-authored with Alain of Korn’s inequality, based notably on a Vries equations. For the most part, the Bensoussan, Applications of variational fundamental result in distribution theory results found in this book are either due to inequalities to stochastic control (1978) and known as ‘Lions’s lemma’ (although himself or to his students – in particular, Impulse control and variational inequalities several other results of his bear the same Haïm Brezis and Luc Tartar. (1983), he continued his investigations by name!). He further developed Most of the works mentioned so far, considering in particular the optimal applications of the theory of variational together with the many generalisations control of systems that are not necessarily equations or inequalities to mechanics, by they led to, were assembled in the well posed, or that have multiple states. mathematically analysing Bingham fluid, monumental treatise Mathematical analysis After having so thoroughly analysed the friction, viscoelasticity and plasticity and numerical methods for sciences and main aspects of optimal control theory, models. These applications constitute the technology (1984-5), conceived and edited Lions shifted his interests to the study of EMS December 2001 23 OBITUARY ‘controlability’, a discipline that basically (as he was fond of saying) of the Merit, a distinction he received at the seeks to answer the following type of combination of partial differential hands of President Chirac on 23 February question: given a system in an arbitrary equations, boundary conditions, 1999. He was a member of twenty-two initial state, how can one devise a way of transmission conditions, non-linearities, foreign academies and Honoris Causa acting on it in such a way that its solution physical assumptions, etc., that enter these Doctor of nineteen universities. reaches a given final state in a finite time – models, Jacques-Louis Lions, together with He also received the most prestigious for instance, by imposing adequate Roger Temam and Shouhong Wang, was prizes and delivered the most coveted boundary conditions? able to study the existence and uniqueness lectures. He was in particular awarded During his prestigious ‘John von of solutions, in order to establish the three Prizes by the French Academy of Neumann Lecture’ at the SIAM Congress existence of attractors and to propose Sciences, the John von Neumann Prize in in Boston in 1986, he presented for the numerical methods. He even succeeded in 1986, the Harvey Prize from the Technion first time his now-famous ‘HUM’ (Hilbert teaching these works on a blackboard, a in 1991, and the Lagrange Prize at the Uniqueness Method) for the exact pedagogical tour de force! ICIAM meeting in Edinburgh in 1999. controlability of linear time-dependent In 1995, he began another series of Jacques-Louis Lions was proud to have had equations. He chose this particular works. With Evariste Sanchez-Palencia he terminology to emphasise the fact that the developed the theory of sensitive feasibility of such controlability is related problems, exemplified by the boundary in an essential way to the uniqueness of the value problems that appear in the theory solution to the adjoint problem, typically of linearly elastic membrane shells. In obtained by the Holmgren or the such problems – which in a sense constitute Carleman theorem. the antithesis of well-posed problems – This lecture was the starting point of arbitrarily small, yet arbitrarily smooth, numerous works by himself and his School. changes in the right-hand sides of the In particular, he began by publishing no equations may induce ‘sudden’ changes in fewer than three books on the subject in the properties of their solutions. It is the same year: Exact controlability, perhaps no coincidence that the analysis of perturbations and stabilisation of distributed such problems relies in particular on systems in two volumes (1988) and, with uniqueness theorems that bear John Lagnese, Modelling, analysis, and resemblance with those needed in the control of thin plates (1988), which contains HUM. an abundance of applications to the theory In his last works, Jacques-Louis Lions of elastic plates. In 1995, he established returned to the numerical analysis of with Enrique Zuazua the generic character parallel algorithms and domain of the controlability of the three- decomposition methods, in a long series of dimensional Stokes equations: if there is Notes aux Comptes Rendus de l’Académie des no approximate controlability for a given Sciences, most often co-authored with the rare honour of having shaken the hand open set, then it is always possible to find Olivier Pironneau and published from of Emperor Akihito, when he received the another arbitrarily close open set for which 1997 to 2001. In fact, these kinds of topics highly prestigious Japan Prize in 1991. It this type of controlability holds. had been on his mind for a long time: as was the climax of a perfectly and These works constituted yet another early as the 1980s, he had already been an meticulously organised week that had mark of his continuing interest in real-life ardent advocate of installing a parallel particularly impressed him! applications. He also was concerned to computer at INRIA. The main idea in On three occasions he was an invited propose numerically feasible these Notes is to introduce parallelism in speaker at the International Congress of approximation methods. These formed the continuous problem, rather than in the Mathematicians – in 1958, 1970, and 1974. the theme of an article co-authored with discrete one – an approach that is in fact He gave the John von Neumann Lecture at Roland Glowinski – an article so long that quite general, since it applies equally well the SIAM meeting in Boston in 1986, was its nearly three hundred pages took up two to any problem that is approximated by an plenary speaker at the ICIAM Congress in consecutive issues of Acta numerica (1994- iterative method, such as a fractional step Hamburg and at the SIAM Congress in 5). method, a decomposition method into Philadelphia in 1995, and held the Galileo Even though the last works of Jacques- subproblems in optimisation theory, a Chair at the University of Pisa in 1996. He Louis Lions lay in different areas, they domain decomposition method, and so also had the extremely rare honour for a continued to be partly influenced by the forth. scientist, especially for a mathematician, of methodology he had developed for One can only be impressed by these speaking before a parliament! As part of questions of controlability. immense works, whether by the quality, the celebrations for ‘World Mathematical In 1990, he started to express his great diversity, and novelty of the mathematics Year 2000’, he delivered an address interest in climatology in El planeta tierra. used, or by the permanent quest for new entitled ‘Will it ever be possible to In this book, which was directly published applications that were previously believed describe, understand, and control the in Spanish, he described in a masterly to be inaccessible. inanimate and animate world by means of fashion and with a remarkably accessible Like John von Neumann, whom he the languages of mathematics and style the most important problems in this deeply admired, Jacques-Louis Lions was a informatics?’ in front of the Cortes, who science, such as modelling, numerical visionary, who very quickly understood specially gathered for the occasion in simulation, sensitivity to initial conditions, that the availability of ever-increasing Madrid on 21 January 2000. etc. His last courses at the Collège de computational power could revolutionise He belonged to the most famous France, from 1994 to 1998, were on these the modelling of phenomena and thereby academies, such as the USSR Academy of subjects. improve our knowledge and mastery of the Sciences and the American Academy of The models found in climatology physical world, provided however that the Arts and Sciences, to which he was elected include complex systems of partial required mathematics was simultaneously in 1982 and 1986. In 1996, he was differential equations, such as those of created and developed. He admirably simultaneously elected to the Royal Society Navier-Stokes and of thermodynamics. contributed to this latter task. of the United Kingdom, the National But these systems had never been seriously Jacques-Louis Lions justly received Academy of Sciences of the USA, and the analysed from a mathematical viewpoint, numerous honours. Although he always Third World Academy of Sciences. Two although they had been extensively used remained modest about them, their list is years later he was elected to the Academia since the 1960s for numerical simulation in truly astonishing. He was Commander of Sinica of China and the Accademia weather forecasting. the French Legion of Honour and Great Nazionale dei Lincei in Rome. The In spite of the ‘truly diabolic complexity’ Officer of the French National Order of Pontifical Academy of Sciences, to which 24 EMS December 2001 OBITUARY he was elected in 1990, seemed to be equations aux dérivées partielles, Dunod, 1968; Ciarlet), 42 vols., Masson, 1985-97. particularly dear to him; it may be less well English translation: Optimal control of systems Handbook of numerical analysis (with P. G. known, but it is an unusually rare honour governed by partial differential equations, Springer- Ciarlet), 7 vols., North-Holland, 1990-2000. to become one of its members! Verlag, 1970. Nonlinear partial differential equations and their Who was the man behind all these Problèmes aux limites non homogènes et applications applications, Collège de France seminar (with D. endeavours? What I knew of him (with E. Magenes), 3 vols., Dunod, 1968-70; Cioranescu), 2 vols., Pitman, 1998-2001. convinced me that both his human and English translation: Non-homogeneous boundary professional qualities were truly value problems and applications, Springer-Verlag, Books dedicated to Jacques-Louis Lions exceptional. 1972-3. Analyse mathématique et applications, Jacques-Louis Lions wrote abundantly, Quelques méthodes de résolution des problèmes aux Contributions en l’honneur de Jacques-Louis very rapidly, and with an astonishing ease limites nonlinéaires, Dunod, 1969. Lions, Gauthier-Villars, 1988. – not only in mathematics, but also Les inéquations en mécanique et en physique (with Frontiers in pure and applied mathematics, A countless letters, his favourite means of G. Duvaut), Dunod, 1972; English translation: collection of papers dedicated to Jacques-Louis communication. He was a master with the Inequalities in mechanics and physics, Springer- Lions on the occasion of his sixtieth birthday fax, which he used with amazing efficiency! Verlag, 1976. (ed. R. Dautray), North-Holland, 1991. For instance, it was not uncommon for Some aspects of the optimal control of distributed Equations aux dérivées partielles et applications, each of his various collaborators at any parameter systems, CBMS Conference 6, SIAM, Articles dédiés à Jacques-Louis Lions, given time to receive four or five faxes per 1972. Gauthier-Villars, 1998. week, sometimes with up to thirty pages if Sur le contrôle optimal des systèmes distribués, their contents were mathematical. Monographie 20, Enseignement Even though he wrote abundantly, he Mathématique, 1973. Olga Arsienevka confessed that he rarely kept track of his Perturbations singulières dans les problèmes aux manifold letters, perhaps because he could limites et en contrôle optimal, Lecture Notes in Oleinik rely entirely on his memory, or perhaps Mathematics 323, Springer-Verlag, 1973. because he preferred to spare himself a Analyse numérique des inéquations variationnelles Professor Olga Arsienevna Oleinik herculean archival task! Let us hope that (with R. Glowinski and R. Trémolières), 2 vols., passed away on 11 October at the age of his correspondents had the good sense to Dunod, 1976. 76. She made her mark throughhout keep his letters, which could thus be later Numerical analysis of variational inequalities, the world with her articles (almost three compiled. North-Holland, 1981. hundred!) and her monographs. After By any measure, his abilities were Sur quelques questions d’analyse, de mécanique et de having completed her thesis under the astounding. For instance, he once told me contrôle optimal, Presses de l’Université de guidance of Professor Petrovski, she that it took him only a few weeks to write Montréal, 1976. began her career in the Moscow State the several hundred pages of his Applications des inéquations variationnelles au University. She became professor in the ‘Diplodocus’ lecture notes, mentioned contrôle stochastique (with A. Bensoussan), same university, and for a long period earlier. Likewise, his indifference to lack Dunod, 1978. was held the Chair of Differential of sleep or the most extreme jet-lag, and Asymptotic analysis for periodic structures (with A. Equations. She has guided much his freshness after lengthy flights, were Bensoussan and G. Papanicolaou), North- research, was the adviser of more than always a subject of astonishment among his Holland, 1978. fifty mathematicians, some twenty of travel companions. Some methods in the mathematical analysis of systems whom obtained the degree of Doctor of As John Ball put it so well, ‘Jacques- and their control, Science Press, Beijing and Science. The range of interests of Louis Lions was a man of considerable Gordon & Breach, 1981. Professor Oleinik was very wide, from personal magnetism and charm, whose Applications of variational inequalities to stochastic the study of real analytic manifolds (in charisma, brilliance as a teacher, and control, North-Holland, 1982. connection with Hilbert’s sixteenth accessibility attracted others to work with Contrôle impulsionnel et inéquations variationnelles problem) to the questions of existence him’. And indeed, it was obvious that (with A. Bensoussan), Gauthier-Villars, 1982. and uniqueness of solutions of linear Jacques-Louis Lions had an ample share of Impulse control and variational inequalities, and non-linear partial differential charisma, even if charisma is not easy to Heyden & Son, 1984. equations. define in a rigorous manner! He was also Contrôle des systèmes distribués singuliers, She is the originator of very general incredibly open and displayed such Gauthier-Villars, 1983. and elegant proofs of Korn’s inequality, amiable and simple manners that any one Analyse mathématique et calcul numérique pour les an essential tool in the theory of of his current students and collaborators sciences et les techniques (with R. Dautray), 3 vols., elasticity. She gave talks at numerous felt that they were at the centre of his Masson, 1984-8. international congresses and seminars in attention. Mathematical analysis and numerical methods for universities throughout the world. She He was also very brave in the face of science and technology, 9 vols., Springer-Verlag, was a member of the Russian Academy physical danger and suffering. Even when 1988-93. of Sciences and other academies, and the pain became unbearable, he never Contrôlabilité exacte, perturbations et stabilisation de was also a Doctor Honoris Causa of many complained, keeping on the contrary his systèmes distribués, 2 vols., Masson, 1988. foreign universities. Professor Oleinik compassion for others. All those who met Modelling, analysis and control of thin plates (with was awarded the medal of the Collège de him will cherish the memory of his warm J. Lagnese), Masson, 1988. France. J. Leray and J.-L. Lions invited personality, the vision that he so well El planeta tierra, Instituto de España, Espasa- her several times to this eminent conveyed, and his profound intelligence. Calpe, 1990. institution, since some of her work was Sentinelles pour les systèmes distribués à données related to that of those two distinguished Books by Jacques-Louis Lions incomplètes, Masson, 1992. mathematicians. Lectures on elliptic partial differential equations, Models for the coupled atmosphere and ocean (with She will also remembered as a lady Tata Institute, Bombay, 1957. R. Temam and S. Wang), Computational with a very strong personality. She was Equations différentielles opérationnelles et problèmes Mechanics Advances 1, North-Holland, very generous with her colleagues, and aux limites, Springer-Verlag, 1961. Amsterdam, 1993. her friendship, once acquired, was Problèmes aux limites dans les équations aux limitless. Her loss will be deeply felt by dérivées partielles, Presses de l’Université de Series edited by Jacques-Louis Lions the international mathematical Montréal, 1962. Nonlinear partial differential equations and their community. Méthodes de quasi-réversibilité et applications (with applications, Collège de France Seminar (with R. Lattès), Dunod, 1967; English translation: H. Brezis), 12 vols., Pitman-Longman, 1981-94. Mireille Chaleyat-Maurel, Université Pierre Quasi-reversibility methods and applications, Mathématiques appliquées pour la maîtrise (with P. et Marie Curie, Laboratoire de Probabilités, American Elsevier, 1969. G. Ciarlet), 21 vols., Masson, 1982-97. 16, rue Clisson et 175/179 rue du Chevaleret Contrôle optimal de systèmes gouvernés par des Recherches en mathématiques appliquées (with P. G. Bureau 4D16, 75013 Paris (France) EMS December 2001 25 SOCIETIES

UkranianUkranian MathematicalMathematical CongrCongressess (UMC-2001)(UMC-2001) Anatoly M. Samoilenko

The Ukrainian Mathematical Congress M.L. Horbachuk) greeting speeches at the opening was held in Kiev on 21-23 August 2001. Topology and geometry (Co-Chairs: ceremony of the Congress: It was dedicated to the 200th O.A. Borisenko and V.V. Sharko) I.R. Yukhnovsky, Head of the anniversary of the birth of M.V. Mathematical theory of control (Co- Committee on Science and Education at Ostrohradsky, a prominent Ukrainian Chairs: M.Z. Zhurovs’ky, V.S. Mel’nyk the Ukrainian Parliament, academician mathematician. and A.A. Chykrii) of the National Academy of Sciences of The Congress was organised by the Section sessions were held at the Ukraine (on behalf of the Ukrainian Institute of Mathematics of the National Institute of Mathematics of the National Parliament); Ya.S. Yatskiv, First Deputy Academy of Sciences of Ukraine, under Academy of Sciences of Ukraine and Minister of Education and Science of the auspices of the National Academy of M. Drahomanov National Pedagogic Ukraine, academician of the National Sciences of Ukraine, the Ministry of University. Academy of Sciences of Ukraine (on Education and Science of Ukraine, the 385 scientists participated in section behalf of the Ministry of Education and Institute of Applied Mathematics and sessions. Among them were 82 foreign Science of Ukraine); S.O. Dovhyi, Head Mechanics of the National Academy of mathematicians (52 from the CIS and of the Ukrainian State Committee on Sciences of Ukraine, T. Shevchenko 30 from other foreign countries). In Communications and Information (on Kiev National University, all, scientists from 27 countries behalf of the Ukrainian Government); M. Drahomanov National Pedagogic participated in the sessions; the I.V. Skrypnik, Academician-Secretary of University, the Ukrainian Charitable greatest number of foreign participants the Department of Mathematics and Foundation for Furthering came from Russia, USA, Germany, academician of the National Academy Development of Mathematical Science, Italy, Byelorussia and Uzbekistan. In of Sciences of Ukraine (on behalf of the the ‘Ukrtelecom’ joint-stock company, total, more than 1500 scientists from 40 Ukrainian Mathematical Society and and Kiev City State Administration. countries (including about 260 from the the Department of Mathematics of the This event became the first attempt to CIS and 160 from other foreign National Academy of Sciences of gather at one major scientific meeting countries) participated in the Ukrainian Ukraine); Rolf Jeltsch, EMS President all the scientists of Ukraine that work in Mathematical Congress and satellite (on behalf of the European mathematics and related fields, thus conferences. Below, we present the list Mathematical Society); Blagovest making it possible to assess the of satellite conferences. Sendov, academician of the Bulgarian contemporary state of this important 10-17 June: Stochastic Analysis and its Academy of Sciences, foreign member scientific direction and prospects for its Applications (Lviv) of the National Academy of Sciences of further development in Ukraine. 2-8 July: Third International Algebraic Ukraine (on behalf of the Bulgarian Within the framework of the Conference in Ukraine (Sumy) Academy of Sciences); W. Wendland Congress, twelve satellite international 9-15 July: Fourth International (Stuttgart); Nguyen Van Dao (Vietnam), scientific conferences were held in Conference on Symmetry in Non-linear President of the Hanoi National different fields of contemporary Mathematical Physics (Institute of University, foreign member of the mathematics. Mathematics, National Academy of National Academy of Sciences of The work of the Congress proceeded Sciences of Ukraine, Kyiv) Ukraine; M.M. Lavrent’ev (Russia), in thirteen parallel sections in the main 7-12 August: International Conference on Director of the Institute of Mathematics fields of mathematics: Complex Analysis and Potential Theory of the Siberian Division of the Russian Algebra and theory of numbers (Chair: (Kyiv) Academy of Sciences, academician of A.V. Roiter) 13-17 August: Theory of Functions and the Russian Academy of Sciences; Dynamical systems (Chair: Mathematical Physics (Kharkiv) D. Matarazzo (Italy); Roman O.M. Sharkovsky) 22-26 August: International Conference Andrushkiv (USA), Deputy President of Differential equations and non-linear on Functional Analysis (Institute of the T. Shevchenko Scientific Society; oscillations (Chair: A.M. Samoilenko) Mathematics, National Academy of V.G. Bar’yakhtar, member of the Complex analysis and potential theory Sciences of Ukraine, Kyiv) Presidium of the National Academy of (Chair: P.M. Tamrazov) 22-28 August: XV International Sciences of Ukraine, academician of the Mathematical physics (Co-Chairs: Conference on Non-linear Partial National Academy of Sciences of A.H. Nikitin and D.Ya. Petryna) Differential Equations NPDE-2001 (Kyiv) Ukraine; V.O. Marchenko, academician Teaching methods and history of 27-29 August: Differential Equations and of the National Academy of Sciences of mathematics (Co-Chairs: Non-linear Oscillations (Chernivtsi) Ukraine; Yu.O. Mitropolsky, Honorary O.M. Bogolyubov, M.I. Shkil’ and 27-29 August: Computational Director of the Institute of Mathematics M.I. Yadrenko) Mathematics and Mathematical Problems of of the National Academy of Sciences of Non-linear analysis (Chair:I.V. Skrypnik) Mechanics (Drohobych) Ukraine, member of the Presidium of Computational mathematics and 27-29 August: International Algebraic the National Academy of Sciences of mathematical problems of mechanics (Co- Conference (Uzhhorod) Ukraine, academician of the National Chairs: V.M. Koshlyakov, 11-14 September: Fourth International Academy of Sciences of Ukraine; I.O. Lukovs’ky, V.L. Makarov and Conference on Geometry and Topology V.V. Petryshyn (USA), foreign member I.V. Serhienko) (Cherkasy) of the National Academy of Sciences of Probability theory and mathematical 1-5 October: New Approaches to the Ukraine; M.I. Shkil’, Rector of the statistics (Co-Chairs: V.S. Korolyuk and Solution of Differential Equations M. Drahomanov National Pedagogic M.I. Portenko) (Drohobych) University, academician of the Academy Theory of approximations and harmonic In view of the large number of of Pedagogic Sciences. analysis (Co-Chairs: M.P. Korneichuk lectures delivered at the Congress, we Anatoly M. Samoilenko was Head of the and O.I. Stepanets’) mention only well-known Organising Committee of UMC-2001, is Theory of operators and differential mathematicians and those President of the Ukrainian Mathematical Society operator equations (Co-Chairs: representatives of the Ukrainian and is an Academician of the National Academy Yu.M. Berezans’ky and Parliament and Government who made of Sciences of Ukraine. 26 EMS December 2001 SOCIETIES Opening speech by will start in two weeks. The idea is to the educational level, starting with the offer existing journals to move from Bologna declaration of 1999, which has Rolf Jeltsch, EMS expensive commercial publishers to our been signed by 29 European Ministers of non-profit organisation. Education. They want to introduce a President In addition to these activities we work common framework for comparable on a political level in the European degrees, following the concept of a at the Ukranian Union. We try to make the scientific bachelor and a masters degree. Clearly programmes of the EU more usable for this change will have a great impact. Mathematical Congress mathematicians. For example, for you it Let me end with the remark that the will be of interest that up to now one EMS is happy to see the strong activities Let me thank the organisers and Prof. could not support Ukrainian participants of the Ukrainian mathematical Skrypnyk for the invitation and the very at conferences from EU money. However, community and its Mathematical Society warm welcome. I am very happy that I we have been able to push that this will be in all of mathematics, pure and applied, am allowed to represent the European changed in the 6th Framework and not to forget the important teaching Mathematical Society at this important programme which starts in 2003. of mathematics. This congress is the Conference. I read though the Moreover, it looks like the handling of showpiece for these activities. I am sure programme this morning and was very funds will be easier too. you all will enjoy the lectures, as I will. impressed by the richness of the Great changes are also happening on Thank you for your attention. presentations, with almost 400 lectures. Let me take the opportunity to tell you a little bit about the European Mathematical Society. The EMS was The life and scientific work of founded in 1990. It has a double structure, in the sense that it is a society of societies, but also of individual M. V. Ostrogradsky (born 1801) members. It consists of about 50 member societies covering all of Europe, from Iceland to Mykhailo Vasyliovych Ostrogradsky was of great importance in many branches of Georgia and from Norway to Israel and born in Pashenna village (now mathematics and mechanics. Portugal at the southern end. Subject- Pashenivka) in Poltava region on 24 Ostrogradsky’s scientific work was wise we cover all of mathematics, pure September 1801. His father and mother carried out during the first half of the and applied, up to and including came from the Cossack families of 19th century, the period when industrial applications. Ostrogradsky and Sakhno-Ustimovich, mathematicians tremendously extended It may not be known to you that you well known since the 17th century. He the scope of applications of their can use your reviewing of articles for the studied at the Poltava gymnasium and research, due to the success of the Zentralblatt to become an individual the Kharkiv University (Department of natural sciences. His research, too, was member. Members receive our Newsletter Physics and Mathematics), from which directed chiefly to the study of general every three months. he graduated with distinction in 1820 laws of nature. What are our scientific activities? The although did not get the diploma In his first work on the theory of heat, largest is of course the European because of the intrigues of the submitted to the St Petersburg Academy Congress of Mathematics. We are reactionary officialdom that ruled in the of Sciences in 1928, the young scientist already working hard together our university at that time. From 1822 to had already proved the formula that Swedish colleagues on the 2004 congress 1828 he continued his education in connects the integral over a volume and in Stockholm. I know that our colleagues Paris, where he obtained significant the integral over the surface (the from Sweden will seek funds to support scientific results. Ostrogradsky-Gauss formula). He was participants from Eastern Europe. Ostrogradsky’s first scientific work, The the first who understood the role of this During these congresses the EMS gives theory of waves in a vessel of cylindrical form formula and emphasised its importance ten prizes to young mathematicians in all (written in the jail, for not having paid throughout mathematics. One of the fields, and the Felix Klein Prize for an the apartment rent) was approved and main achievements of this work is a application in industry. published by the Paris Academy, and he formulation of the expansion of a For young researchers we organise two was proposed a position in the Lycée function as a series in eigenfunctions of a summer schools every year. This year we Henri IV. differential operator, and this became had one in St Petersburg, and one in By the time Ostrogradsky came back to the central problem in analysis for the Prague; its topic is the simulation of fluid Russia, he was already a famous scientist. whole century. and body interaction. Next year’s From 1828 he worked as a professor in His work A memoir on calculating summer schools will be in Israel on the officer classes of the Naval College, variations of multiple integrals, submitted Computational algebraic geometry and followed by the Communications to the St Petersburg Academy of Sciences applications, and in Romania in fluid Engineering Institute (from 1832), the in 1834, attracted a great deal of mechanics. At the beginning of Central Engineering College (from attention by contemporary September, EMS is co-organising a large 1840) and the Central Artillery College mathematicians. The results obtained in Conference in applied mathematics with (from 1841). this memoir laid foundations for the SIAM, the Society for Industrial and He spent the summer holidays in integral calculus of functions of many Applied Mathematics. Pashenna village working on his variables. These have long since become Before I move to other activities let me research. He died in Poltava on 1 classical and are now the main tool in the tell you that you can find a lot of January 1962 and, according to his will, theory of partial differential equations information about the EMS on our web was buried in Pashenna village, in his and the calculus of variations. page, http://www.emis.de In particular you family’s sepulchre. His series of works on the theory of will find the address of the committee to M. V. Ostrogradsky occupies one of integration of algebraic functions was a support Eastern Europeans to attend the most prominent places in the history significant contribution to the theory of conferences. Unfortunately the EMS is of mathematical science. Extraordinary algebraic functions started by Abel, financially weak and hence these funds talent, a bold and brilliant mind, high Gauss and Jacobi and, together with are very limited. mathematical erudition, and a good Liouville’s works, had a significant Currently the EMS is setting up a knowledge of the contemporary natural influence on the subsequent publishing house. The managing sciences permitted him to obtain results development of the theory. director will be Dr. Hintermann and he EMS December 2001 27 In addition to the above-mentioned works that contained a programme for his research, Ostrogradsky has many works related to the direct integration of ICIAM 2003 concrete problems of mathematical physics, as well as to problems in algebra, Update special functions, geometry, probability theory and the calculation of integrals. from the Congress Director Many theorems and formulas obtained by him became part of the standard curriculum in analysis and differential October 2001 equations, although his name is not In previous updates, I described the processes for choosing the invited speakers for always mentioned. ICIAM 2003. Vitally important in this was the excellent work by the International A significant part of Ostrogradsky’s Program Committee, ably chaired by Professor Ian Sloan. works deals with analytical mechanics. He was fortunate to find, independently We now take great pleasure in announcing the following 27 invited speakers for ICIAM of the Irish scientist Hamilton, one of the 2003: fundamental principles in mechanics, the principle of least action, and to obtain a Brian Anderson, Australia (systems, control and signal processing) generalised dynamics equation that has Marsha Berger, USA (mesh generation, CFD, scientific computing) numerous applications in modern Yann Brenier, France (non-linear PDE) physics, for studying the motion of Franco Brezzi, Italy (finite element methods, engineering applications) particles, astronomy, etc. Not only did Jennifer Tour Chayes, USA (statistical physics, Microsoft theory group) he solve many important general Mark Davis, UK (financial mathematics) problems, he also found solutions of James Demmel, USA (numerical linear algebra, simulation) important particular problems in Peter Deuflhard, Germany (modelling, simulation, optimisation) hydrostatics, hydrodynamics, elasticity David Donoho, USA (mathematical statistics, wavelets, visualisation) theory, gravitation theory, ballistics, the Yoshikazu Giga, Japan (Navier-Stokes, non-linear PDE) theory of shocks and celestial mechanics. Alice Guionnet, France (random interactions, probability, particle He is the author of fundamental material methods) in celestial and analytic mechanics. Tom Hou, USA (multiscale and free boundary problems) M. V. Ostrogradsky contributed to the Jonathan Keating, UK (dynamical systems, asymptotics, quantum chaos) development of the mathematical culture Rupert Klein, Germany (CFD, modelling, combustion) in Russia, so much so that it cannot be Nancy Kopell, USA (dynamics of the nervous system, mathematical overestimated. He founded a school of biology) Russian mathematicians who worked in Tom Leighton, USA (computer science, parallel algorithms, the net) mechanics and applied mathematics. Peter A. Markowich, Austria (semiconductors, kinetics, modelling) Being a Full Member of the St Petersburg Alexander Mielke, Germany (non-linear PDE, dynamics, continuum mechanics) Academy of Sciences, Ostrogradsky was Harald Niederreiter, Singapore (quasi-Monte Carlo methods, discrete very popular as a lecturer. His public mathematics) lectures helped to promote high ideas of Michael Ortiz, USA (solid mechanics, materials) science among Russian intellectuals, and George Papanicolaou, USA (waves, diffusion, multi-scale phenomena) in particular to extend the achievements Neil Sloane, USA (error correcting codes, integer sequences) of the French scientific school which was Philippe Toint, Belgium (non-linear optimisation) at the centre, at that time, of the Ernie Tuck, Australia (ship hydrodynamics, applied fluids) mathematical ideas in which he was most Henk van der Vorst, Netherlands (numerical linear algebra, iterative methods) interested. The French scientists Ying Lung-an, China (non-linear PDE, numerical methods) Cauchy, Laplace, Poisson, Lamé, Poinsot Vladimir Zakharov, Russia/USA (turbulence, integrable systems, kinetics) and others had a very high opinion of Ostrogradsky’s works. He was elected a Our webmaster, Dr Ross Moore, has constructed a lively and colourful page for each corresponding member of the Paris speaker and you are cordially invited to visit for an inspection. We hope you will agree Academy of Sciences, and a full member the slate of speakers is an outstanding representation of modern industrial and applied of the Rome, Turin and American mathematics. academies. There were many prominent scientists Recent events in the USA might have raised doubts about the attractiveness of air travel among Ostrogradsky’s students: I. O. to Australia. On that score, I’d like to reassure readers that Australia is a vibrant Vyshnegradsky, founder of automatic multicultural country in which peoples from approximately 150 countries live control theory; M. P. Petrov, founder of harmoniously. Australia has a long and cherished democratic tradition; indeed we are the theory of hydrodynamic friction, D. I. currently celebrating our 100 years of federation as a democratic nation. Terrorism is Zhuravsky, founder of the theory of more remote to Australia than to most developed countries. Moreover, the local calculations in bridge construction, and airlines have an excellent safety record. others. He wrote a number of textbooks and manuals. He also developed a fine It is now time to start making concrete plans to attend ICIAM 2003. If you wish to system of teaching methodology, and he make some form of a presentation, then the principal vehicles to do this will be influenced publishing in Russia, in the minisymposia, contributed presentations and poster presentations. Some details are middle of the 19th century, a number of already displayed on the web site www.iciam.org, and others will be added as deadlines textbooks that advocated progressive and procedures become clearer. methods in teaching. The ideas that come from the works of But now is the time to make your plans. We look forward to giving you a warm Aussie M. V. Ostrogradsky are topical in our welcome in July 2003. time, too. They find new applications, first of all, in mathematical physics and Dr Noel Barton theoretical physics, and in other branches Congress Director of modern science.

28 EMS December 2001 CONFERENCES hydrodynamics, coastal sea modelling, river, lake and estuary dynamics, wave modelling, multi-phase flow, acoustics, environmental fluid FForthcomingorthcoming conferconferencesences mechanics, high-performance computing in fluid mechanics, bio-fluids, material properties and Compiled by Kathleen Quinn fluids, industrial applications Call for papers: papers are invited on the topics outlined and others falling within the scope of Please e-mail announcements of European Web site: the meeting. Abstracts of no more than 300 conferences, workshops and mathematical http://www.worldses.org/wses/calendar.htm words should be submitted to the conference meetings of interest to EMS members, to secretariat, and should clearly state the purpose, [email protected]. Announcements should results and conclusions of the work to be be written in a style similar to those here, and March 2002 described in the final paper. Final acceptance sent as Microsoft Word files or as text files (but 18-19: Workshop on Under- and Over- will be based on the full-length paper, which if not as TeX input files). Space permitting, each determined Systems of Algebraic and accepted, must be presented at the conference. announcement will appear in detail in the next Differential Equations, Karlsruhe, Germany Each submitted paper is subject to a separate issue of the Newsletter to go to press, and Information: registration thereafter will be briefly noted in each new issue Web site: http://iaks-www.ira.uka.de/iaks- Programme committee: C.A. Brebbia (UK), until the meeting takes place, with a reference to calmet/ ADE M. Rahman (Canada), R. Verhoeven (Belgium) the issue in which the detailed announcement [For details, see EMS Newsletter 41] Organising committee: A. Chakrabarti (India), appeared. 21-22: Eighth Rhine Workshop on Computer G. Comini (Italy), L. Debnath (Florida), J.P. du Algebra, Mannheim, Germany Plessis (South Africa), M.M. El-Refaee Information: (Kuwait), R.C. Gupta (Singapore), D.B. Ingham January 2002 Web site: http://www.uni-mannheim.de/RWCA (Leeds), A. Jeffrey (Newcastle-upon-Tyne), A. 28-1 February: International Conference on [For details, see EMS Newsletter 41] Mendes (UK), T.B. Moodie (Canada), M.A. Factorization, Singular Operators and 26-4 April: International Centre for Noor (Canada), W. Perrie (Canada), H. Pina Related Problems, Funchal, Madeira, Mathematical Sciences EuroSummer School (Portugal), D. Prandle (UK), M.G. Satish Portugal and Instructional Conference on (Canada), P. Skerget (Slovenia), P.A. Tyvand [dedicated to the 70th birthday of Professor Combinatorial Aspects of Mathematical (Norway), L.C. Wrobel (Brunel) Gueorguii Litvinchuk] Analysis, Edinburgh, UK Organisers: Wessex Institute of Technology Programme committee: A. Antonevich Information: and University of Ghent, Belgium (Belarussia), A. Boettcher (Germany), B. Web site: Proceedings: will be published in hard cover Bojarskii (Poland), R. Duduchava (Georgia), M. www.ma.hw.ac.uk/icms/meetings/2002/cama book form by WIT Press; available to delegates Kaashoek (Netherlands), N. Karapetiants February 2002 at the time of registration and widely distributed (Russia), Yu. Karlovich (Mexico), V. [For details, see EMS Newsletter 41] after the conference through the international Kokilashvili (Georgia), N. Krupnik (Israel), V. book trade. Further details can be found at Mazya (Sweden), V. Rabinovich (Mexico), B. www.witpress.com Silbermann (Germany), I. Simonenko (Russia), April 2002 Location: the Cultural Centre of the Ghent I. Spitkovsky (USA), N. Vasilevskii (Mexico) 1-30 June: Trimester on Algebraic Topology, University ‘Het PAND’, a former Dominican Organising committee: Stefan Samko, Barcelona, Spain monastery, located in the historical center of the Chairman (Algarve), Victor Kravchenko Topics: algebraic topology, especially some city, on the banks of the river Leie (Algarve), Jose Molarinho Carmo (Madeira), topics in modern homotopy theory, including Deadlines: for abstracts, as soon as possible; for Jose Castanheira da Costa (Madeira), Rita homotopy finite group theory, functor calculus papers, 18 December Vasconcelos (Madeira), Antonio Ferreira dos and model category structures Information: contact Stacey Hobbs, Conference Santos (Lisboa), Francisco Teixeira (Lisboa), Main visitors: S. Dourlens, J. Greenlees, J. Secretariat, AFM 2002, Wessex Institute of Amarino B. Lebre (Lisboa), Ana Moura Santos Grodal, N. Kitchloo, R. Levi, J. Moller, D. Technology, Ashurst Lodge, Ashurst (Lisboa) Notbohm, B. Oliver, P.-E. Parent, N. Strickland Southampton SO40 7AA, UK, Information: contact Prof. Dr Stefan Samko, Location: Centre de Recerca Matemàtica, tel: 44 (0) 238 029 3223, fax: 44 (0) 238 029 Universidade do Algarve Faculdade de Ciencias Bellaterra 2853 e Tecnologia, Campus de Gambelas, Faro, 8000, e-mail: [email protected] Portugal Web site: http://www.wessex.ac.uk/conferences/ e-mail: [email protected] May 2002 2002/afm02/index.html Web site: http://www.digiways.com/fsorp/ 13-17: 34th Journées de Statistique, Brussels 19-26: Symmetry and Perturbation Theory and Louvain-la-Neuve, Belgium (SPT2002), Cala Gonone, Sardinia, Italy Information: Organisers: S. Abenda (Bologna), G. Gaeta February 2002 Web site: www.stat.ucl.ac.be/JSBL2002 (Milano and Roma), S. Walcher (Munich) 1-30 April: Special Research Trimester on [For details, see EMS Newsletter 41] Information: Dynamical Systems, Pisa 15-17: Fourth International Conference on Web site: Information: Advances in Fluid Mechanics, Ghent, http://web.tiscalinet.it/spt_spt/spt2002.html Web site: Belgium 22-24: Discrete Groups and Geometric http://www.math.sns.it/degiorgi/dynsys/ Aim: to provide a forum for the interchange of Structures, with Applications [For details, see EMS Newsletter 41] new ideas and the presentation of the latest work (Crystallographic Groups and their 11-15: Neural Networks and Applications in the field. Work discussed will appear in Generalizations III), Kortrijk, Belgium (NNA ‘02), Interlaken, Switzerland future volumes of the book series Advances in Main speakers: Y. Benoist (Paris), B. Farb Information: Fluid Mechanics, the Editorial Board of which (Chicago), D. Fried (Boston), F. Labourie Web site: serves as the scientific advisory committee for (Orsay), A. Lubotzky (Jerusalem, to be http://www.worldses.org/wses/calendar.htm the conference. The basic mathematical confirmed), G. Soifer (Bar Ilan), R. Grigorchuk 11-15: Fuzzy Sets and Fuzzy Systems (FSFS formulations of fluid mechanics and their (Moscow) ‘02), Interlaken, Switzerland computer modelling will be discussed, as well as Topics: recent developments concerning Information: the relationship between experimental and interactions between group theory and geometry, Web site: analytical results including geometric group theory, group actions http://www.worldses.org/wses/calendar.htm Topics: experimental versus simulation on manifolds, crystallographic groups and 11-15: Evolutionary Computations (EC ‘02) methods, numerical methods in fluid mechanics, generalisations (affine, polynomial, almost- Interlaken, Switzerland boundary element methods, fluid-structure crystallographic), discrete subgroups of Lie Information: interaction, convection, heat and mass transfer, groups, graphs of groups; applications in and EMS December 2001 29 CONFERENCES beyond the fields mentioned Castellini, SIMAI, c/o IAC/CNR - Viale del Gosson (Karlskrona), T. Iwai (Kyoto), R. Picken Programme committee: H. Abels (Bielefeld), Policlinico, 137 - I-00161 Rome; tel. +39-06- (Lisboa) and I. Vaisman (Haifa) Y. Felix (Louvain-la-Neuve), W. Goldman 88470213; fax +39-06-4404306; e-mail: International Standing Committee: B. (College Park), F. Grunewald (Duesseldorf), P. [email protected]; or P. Rughetti, Konopelchenko (Lecce), M. de Leon (Madrid), Igodt (Leuven/Kortrijk), K.B. Lee (Norman, IAC/CNR - Viale del Policlinico, 137 - I-00161 A. Odzijewicz (Bialystok), H. Sato (Nagoya) Oklahoma) Rome, tel. +39-06-88470249; fax +39-06- and W. Schempp (Siegen) Organising committee: K. Dekimpe, P. Igodt, 4404306; e-mail: [email protected] Sponsors: Bulgarian Academy of Sciences, W. Malfait (all at Kortrijk), Y. Felix (Louvain- Web site: http://www.iac.rm.cnr.it/simai (click California State University Chico, European la-Neuve) on ‘simai 2002’) Mathematical Society Programme: short communications and posters 28-31: 2nd International Conference on Proceedings: to be published by an Abstracts: should be sent to Advanced Computational Methods in internationally recognised scientific publisher. [email protected] Engineering (ACOMEN 2002), Liège, Proceedings of previous conferences can be Sponsors: K.U. Leuven Campus Kortrijk, Fund Belgium found at http://coral.dir.bg/geom.htm for Scientific Research Flanders (Belgium), Theme: advanced numerical and computational Fees: a nominal registration fee of $150 if paid F.W.O. Scientific Research Network methods, such as (adaptive) finite element, finite through a bank transfer up to 31 March; this ‘Fundamental methods and techniques in volume and finite difference methods, boundary covers a copy of the proceedings and the mathematics’ element methods, spectral methods and domain organised activities. Later registration paid Location: K.U. Leuven Campus decomposition techniques, applied to direct and directly upon arrival is $200 Information: inverse problems in the following themes: solid Information: e-mail: [email protected] and structural mechanics, acoustics and e-mail: [email protected], Web site: http://www.kulak.ac.be/workshop vibration control, heat/mass transfer and phase [email protected] 25-3: XXII International Seminar on Stability change, environmental engineering, fluid flow Web site: http://www.bio21.bas.bg/conference/ Problems for Stochastic Models (SPSM) and and porous media, electric and magnetic fields, 10-16: Aarhus Topology 2002, Aarhus, Seminar on Statistical Data Analysis (SDA), industrial topics, computational mathematics Denmark Varna, Bulgaria and simulation Information: Information: Aim: to act as a forum for engineers and applied Web site: http://www.imf.au.dk/AT2002/ Web site: http://stabil.fmi.uni-sofia.bg mathematicians, dealing with advanced [For details, see EMS Newsletter 41] [For details, see EMS Newsletter 41] numerical strategies, computational methods and 11-13: Third International Symposium on 27-29: Spring School on Frobenius Manifolds simulation in various engineering disciplines Remote Sensing of Urban Areas, Istanbul, in Mathematical Physics, Enschede, The Invited speakers: C. Beckermann (Iowa), T. Turkey Netherlands Belytschko (Illinois), A. Bossavit (France), M. Topics: new observation sensors (systems) for Information: Géradin (Belgium), K. Morgan (Wales), E. urban monitoring, high spatial resolution e-mail: [email protected] Onate (Spain, president of ECCOMAS), H. Van satellite sensor data for urban applications, 27-31: 6th Congress of SIMAI (Italian Brussel (Belgium), H. Van Duijn (Netherlands) digital photogrammetric applications in urban Society for Applied and Industrial Organising committee: M. Hogge (Liège), H. areas, monitoring urban growth (trend analysis, Mathematics), Chia, Island of Sardinia, Italy De Schepper (Ghent), R. Van Keer (Ghent), E. change detection), differentiation of the inner Scope: applied mathematics and the applications Noldus (Ghent) parts of cities, creating urban digital elevation of mathematics in technology, finance, Location: Campus Sart Tilman, Liège models, GIS/GPS technology for urban medicine, environment and society University applications, urban management systems, Main speakers: U. Barberis (Genoa), H. Information: hydrological/geological assessment of urban Berestycki (Paris), A. Murli (Naples), H. e-mail: [email protected] areas, meteorological/ecological assessment of Ockendon (Oxford), R. Rannacher (Heidelberg) Web site: http://cage.rug.ac.be/~acomen urban areas, national and international projects Languages: English and Italian using remote sensing and GIS, ecological Abstracts: in English, up to a maximum of 4 (urban) risk analysis in urban areas using remote pages, should be sent to June 2002 sensing, remote sensing and GIS for [email protected], indicating the type of 4-13: 3rd Linear Algebra Workshop BLED historical/archeological applications, rural presentation (invited, oral or poster; mini- 2002, Bled, Slovenia applications (natural resource management symposium or focus session) in the subject line Information: systems), using remote sensing and GIS for of the e-mail. The volume of abstracts and the Web site: http://www.ijp.si/ftp/pub/STOp/law/ sustainable urban development, digital/virtual Congress programme will be distributed at the [For details, see EMS Newsletter 41] city models and GIS based traffic management, registration desk. The format (Latex or Word) 5-9: Conference in Honour of Hans Wallin, radar remote sensing of urban areas, thermal for the preparation of the abstracts can be Umea, Sweden infra-red remote sensing of urban areas, remote downloaded from Information: sensing of urban vegetation, remote sensing of http://www.iac.rm.cnr.it/simai, by clicking on Web site: http://www.math.umu.se/aktuellt/ contaminated land in urban areas ‘simai 2002’ HWkonferens.htm Organising committee: Derya Maktav Programme committee: U. Barberis (Genoa), [For details, see EMS Newsletter 41] (Istanbul, Chair), Carsten Jürgens (Regensburg, V. Boffi (Rome), F. Brezzi (Pavia), E. De 6-15: Fourth International Conference on Co-chair), Filiz Sunar Erbek (Istanbul), Farouk Bernardis (Rome), G. Fotia (Cagliari), N. Geometry, Integrability and Quantization, El-Baz (Boston), Garik Gutman (NASA), Gomiero (Marano Ticino, NO), M. Primicerio Varna, Bulgaria Manfred Ehlers (Vechta), Ediz Hun (President, (Florence; President), L. Puccio (Messina), V. Aim: to bring together experts in classical and Environment Commission, Turkey), Orhan Valente (Rome) modern differential geometry, complex analysis, Altan (Istanbul), Hasan Akgün (Büyükçekmece Organising committee: V. Boffi (Rome; mathematical physics and related fields, to Municipality, Turkey), Arnon Karnieli (Ben President), N. Dessi (Cagliari), G. Fotia assess recent developments in these areas and to Gurion University), Robert Laurini (Lyon) (Cagliari), M. Gaviano (Cagliari), F. Maggio stimulate research in related topics Deadline: for abstract submission, 15 December (Cagliari), S. Seatzu (Cagliari; Vice-President), Main speakers: A. Calini (curve geometry and Information: contact Prof. Dr. Derya Maktav V. Valente (Rome) soliton theory), G. Naber (equivariant (Symposium Chair), Istanbul Technical Location: Congress Center at the Grand Hotel localisation: exactness of the stationary phase University, Department of Remote Sensing; e- Chia, Laguna approximation), R. Schmid (diffeomorphism, mail: [email protected]; Carsten Deadlines: for proposals of mini-symposia, gauge and loop groups, Lie groups of Jürgens,(Co-chair), Regensburg University, focus sessions and round tables, 15 December; pseudodifferential and Fourier integral Department of Geography; e-mail: for all presentations (oral and poster operators), W. Zakrzewski (geometry of sigma [email protected]; communications; communications in the frame models, to be confirmed) or, for general correspondence, inquiries and of mini-symposia and focus sessions; contents Organising committee: Ivailo M. Mladenov submission of papers, Filiz Sunar Erbek, of round tables; invited lectures), 28 February (Sofia), Gregory L. Naber (Chico) Ýstanbul Teknik Üniversitesi, Ýnþaat Fakültesi, Information: contact organising secretariat: G. Advisory committee: P. Exner (Praha), M. de 80626 Maslak, Istanbul, Turkey; tel: 0090-0212-

30 EMS December 2001 CONFERENCES 2853801; fax:0090-0212-5737027; e-mail: Sladek (Slovakia), S. Syngellakis 17-22: School on Population Dynamics, [email protected] (Southampton), Masa Tanaka (Japan), N. Bedlêwo, Poland Web site: http://www.ins.itu.edu.tr/deryamaktav Tosaka (Japan), T. Tran-Cong (Australia), W.S. Scope: organised within the EU Programme 17-19: 24th World Conference on Boundary Venturini (Brazil), O. von Estorff (Germany), Centre of Excellence coordinated by the Stefan Element Methods incorporating Meshless L.C. Wrobel (Brunel), T. Wu (USA) Banach International Mathematical Centre Solutions Seminar Sintra, Portugal Organisers: Wessex Institute of Technology, through the Package ‘Mathematical Modelling Scope: the internationally recognised forum for UK and University of Coimbra, Portugal and Analysis of Cellular Populations’ disseminating the latest boundary element Organising committee: C.A. Brebbia (UK), A. Theme: mathematical theory and methods method and its applications. BEM is a very Tadeu (Portugal), V. Popov (UK) applied to study populations of entities, active area of research with the method being Sponsors: International Society of Boundary including cells, genes, and biomolecules successfully applied to solve difficult Elements (ISBE), International Journal of Topics: adaptive dynamics, ecology, engineering and scientific problems. This Engineering Analysis with Boundary Elements epidemiology, physiology, structured includes the solution of non-linear and time- Proceedings: will be published in hard cover populations dynamics dependent problems. Considerable advances book form by WIT Press; available to delegates Programme: main courses: O. Arino (France), have also been made in the solution of complex at the time of registration, and widely distributed ecology; O. Diekmann, adaptive dynamics; M. fluid dynamic problems and the use of high after the conference through the international Iannelli (Italy), epidemiology; M.C. Mackey performance computing. The conference will book trade (Canada), physiology; G.F. Webb (USA), deal with the topics listed, as well as papers of a Deadlines: for abstracts, as soon as possible; for structured populations dynamics. There will more theoretical character. State-of-the-art papers, 15 January also be a series of one-hour lectures given by reviews and advanced mathematical and Information: contact Rachel Green, Conference members of the scientific committee and 15 computational aspects will also be discussed Secretariat, BEM 24, Wessex Institute of min. communications by participants Special feature: seminar on meshless methods, Technology, Ashurst Lodge, Ashurst, Programme committee: O. Arino (France), O. which will discuss the use of integral equations Southampton, SO40 7AA, UK; Diekmann (The Netherlands), M. Kimmel without meshes. Many techniques will be tel: 44 (0) 238 029 3223; fax: 44 (0) 238 029 (USA), A. Lasota (Poland), M.C. Mackey highlighted including, fundamental solutions, 2853 (Canada), P.K. Maini (UK), F. Przytycki (Main Galerkin, diffuse methods, localised collocation, e-mail: [email protected] Coordinator of the Project of Centre of cloud and diffusive methods and modified Web site: http://www Excellence, Poland), R. Rudnicki (Coordinator Trefftz techniques 17-21: Seventh International Conference on of the Package, Poland), Z. Taib (Sweden) Topics: dynamics and vibrations, fracture p-adic Functional Analysis, University of Organising committee: T. Kulpa (Poland), K. mechanics and fatigue, inelastic problems, Nijmegen, The Netherlands Pichór (Poland), R. Rudnicki (Chair, Poland), composite materials, plates and shells, contact Scope: analysis over valued fields other than the M. Tyran-Kamiñska (Poland) mechanics, geomechanics, material processing real or complex numbers (such as the p-adic Sponsors: European Commission, Polish State and metal forming, soil and soil structure number field or Krull valued fields). The main Committee for Scientific Research, Institute of problems, electrostatics and electromagnetics, mathematics subject classifications are 46S10, Mathematics Polish Academy of Sciences, biomechanics, inverse problems, fluid flow, 47S10, 32P05, 26E30 University of Silesia interfacial and free surface flow, transport Scientific committee: W. Schikhof (Nijmegen, Location: Mathematical Conference Centre, a problems, wave propagation problems, Netherlands), A. Escassut (Clermont Ferrand, palace complex in Bedlêwo acoustics, dual reciprocity method and basis France), C. Perez-Garcia (Santander, Spain) Grants: possible reduction of fee for a limited functions, fundamental principles, computational Speakers (preliminary list): J. Araujo, J.M. number of participants techniques, advanced formulations, sensitivity Bayod, M. Berz, A. Boutabaa, B. Diarra, A. Deadlines: for financial support, 20 January; for analysis and optimization, meshless methods Escassut, N. De Grande-De Kimpe, L. Van registration, 20 April seminar, fundamental solution method, source- Hamme, J. Kakol, A. Katsaras, H. Keller, A. Information: field superposition, diffuse methods, local Khrennikov, A. Kochubei, A. Lemin, H. e-mail: [email protected] meshless methods, modified Trefftz methods, Ochsenius, C. Perez-Garcia, Dinamerico Pombo Web site: http://www.math.us.edu.pl/cmmpd/ natural element methods, charge simulation jr, S. Priess, P. Ribenboim, A. Salinier, W. 18-22: Barcelona Conference on Stochastic methods, element-free Galerkin, cloud methods, Schikhof, N. Shell, W. Sliwa, S. Vega Inequalities and their Applications point collection methods Information: (EuroConference), Bellaterra, Barcelona, Call for papers: papers are invited on the topics e-mail: [email protected] Spain outlined and others falling within the scope of Web site: http://www.sci.kun.nl/math/p- Scientific committee: E. Giné, Ch. Houdré and the meeting. Abstracts of no more than 300 adic2002/ D. Nualart words should be submitted to the conference 17-21: XVth Householder Symposium on Organising committee: D. Nualart, F. Utzet, A. secretariat, and should clearly state the purpose, Numerical Linear Algebra, Peebles, Scotland Kohatsu and M. Jolis results and conclusions of the work to be Theme: numerical linear algebra Information: described in the final paper. Final acceptance Call for papers: see web site Web site: http://www.crm.es/stochineq will be based on the full-length paper, which if Programme committee: N. Higham 24-28: Conference on Mathematical accepted, must be presented at the conference. (Manchester, Chair), A. Bunse-Gerstner Modelling of Population Dynamics, Bêdlewo, Each submitted paper is subject to a separate (Bremen), T. Chan (Los Angeles), C. Davis Poland registration (Toronto), D. O’Leary (Maryland), M. Overton Scope: organised within the EU Programme Programme committee: G. Beer (Austria), (Courant Institute), G.W. Stewart (Maryland), Centre of Excellence coordinated by the Stefan M.B. Bush (Australia), C.Y. Cha (USA), C.S. H. van der Vorst (Utrecht), P. Van Dooren Banach International Mathematical Centre Chen (USA), A.H.-D. Cheng (USA), G. De Mey (Louvain-la-Neuve), C. Van Loan (Cornell) through the Package ‘Mathematical Modelling (Belgium), V. DeGiorgi (USA), N.A. Dumont Organising committee: P. Knight (Strathclyde), and Analysis of Cellular Populations’ (Brazil), A. El-Zafrany (UK), L. Gaul A. Ramage (Strathclyde), A. Wathen (Oxford) Topics: the focus will be on mathematical (Germany), G.S. Gipson (USA), M.A. Golberg Location: Peebles Hotel Hydro, Peebles, modelling and model analysis of populations at (USA), L. Gray (USA), S. Grilli (USA), K. Scotland various levels, including cells, genes, Hayami (Japan), M.S. Ingber (USA), D.B. Grants: support available for students and biomolecules and of population dynamics in the Ingham (Leeds), N. Kamiya (Japan), D.L others with limited access to other funding following broad themes: ecology, epidemiology Karabalis (Greece), A.J. Kassab (USA), J.T. Notes: the 11th Householder Prize for the best and infectious diseases, evolution, immunology Katsikadelis (Greece), E. Kita (Japan), W.J. thesis in numerical algebra written since 1 and cancer growth, physiology Mansur (Brazil), S. Mukherjee (USA), K. January 1999 will be awarded at the meeting Main speakers: U. An der Heiden (Germany), Onishi (Japan), F. Paris (Spain), H. Power Deadline: for abstracts, 11 December P. Auger (France), K.-P. Hadeler (Germany), K. (Nottingham), P. Prochazka (Czech Republic), Information: Sigmund (Austria), H.R. Thieme (USA). J.J. Rencis (USA), T.J. Rudolphi (USA), B. e-mail: [email protected] Programme committee: O. Arino (France), O. Sarler (Slovenia), E. Schnack (Germany), A.P. Web site: Diekmann (Netherlands), M. Kimmel (USA), A. Selvadurai (Canada), L. Skerget (Slovenia), V. http://www.maths.strath.ac.uk/~matrix/ Lasota (Poland), M.C. Mackey (Canada), P.K.

EMS December 2001 31 CONFERENCES Maini (UK), F. Przytycki (Main Coordinator of Hatzikyriakou (Greece), H-W. Henn (Germany), [in honour of the 70th anniversary of the birth of the Project of Centre of Excellence, Poland), R. D. Holton (New Zealand), M. Isoda (Japan), C. Prof. M.M. Lavrent’ev] Rudnicki (Coordinator of the Package, Poland), Julie (South Africa), F. Kalavassis (Greece), U. Theme: ill-posed problems, inverse problems, Z. Taib (Sweden) Kirchgraber (Switzerland), M. Kourkoulos tomography and other imaging modalities, Organising committee: T. Kulpa (Poland), K. (Greece), E. Koleza (Greece), B. Kutzler numerical analysis and applications Pichór (Poland), R. Rudnicki (Chair, Poland), (Austria), Th. Kyriazis (Greece), C. Laborde Call for papers; registration: see web site M. Tyran-Kamiñska (Poland) (France), M. Lambrou (Greece), Ch. Lemonidis Programme committee: V.G. Romanov ( Sponsors: European Commission, Polish State (Greece), J. van Maanen (Holland), W. Russia), Yu.E. Anikonov (Russia), M.I. Committee for Scientific Research, Institute of McCallum (USA), M. Majewski (United Arab Belishev (Russia), Yu.Ya. Belov (Russia), A.L. Mathematics Polish Academy of Sciences, Emirates), V. Makrakis (Greece), J. Mamona- Bukhgeim (Russia), G. Chavent (France), D. University of Silesia Downs (Greece), S. Negrepontis (Greece), B. Colton (USA), A.M. Denisov (Russia), H.W. Proceedings: to be published in Banach Center Osgood (USA), P. Pamfilos (Greece), S. Engl (Austria), A.M. Fedotov (Russia), Y. Iso Publications Papastavridis (Greece), T. Patronis (Greece), M. (Japan), S.I. Kabanikhin (Russia), O.A. Location: Mathematical Conference Centre, a Petrakis (Greece), J.D. Phillips (USA), D. Potari Klimenko (Russia), R. Kress (Germany), M.M. palace complex in Bêdlewo (Greece), D. Quinney (UK), A. Radunskaya Lavrent’ev (jr.) (Russia), A. Lorenzi (Italy), Grants: possible reduction of fee for a limited (USA), Ch. Sakonidis (Greece), G. Schubring B.A. Mair (USA), G.I. Marchuk (Russia), Z. number of participants, especially for PhD (Germany), M-K. Siu (China), J. Uhl (USA), B. Nashed (USA), V.V. Pickalov (Russia), P. students and young researchers Waits (USA), T. Wang (USA), L-P. Yee Sabatier (France), O. Scherzer (Germany), S.I. Deadlines: for financial support, 20 January; for (Singapore), Th. Zachariades (Greece) Smagin (Russia), V.N. Strahov (Russia), Y.M. registration, 20 April Academic sponsors (provisional): Bowdoin Sultangazin (Kazakhstan), J. Sylvester (USA), Information: College, Capital University, Duke University, G. Uhlmann (USA), V.V. Vasin (Russia), A.G. e-mail: [email protected] ETH-Zurich, Ewha Womans University, Yagola (Russia), Sh. Yarmukhamedov Web site: http://www.math.us.edu.pl/cmmpd/ Franklin University, Harvey Mudd College, (Uzbekistan) 27- 3 July: Fifth International Conference on Middle East Technical University, Pomona Sponsors: Sobolev Institute of Mathematics, Curves and Surfaces, Saint-Malo, France College, Project Kaleidoscope, Stanford Novosibirsk State University, Krasnoyarsk State Information: University, Ohio State University, Université University, Russia Foundation for Basic e-mail: saint-malo@imag Paris 7 Denis Diderot, University of Arizona, Research Web site: http://www-lmc.imag.fr/saint-malo/ University of Athens, University of Crete, Deadlines: for preregistration, 31 December; for University of Southern Queensland, John Wiley abstracts, 31 May and Sons Inc. Information: July 2002 Location: Conference Centre of Knossos Royal e-mail: [email protected] Village, Hersonissos, Crete, Greece Web site: www.math.nsc.ru/conference/mml 1-6: Advanced Course on Mathematical Grants: probably support for participants from 10-11: Colloquium Logicum 2002, Münster, Finance: Models, Bellaterra, Barcelona, countries in a difficult economic situation and Germany Spain young mathematicians [satellite conference of Logic Colloquium 2002] Coordinator: Joan del Castillo Deadlines: for early registration, 31 January; for Information: Information: abstracts, already passed; for full papers 30 Web site: http://wwwmath.uni-muenster.de/ Web site: http://www.crm.es/matfin January LC2002/ 1-6: 2nd International Conference on the Information: [For details, see EMS Newsletter 41] Teaching of Mathematics at Undergraduate e-mail: [email protected], 25-30: Wireless And Optical Communications Level, Chersonissos, Crete, Greece [email protected], [email protected] (WOC ‘02), Miedzyzdroje, Poland Topics: educational research, technology, Web site: http://www.math.uoc.gr/~ictm2 Information: innovative teaching methods, curricula 2-6: 2002 Barcelona Conference on Algebraic Web site: innovations, preparation of teachers, Topology (EuroConference), Barcelona, http://www.worldses.org/wses/calendar.htm mathematics and other disciplines, distance Spain 25-30: Nanoelectronics, Nanotechnologies learning Scientific committee: C. Broto, C. Casacuberta, (NN ‘02), Miedzyzdroje, Poland Main speakers: Hyman Bass (USA), Deborah H. Miller Information: Ball (USA), Jean-Pierre Bourguignon, (France), Organising committee: J. Aguadé, C. Web site: Miguel De Guzman (Spain), Peter Galbraith Casacuberta http://www.worldses.org/wses/calendar.htm (Australia), Oh Nam Kwon (Korea), Joanna Information: Mamona-Downs (Greece), Verdiana Masanja Web site: http://www.crm.es/2002bcat (Tanzania), Alan Schoenfeld (USA), Man 15-18: Modular Curves and Abelian Varieties September 2002 Keung Siu (Hong Kong, China), David Smith (EuroConference), Bellaterra, Barcelona, 3-7: 8th International Conference on (USA), Tosun Terzioglu (Turkey) Spain Stability, Control and Rigid Bodies Call for papers: abstracts for paper or poster Coordinator: J. Quer Dynamics, Donetsk, Ukraine presentation should be submitted; authors of Information: Theme: problems of general mechanics, proposals accepted for paper presentation may Web site: http://www.crm.es/mcav02 stability and control theories submit an article for inclusion in the 16-22: 7th International Spring School: Topics: stability theory, control in dynamical proceedings. Full papers will be reviewed by Nonlinear Analysis, Function Spaces and systems, dynamics of rigid body and of multi- members of the international programme Applications (NAFSA 7), Prague, Czech body systems, methods of rigid body dynamics committee. The proceedings will be published Republic in the theory of elasticity by J. Wiley Inc. and available at the conference. Information: Main speakers: A. Agrachev (Russia), L. Chua See below for deadlines Web site: http://www.math.cas.cz/~nafsa7 (USA), C. Corduneanu (USA), A. Fradkov International programme committee: I. [For details, see EMS Newsletter 40] (Russia), B. Jakubczyk (Poland), W. Respondek Vakalis (USA; Chair), D. Hughes-Hallett (USA; (France), V. Rumyantsev (Russia), H. Troger Co-chair), Ch. Kourouniotis (Greece; Co-chair), (Austria), S. Vasilyev (Russia) C. Tzanakis (Greece; Co-chair), M. Abboud August 2002 Languages: Ukrainian, Russian, English (Lebanon), A. Arcavi (Israel), H. Arikan 3-10: Logic Colloquium 2002 (ASL European Programme: 45-minute invited plenary (Turkey), M. Artigue (France), G. Baker (USA), Summer Meeting), Münster, Germany lectures, 30-minute section lectures, short E. Barbin (France), W. Barker (USA), J. Information: presentations (15-minute communications and Belward (Australia), B. Blyth (Australia), R. Web site: http://www.math.uni-muenster. posters) Borelli (USA), P. Cretchley (Australia), F. de/LC2002/ Call for papers: abstracts (up to 1 page, in Demana (USA), J. Engelbrecht (South Africa), [For details, see EMS Newsletter 41] TeX) should be submitted by e-mail Y. Ersoy (Turkey), V. Farmaki (Greece), F. 5-9: International Conference on Ill-Posed Programme committee: A. Agrachev (Russia), Furinghetti (Italy), E. Gavosto (USA), A. and Inverse Problems, Novosibirsk, Russia F. Chernousko (Russia), L. Chua (USA), C. Gleason (USA), N. Hadjisavvas (Greece), C. 32 EMS December 2001 CONFERENCES Corduneanu (USA), M. Fliess (France), A. Jaeger (Heidelberg), J. Kacur (Bratislava), J. Theory and Applications (SSTA2002), Fradkov (Russia), L. Hatvani (Hungary), B. Komornik (Bratislava), G. Meyer (Atlanta), K. Gdañsk-Jurata, Poland Jakubczyk (Poland), D. Klimov (Russia), V. Mikula (Bratislava), M. Rumpf (Duisburg), J.A. Aim: to bring together scientists, designers, Kuntsevich (Ukraine), V. Koshlyakov Sethian (Berkeley), M. Vajtersic (Bratislava), G. engineers and other specialists in shell (Ukraine), I. Lukovskii (Ukraine), G. Liu Wittum (Heidelberg) structures in order to discuss important (China), V. Matrosov (Rusiia), K. Peiffer Organising committee: A. Handlovicova, M. results and new ideas in this field of activity (Belgium), F. Pfeiffer (Germany), W. Komornikova, Z. Kriva, K. Mikula, P. Struk, D. Topics: theory and analysis of shells (linear Respondek (France), V. Rumyantsev (Russia), Sevcovic, M. Stevulova and non-linear theory, constitutive laws, A. Savchenko (Ukraine), W. Schiehlen Location: Hotel Permon, Podbanske shells and plates with internal (Germany), V. Shevchenko (Ukraine), V. Deadlines: preliminary registration, 31 microstructure, hybrid and branched Storozhev (Ukraine), H. Troger (Austria), S. December; submission to proceedings, 30 April; structures, beam-shell interaction, stability, Vasilyev (Russia), V. Vujichich (Yugoslavia) registration, 31 May; payment, 31 May (regular dynamics, optimisation, reliability, Organising committee: A. Kovalev (Chair, conference fee); final submission of revised sensitivity, limit load analysis); numerical Institute of Applied Mathematics and Mechanics version to proceedings, 21 June; late analysis of shell structures and elements of the National Academy of Sciences of registration, 15 August; final payment, 15 (computer methods, analysis of non-standard Ukraine), A. Stupin (Co-chair, Donetsk National August (late conference fee) problems, development of software University), B. Konosevich (secretary, IAMM Information: packages); design and maintenance of shell NASU) Web site: http://www.math.sk/alg2002 structures (industrial applications in civil, Proceedings: on presentation of the programme e-mail: [email protected] power, mining and mechanical engineering, committee, selected proceedings to be published 10-20: Advanced Course on Geometric 3- and in the automotive, shipbuilding, in scientific journals Manifolds, Bellaterra, Barcelona, Spain aerospace and chemical processing Location: the boarding-house of Donetsk Coordinator: Joan Porti industries, shell design codes and procedures National University on the Azov sea coast Information: (e.g. Eurocode), case studies of various shell Deadlines: for pre-registration, 31 January; for Web site: http://www.crm.es/geom-mani structures and failure problems) abstracts, 31 May 20-25: International Conference on Programme: general lectures and contributed Information: Computational Methods in Science and papers presented as lectures e-mail: [email protected] Engineering (CMMSE-2002), Alicante, Spain Languages: English and Polish Web site: Theme: numerical analysis, computational Scientific committee: Wojciech Pietraszkiewicz http://www.iamm.ac.donetsk.ua/conf2002.html physics, computational chemistry (chairman), Jan Awrejcewicz, Jacek 4-7: International Conference on Dynamical Topics: celestial mechanics, computational Chróœcielewski, Micha³ Kleiber, Pawe³ Methods for Differential Equations, chemistry and physics, computational K³osowski, Piotr Konderla, Marian Królak, Valladolid, Spain engineering, computational mathematics, Tomasz Lewiñski, Czes³aw Szymczak, Information: computational statistics, high-performance Krzysztof Wiœniewski, Roœcis³aw Tribi³³o, Web site: http://wmatem.eis.uva.es/~dmde02/ computing, industrial mathematics, Zenon Waszczyszyn, Czes³aw WoŸniak, Jerzy [For details, see EMS Newsletter 41] mathematical economics and finance, Zió³ko 8-13: ALGORITMY 2002, Conference on mathematical models for the information society Organising committee: Department of Scientific Computing, High Tatra Mountains, Chairs: J.M. Ferrandiz (Spain), D.L. Structural Mechanics, Faculty of Civil Podbanske, Slovakia Richardson (USA) (celestial mechanics), E. Engineering, Technical University of Gdañsk, Theme: applied mathematics, numerical Brandas (Sweden), D. Truhlar (USA), D. Belkic Poland methods, computational science and (Sweden) (computational chemistry and Proceedings: accepted abstracts (2 pages) will visualisation physics), K.J. Bathe (USA), R. Lewis (UK) be included in the conference book of abstracts, Scope: computational realisations and analysis (computational engineering), J. Butcher (New available for the participants at registration. of algorithms solving real problems from all Zealand), D.J. Higham (UK), T. Simos Full-length manuscripts of selected papers will branches of sciences, engineering, technology, (Greece), J. Xu (USA) (computational be further considered for publication in a special medicine, finance and other applications mathematics), M.J. Bayarri (Spain) volume of a recognised technical journal Topics: computational fluid dynamics, non- (computational statistics), H. Arabnia (USA), Location: Hotel Neptun in the leisure region of linear heat and mass transfer, modelling of flow C.J.K. Tan (Canada) (high performance the Hel Peninsula on the Baltic Sea in porous media, image processing and computing), C. Dawson (USA) (industrial (http:\\www.hotelneptun.gda.pl) computer vision, data analysis and pattern mathematics), M. Ojeda (Spain), P. Vojtás Grants: a limited number of fellowships for recognition, computational finance, free (Eslovaquia) (mathematical models for the distinctive young researchers (less than 35 years boundary problems, inverse problems, scientific information society) old) from Eastern Europe, to cover participation visualisation, software for scientific Proceedings: selected papers will appear in in the Conference but not travel computations several special issues of the Journal of Fees: registration fee, which covers full-board Main speakers: A. Bourlioux (Montreal), F. Computational and Applied Mathematics accommodation and the book of abstracts, is Cao (Paris), R. Eymard (Paris), M. Falcone (www.elsevier.nl/inca/publications/), and the approximately $300 US; $250 US for (Rome), P. Frolkovic (Heidelberg/Bratislava), J. Journal of Computational Methods in the accompanying persons Fuhrmann (Berlin), M. Gander (Montreal) R. Sciences and Engineering Deadlines: for pre-registration, 31 December; van Keer (Ghent), M. Lukacova-Medvidova (www.demon.co.uk/cambsci/jcmse.html) for submission of 2-page abstracts, 30 April (Brno), M. Ohlberger (Freiburg), M. Rumpf Location: University of Alicante, Spain Information: contact SSTA2002 Organising (Duisburg), A. Schmidt (Bremen), J.A. Sethian Deadline: for abstracts, 15 December Committee, Department of Structural (Berkeley), G. Wittum (Heidelberg) Information: Mechanics, Faculty of Civil Engineering, Programme: invited plenary lectures, 25- e-mail: [email protected] Technical University of Gdañsk, G.Narutowicza minutes contributed talks, poster session Web site: www.ua.es/cmmse2002/ 11/12, 80-952, Gdañsk, Poland; tel: +48-58-347- Call for papers: refereed conference 23-27: Ramification in Arithmetic and 21-47; fax: +48-58-347-16-70 proceedings of contributed lectures will be Geometry, Paris, France e-mail: [email protected] published before the conference. Papers related Organisers: A. Abbes (Paris), B. Erez Web site: http://www.pg.gda.pl/ssta2002 to the topics of the conference are invited (Bordeaux), T. Saito (Tokyo) (previous issues are at http://www.iam. Location: Institut Galilee, Universite Paris 13 fmph.uniba.sk/amuc/_vol70n1.html). Information: February 2003 Proceedings of plenary lectures and selected http://www-math.math.univ-paris13.fr 5-7: 4th IMACS Symposium on papers of participants will appear after the /~ramifica/ Mathematical Modelling, Vienna, Austria conference in the Springer-Verlag journal Information: Computing and Visualization in Science Web site: Programme committee: E. Baensch (Berlin), P. October 2002 http://simtech.tuwien.ac.at/MATHMOD Brunovsky (Bratislava), G. Dziuk (Freiburg), W. 9-11: 7th Conference on Shell Structures, [For details, see EMS Newsletter 41]

EMS December 2001 33 RECENT BOOKS vidual chapter concludes with exercises that are substantial for understanding what follows. The typography of the book is not ideal and the notation is a bit complicated. RecentRecent booksbooks The topic of the book is very geometrical, edited by Ivan Netuka and Vladimír Sou³ek and more pictures could have been expect- ed. In particular, many of the computa- tions could be nicely complemented by pic- Books submitted for review should be sent to the bras, elementary dimension theory in lat- tures appealing to geometrical intuition. following address: tices, algebras with involution and order Despite these remarks, the textbook is a Ivan Netuka, MÚUK, Sokolovská 83, 186 75 derivation. A self-contained elementary good and useful introduction to hyperbol- Praha 8, Czech Republic. introduction to C*-algebras and von ic geometry, and can be recommended for Neumann algebras is presented in Chapter undergraduate courses. (zs) S. Abbott, Understanding Analysis, 2. The next chapter presents the duality of Undergraduate Texts in Mathematics, the ideal structure of C*-algebras and von D. H. Armitage and S. J. Gardiner, Springer, Berlin, 2001, 257 pp., DM 79, Neumann algebras and the facial structure Classical Potential Theory, Springer ISBN 0-387-95060-5 of the state space; this chapter also Monographs in Mathematics, 2001, 333 pp., This book aims to build up the elements of includes an order-theoretic charac- DM 159, ISBN 1-85233-618-8 analysis properly – that is, with a good terisation of compressions. Chapter 4 is Over the past century, the potential theory level of understanding. It contains funda- devoted to the normal state space of the of Laplace’s equation (classical potential mental results on real numbers, limits and algebra of all bounded operators on a theory) has undergone its most outstand- continuity, differentiation, sequences, Hilbert space, explaining also how it can ing and rapid development. Everybody sums of functions and the Riemann inte- be inscribed in a Euclidean ball and how its working in new branches of potential theo- gral. In many places, the book could be lattice of faces corresponds to the ry (non-linear theories, probabilistic and used for an introductory analysis course. Grassmannian. Chapter 5 concerns states, axiomatic approaches to potential theory, In others, the material presented in the representations and orientations of C*- pluripotential theory, functions of one or text would be appropriate after a calculus algebras. The next chapter surveys the more complex variables, etc.) should bene- course. The author’s intention was ‘to elements of structure theory and continues fit from the knowledge of classical theory. restore intellectual liveliness of the course with a study of symmetries and reflections There are brilliant textbooks and mono- by offering to beginning students access to in von Neumann algebras. Orientations graphs on potential theory, such as those some truly significant achievements of the and von Neumann algebras form the final of Brelot, Helms, Doob, Landkof. The subject’. In other words, he tries to present chapter. book by Armitage and Gardiner follows the relatively advanced topics in an accessible This volume contains complete proofs of most classical text of Helms and comple- way, and thus make the course interesting basic results and commentaries on ments it with new results and approaches. and worthy of effort. advanced topics of independent interest The first chapter introduces and sum- Among the topics treated in the book are with references to the literature, and a dis- marises the main properties of harmonic completeness of the reals, double summa- cussion of applications to physics. The functions (Laplace’s equation, mean value tion and products of series, Baire’s theo- monograph is designed for experts in properties, convergence properties, the rem, continuity of derivatives, a continuous operator algebras, as well as for graduate Kelvin transform, the Poisson integral and nowhere-differentiable function (Takagi students and researchers interested in the Harnack’s inequalities). There follows a approach) and Lebesgue’s criterion for field. It can also serve as a quick intro- chapter on harmonic polynomials. Riemann integrability. In the last chapter, duction to C*-algebras and von Neumann Elementary properties and new results the author shows that for the generalised algebras for any mathematician who wants concerning subharmonic functions are Riemann integral all derivatives are inte- to learn the subject. The book is under- described in Chapter 3 (approximation of grable, and that the set of continuous func- standable with a basic knowledge of real subharmonic functions by smooth ones, tions on a compact interval I, differen- and complex analysis, measure theory and convexity and subharmonicity and har- tiable at least at a point, is of the first cate- functional analysis, and spectral theory. monic majorants). The next chapters are gory in C(I), and presents basic results on (jl) devoted to a penetrating study of poten- Fourier series. tials (Green functions, the Riesz decompo- This book will be useful for gifted stu- J. W. Anderson, Hyperbolic Geometry, sition, the distributional Laplacian, classi- dents for supplementary reading to a basic Springer Undergraduate Mathematics Series, cal boundary limit theorems), polar sets analysis course or for students not special- Springer, London, 1999, 230 pp., DM 59, and capacity (removable singularities, ising in mathematics who wish to put this ISBN 1-85233-156-9 reduced functions, Choquet capacitability material on a solid basis. (jive) This textbook is an introduction to non- theorem, logarithmic capacity, Hausdorff Euclidean geometry designed for under- measure and capacity) and the classical E. M. Alfsen and F. W. Shultz, State graduate students. It is based mainly on Dirichlet problem (Perron-Wiener-Brelot Spaces of Operator Algebras. Basic Theory, the Poincaré half-plane model, and is writ- solutions, harmonic measure, negligible Orientations and C*-products, Mathematics: ten in a very understandable way; with only sets, superharmonic extension). The final Theory and Applications, Birkhäuser, Boston, elementary knowledge needed for its read- three chapters are deeper and introduce 2001, 350 pp., DM 170, ISBN 0-8176-3890- ing. topological concepts from potential theo- 3 and 3-7643-3890-3 In Chapter 1, the author defines the ry: the fine topology (thin sets, fine limits, This monograph is devoted to the theory Poincaré model and its points and lines. Wiener’s criterion, harmonic approxima- of state spaces of C*-algebras and von In the next chapter, the group of transfor- tion), the Martin boundary (minimal har- Neumann algebras and their geometry. mations preserving the system of lines is monic functions, the Martin representa- The states determine representations of carefully studied. Chapter 3 introduces tion, the boundary Harnack principle and the algebra, and its algebraic stucture is the metric properties of geometry as the Martin boundary of Lipschitz domains) encoded in the geometry of the state space. invariants of this group, and Chapter 4 and boundary limits (swept measures and The theory of operator algebras has wide briefly exposes the possibility of getting the Dirichlet problem for the Martin com- applications to physics, and there have new models by transferring the half-plane pactification, minimal thinness, the Fatou- recently been applications to various fields geometry by diffeomorphisms. In Chapter Naïm-Doob theorem). of pure mathematics (foliations and knot 5, convexity, area and trigonometry are Each chapter concludes with a set of theory, Banach manifolds and infinite- studied and the Gauss-Bonnet Formula is exercises, either routine or leading to dimensional holomorphy). proved. Chapter 6 presents the discrete results from the research literature. At the The introduction includes convexity, subgroups of the group of motions. end of the book, there are brief historical ordered vector spaces and ordered alge- The book is well structured. Each indi- notes and an Appendix where less elemen- 34 EMS December 2001 RECENT BOOKS tary results from analysis are stated without between the definitions of Kurzweil- designs, Witt designs, Mathieu groups and proof. The monograph is designed to Henstock and Riemann is at first almost highly transitive designs, a discussion of serve both as a general textbook and as a imperceptible. On the other hand, difference sets and regular symmetric detailed exposition of the classical topics in Riemann’s approach gives an integral that designs, and difference families. The sec- potential theory. It should be accessible to is very weak from a practical point of view; ond volume has chapters on recursive con- graduate students and researchers inter- this was why Lebesgue’s theory of integra- structions, transversal designs and nets, ested in the field of potential theory, and tion was created at the beginning of the asymptotic existence theory, characteristic will be understandable with a basic knowl- last century. The Kurzweil-Henstock theo- of classical designs, and their applications. edge of first-year graduate courses in ry is more general than the Lebesgue one Together with an appendix, tables, bibli- analysis. A knowledge of calculus in high- and it overcomes the problem that the ography, a list of symbols and an index, er dimensions, measure theory, very basic Lebesgue integral does not integrate deriv- there are 1093 pages in total. (jnes) topology and linear algebra are required. atives in general. Another advantage of (jl) Kurzweil-Henstock integration is that to S. Billey and V. Lakshmibai, Singular explain it, only the concept of the real Loci of Schubert Varieties, Progress in B. Bakalov and A. Kirilov, Jr., Lectures on numbers is needed (the theorem on the Mathematics 182, Birkhäuser, Boston, 2000, Tensor Categories and Modular Functors, supremum) and everything can be done on 251 pp., DM 118, ISBN 0-8176-4092-4 and University Lecture Series 21, American this basis, including very general conver- 3-7643-4092-4 Mathematical Society, Providence, 2001, 221 gence results. Along these lines, the The study of Schubert varieties started in pp., US$29, ISBN 0-8218-2686-7 author explains the theory for real func- the nineteenth century as a part of classical The book narrates a big adventure of the tions defined on compact one-dimensional projective geometry. A modern treatment 1990s, a ‘grand unification’ of three seem- intervals in the first part of the book, and of the subject became possible through the ingly unrelated structures: modular tensor then extends it for infinite intervals in the works of Ehresmann, Chevalley, Bernstein, categories, 3-dimensional topological reals. Links with measure theory, measur- Gelfands, Demazure, and the authors of quantum field theories (3D-TQFTs) and 2- ability and the Lebesgue integral are pre- this book. Schubert varieties now provide dimensional modular functors. Tensor sented, even though they are not needed one of the best understood examples of categories are categories with a multiplica- for presenting the Kurzweil-Henstock the- complex projective varieties, and their tion that generalises the tensor product in ory (this is one of the merits of the theory). properties have been studied in many the category of vector spaces. Modular The topics are excellently motivated and papers. Thus, the publication of the book tensor category is then a tensor category the book contains many well-chosen exer- is a very timely event. Already by 1964 with a finite number of simple objects sat- cises, some of them solved in the conclud- Chevalley had shown that Schubert vari- isfying certain non-degeneracy conditions. ing part of the book. (šs) eties are non-singular in codimension 1, The main examples come from represen- and in 1973 Demazure discovered non- tations of quantum groups at unity. D. C. Benson, The Moment of Proof. smooth Schubert varieties. In the past fif- A 3D-TQFT is a rule that assigns to each Mathematical Epiphanies, Oxford University teen years, many major developments in 2-dimensional manifold a vector space (the Press, 2001, 331 pp., £9.99, ISBN 0-19- the field have taken place, making it possi- state space) and to each 3-dimensional 513919-4 ble to do more elaborate computations on manifold with boundary (thought of as a The author acquaints the reader with many singular loci and to solve questions con- bordism of 2-manifolds) a linear operator. topics of mathematics and with related cerning the smoothness of Schubert vari- A slight generalisation allows for 2-mani- interesting curiosities. But the main aim of eties. In these questions, contemporary folds with marked points and 3-manifolds this book is to share with a wide range of techniques from algebraic geometry, rep- with framed tangles. A 2-dimensional readers the pleasure of mathematical resentation theory and combinatorics are modular functor is a functor from the thinking and the joy of discovery. Readers needed. All of these techniques are modular category of 2-dimensional mani- will frequently experience the pleasure of a explained with maximum benefit to folds and isotopy classes of their homeo- sudden insight into a mathematical prob- researchers in the field or graduate stu- morphisms to the category of vector lem, and many will understand what it dents. (ae) spaces. An equivalent definition can be means when somebody speaks about the given in terms of flat connections on the beauty of mathematics, about the elegance J. Billingham and A. C. King, Wave moduli space of curves. of mathematical proofs, and about the Motion, Cambridge Texts in Applied The authors explain that these notions charm of mathematical ideas. (ec) Mathematics, Cambridge University Press, are essentially equivalent. The equivalence 2000, 468 pp., £24.95, ISBN 0-521-63257- of tensor categories and 3D-TQFTs is T. Beth, D. Jungnickel and H. Lenz, 9 and 0-521-63450-4 mediated by Resetikhin-Turaev invariants Design Theory, Vols. 1, 2, Encyclopedia of Waves are everywhere. This is the conclu- of links and 3-manifolds, while the equiva- Mathematics and its Applications 69 and 78, sion that will make after reading the book. lence with modular functors is based on Cambridge Univesity Press, 1999, 607 and The authors remind us that whenever we results of Moore and Seiberg and uses the 492 pp., £60 and £60, ISBN 0-521-44432-2 see or hear anything, we do so because of ‘pair of pants’ decomposition of surfaces. and 0-521-77231-1 the existence of waves. Every heartbeat The book assumes some preliminary This is a new edition of a respectable two- and every nerve impulse owes its existence knowledge of algebraic/differential geome- volume set devoted to the study of designs to electrochemical waves. The authors try and category theory, and is addressed (set systems satisfying strong regularity present the topic of waves for advanced at graduate students and researchers inter- assumptions). If the first 1985 edition was undergraduates in applied mathematics. ested in this beautiful part of mathematics the first comprehensive treatment of the The book is divided into three sections. with a strong physical flavour. (mm) subject, the second edition comes at a time The first section begins with a very basic when there are numerous books that treat introduction: no special knowledge is R. G. Bartle, A Modern Theory of the subject in various aspects and depth. needed in order to understand the book. Integration, Graduate Studies in Mathematics The text has been thoroughly revised and This section deals with the linear theory of 32, American Mathematical Society, complemented to meet new demands and waves and covers a wide range of impor- Providence, 2001, 458 pp., US$59, ISBN 0- capture some of the latest developments. tant applications, such as acoustics, gravity 8218-0845-1 The authors succeed in doing so, and the waves, shallow water waves, waves in elastic The Kurzweil-Henstock theory of integra- present volumes present one of the most bodies and electromagnetism. The second tion is well described in this book. For thorough treatments of the subject. It is part of the book presents the basics of the Kurzweil-Henstock integration, first-year highly recommended for study as well as non-linear theory of waves. The theory is students have no essential difficulties in for content. again explained through a wide range of understanding the main idea of defining The first volume includes examples and applications, including shock waves in traf- the integral, because of its similarity with basic definitions, combinatorial analysis of fic, gas dynamics, non-linear water waves, the Riemann integral. The difference designs, and chapters on groups and molecular diffusion, and the transmission EMS December 2001 35 RECENT BOOKS of nerve impulses. The last part of the forms of hypergeometric series and vertex contains the best description of the fastest book covers more advanced topics, such as models in statistical mechanics, via four- known deterministic algorithm (due to the Burgers’ equation, the Kortweg-de Vries teen interrelated conjectures, to the final author: 53 pages). equation and the non-linear Schrödinger goal. The book is written in a very interest- There are three appendices summaris- equation. ing and attractive way, full of ideas, pic- ing the necessary background material The book is written very clearly, with tures, photographs, historical remarks and (probability theory, harmonic analysis and many diagrams and figures accompanying many exercises. Furthermore, the special convex geometry). Taken with Matoušek’s the text. There are also photographs, problem described above provides an occa- book (Geometric Discrepancy: An Illustrated which are rarely to be found in mathemat- sion for the author to discuss very interest- Guide, Springer, 1999), discrepancy theory ical textbooks. At the end of each chapter ing and basic questions concerning mathe- is fortunate to have two complementary there are sufficient numbers of exercises, matics as a whole – what are the roles of books of excellent quality written by lead- so that readers can test their understand- conjecture and proof in mathematics?, or ers of the field. This is the first book ing of the topics. Although the solutions to more generally, how do mathematicians devoted to the discrepancy method. (jnes) exercises are not included in the book, the really do research? This is an excellent authors provide an e-mail address from book which can be recommended without F. Chung and R. Graham, Erdös on which fully worked solutions can be hesitation, not only to specialists in the Graphs, A. K. Peters, Ltd., Wellesley, 1999, obtained. The book contains three short field, but to any mathematician with time 142 pp., US$25, ISBN 1-56881-079-2 appendices that present different systems to read something interesting and nicely This is a collection of Paul Erdõs (mostly of coordinates, some results of vector cal- written. (vs) open) problems related to graphs and culus, and a table of useful physical con- hypergraphs, with commentary. The top- stants. This textbook will be valuable for P. Le Calvez, Dynamical Properties of ics treated in the book include extremal students of mathematics who wish to apply Diffeomorphisms of the Annulus and of the Ramsey theory, colouring, packing and their mathematics to physics and other Torus, SMF/AMS Texts and Monographs 4, covering, random graphs and enumera- fields. (tf) American Mathematical Society, Société tion, hypergraphs, and infinite graphs. Mathématique de France, Providence, 2000, This is complemented by personal remi- A. Björner, M. Las Vergnas, B. Sturmfels, 105 pp., US$21, ISBN 0-8218-1943-7 niscences by the authors, and by A. N. White and G. Ziegler, Oriented Monotone twist maps are a useful tool in Vászonyi, one of Erdõs’s oldest collabora- Matroids, Encyclopedia of Mathematics and its the theory of conservative and dissipative tors. This book also contains an impressive Applications 46, Cambridge University Press, dynamical systems. The first two chapters list of survey articles devoted to P. Erdõs, 1999, 548 pp., £30, ISBN 0-521-77750-X present a survey of approaches to the the- many of which are collected in: Mathematics This is the second paperback edition of ory of such maps, with generalisations, and of Paul Erdõs I, II (ed. R. L. Graham and J. this book. The main topic of the book, ori- several motivating examples are given. Nešetøil), Springer-Verlag, 1996. It would ented matroids, is an abstract axiomatic The Aubry-Mather variational approach is be useful to have similar collections in generalisation of hyperplane arrange- explained, and criteria for the existence of other branches of Erdõs’s activity – num- ments, point configurations and convex periodic orbits are discussed. The topo- ber theory, in particular. (jnes) polytopes in geometry, directed graphs in logical approach is used for a description discrete mathematics, and in many other of the dynamics on invariant curves. The C. W. Curtis, Pioneers of Representation situations. The book describes the basics second chapter asserts that each diffeo- Theory: Frobenius, Burnside, Schur and of the subject and its applications to other morphism of the closed annulus isotopic to Brauer, History of Mathematics 15, American areas of mathematics. the identity can be represented as a com- Mathematical Society, Providence, 1999, 287 In this revised edition there is a new position of monotone twist maps, and the pp., US$49, ISBN 0-8218-9002-6 appendix with a summary of research done methods in the first part are used to study Representation theory has made enor- since the publication of the first edition in diffeomorphisms isotopic to the identity. mous progress in the last century. This 1993. The authors have also updated and New proofs of some results concerning the book returns to its roots, to the representa- substantially expanded the bibliography, rotation set and periodic orbits of diffeo- tion theory of finite groups. The principal which now has more than 50 pages. The morphisms of the circle are presented. (šs) figures in its development were four excel- book describes a subject situated at the lent mathematicians – Frobenius, crossroads of many fields of mathematics, B. Chazelle, The Discrepancy Method, Burnside, Schur and Brauer. Building on and will therefore be interesting for math- Randomness and Complexity, Cambridge ideas concerning characters of finite ematicians in geometry, representation University Press, 2000, 463 pp., £40, ISBN 0- abelian groups, the first steps in the struc- theory, topology, algebraic geometry and 521-77093-9 ture theory of finite groups, and research computer science, as well as for chemists. This book is written by one of the leaders in finite-dimensional associative algebra, (vs) in the field. It presents a rapidly develop- they created (with others) a beautiful theo- ing field in admirable breath and depth, ry that was subsequently a model and D. M. Bressoud, Proofs and and is written in a beutiful style. From the inspiration for further evolution of the Confirmations, Spectrum Series, Cambridge dust jacket description: ‘This book tells the representation theory of Lie groups. The University Press, 1999, 274 pp., £17.95, story of the discrepancy method in a few book concentrates on the mathematical ISBN 0-521-66170-6 and 0-521-66646-5 short, independent vignettes. It is an aspects of their original papers and The area of the book is algebraic combina- eclectic tale that features, among other describes their content and methods, using torics. The main problem discussed here topics, communication complexity, modern language. The historical aspects is a particular question: to find a formula pseudorandomness, rapidly mixing are treated as well: a full account of the his- for the number of alternating sign matrices Markov chains, points on the sphere via tory of the subject can be found in papers of order n (the non-trivial entries of an modular forms, derandomization, convex by Thomas Hawkins. This very nice book is alternating sign matrix can be only +1 hulls, Voronoi diagrams, linear program- accessible with a basic knowledge of alge- and –1, the sum of the entries in each row ming, geometric sampling, VC-dimension bra, and is recommended. (vs) or column is 1, and the non-zero entries in theory, minimum spanning trees, linear each row or column alternate in sign). The circuit complexity, and multidimension H. G. Dales, Banach Algebras and author presents a description of the evolu- searching.’ The topics discussed include Automatic Continuity, London Mathematical tion of the subject, starting in the 1980s combinatorial discrepancy, upper and Society Monographs New Series 24, Clarendon and ending more than ten years later, lower bound techniques, sampling, geo- Press, Oxford, 2001, 907 pp., £110, ISBN 0- leading to a proof of the conjectured for- metric searching, complexity lower 19-850013-0 mula. bounds, convex hulls and Voronoi dia- This bulky monograph presents a detailed This is a fascinating story, going from grams, linear programming and exten- modern account of basic Banach algebra classical invariant theory to partitions, sions, pseudorandomness, communication theory. The main chapters are devoted to symmetric functions, tableaux, various complexity, minimum spanning trees (this connections between algebraic and topo- 36 EMS December 2001 RECENT BOOKS logical structures for general Banach alge- modest knowledge; all necessary tools are tors’ and that ‘operator space theory will bras, as well as for particular examples. introduced in the text. The last two chap- provide Banach space theorists with excit- The author studies when (and how) alge- ters are more advanced. Chapter 7 con- ing new vistas for research’. braic structures determine various aspects tains a discussion of moduli spaces of The monograph is designed for gradu- of topological ones. polarised abelian varieties. The final chap- ate students and researchers interested in In the first chapter, the algebraic back- ter contains recent results on the geometry the field, and can be understood with a ground is established (including ordered and topology of subvarieties of a complex rudimentary knowledge of functional sets, algebraic semigroups, ideals, mod- torus, and needs much more background. analysis, and in particular of Banach space ules, radicals, spectra, valuation algebras, Most of the results in this book are fully theory. (jl) cohomology and involutions); special proved and the presentation of ideas is attention is paid to the use of logic and set understandable. This small booklet is very B. Engquist and W. Schmid (eds.), theory. The next chapter explains the gen- suitable for a course on this topic. (vs) Mathematics Unlimited — 2001 and eral theory of Banach algebras as well as Beyondd, Springer, Berlin, 2001, 1236 pp., some of the theory of more general topo- E. G. Effros and Z.-J. Ruan, Operator 179 fig., DM 79, ISBN 3-540-66913-2 logical algebras. This chapter also con- Spaces, London Mathematical Society The aim of the editors is to give responses tains sections on the Gel’fand theory, func- Monographs New Series 23, Clarendon Press, and insights to the question: ‘What is the tional calculus, Banach algebras of opera- Oxford, 2000, 363 pp., £60, ISBN 0-19- future of mathematics in the new millenni- tors and Banach modules. The third chap- 853482-5 um?’ through this unique collection of ter is devoted to Banach algebras with an Any normed linear space can be regarded more than sixty contributions by leading involution (including C*-algebras and as a ‘concrete function space’ – that is, as a experts in various fields of mathematics, group algebras). Chapter 4 presents the linear space of bounded functions on a set and ‘to provide the reader with a view of theory of commutative Banach algebras. equipped with the uniform norm. great variety and the vitality of mathemat- After a general introduction, the author Analogously, a (concrete) operator space is ics as we enter the new millennium’. studies particular examples (such as alge- a linear space of bounded operators on a Although a similar goal was followed in bras of continuous functions, uniform alge- Hilbert space. The authors define an another recent collection, Mathematics: bras, algebras of differentiable and (abstract) operator space by axiomatising Frontiers and Perspectives, edited by V. Lipschitz functions, abelian group alge- the properties of concrete operator spaces. Arnold, M. Atiyah, P. Lax and B. Mazur, bras, Banach algebras of power series and Roughly speaking, operator spaces are lin- significant attention is here paid to the convolution algebras). The last chapter, ear spaces equipped with an operator newest interactions between mathematics the culmination of the book, deals with space matrix norm. The roots of such a and other disciplines, such as bioscience, automatic continuity theory itself. In par- theory of operator spaces go back to the economics, material science, communica- ticular, it treats uniqueness of norm, sepa- famous Heisenberg uncertainty principle, tions and computer science, and it is also rating spaces and the stability lemma, con- together with the mathematical work of more focused on ‘applied‘ mathematics. tinuity ideals and singularity sets, the main Jordan, von Neumann and Weyl, and lead- Because of its wide scope, the reader can boundedness theorem, linear functionals, ing to research in the field of algebras of certainly find within its pages many excit- continuous and discontinuous derivations, bounded operators on Hilbert spaces. ing and thought-provoking papers. (jmal) and embedding algebras in Banach alge- This monograph is concerned with a more bras. recent innovation, the quantisation of R. Estrada and R. P. Kanwal, Singular At the end of the book, an appendix Banach space theory. Integral Equations, Birkhäuser, Boston, gives some background from topological In a preliminary chapter the reader is 2000, 427 pp., DM 138, ISBN 0-8176-4085- and metric spaces, complex and functional introduced to spaces with ‘matrix coeffi- 1 and 3-7643-4085-1 analysis, measure theory, integration and cients’. It is followed by a chapter on the This is a textbook on singular and convo- analytic spaces, together with an index of three fundamental results in operator the- lution integral equations. After presenting symbols, theorems, identities and exam- ory, and complete proofs of Ruan’s repre- the basic mathematical tools, the authors ples. A general index and an extensive list sentation theorem, the Arveson-Wittstock outline the basic theory of convolution of references are included. This volumi- theorem (a generalisation of the Hahn- equations. In Chapter 3, direct methods of nous text is recommended to graduate stu- Banach theorem) and the Paulsen- solutions of convolution equations are dents and experts in the field of Banach Wittstock decomposition theorem for com- explained, and in Chapter 4, singular inte- algebras, and to those working in function- plete contractions; there is also a short sec- gral equations with variable Hölder contin- al analysis and in algebra. (jl) tion on a characterisation of injective oper- uous coefficients are discussed, when the ators spaces. The next chapter concerns range of integration is either a closed con- O. Debarre, Tores et variétés abéliennes tensor products (projective and injective tour or an open arc (the so-called complexes, Cours Spécialisés 6, Société tensor products, the Haagerup tensor Carleman equation). Chapters 5 and 6 Mathématique de France, Paris, 1999, 125 product). These are used to generalise deal with distributional solutions of singu- pp., ISBN 2-86883-427-2 Grothendieck’s theory of approximation lar integral equations on a compact inter- The main topic treated in this book is the properties. This part discusses nuclear, val, as well as on the entire real line; the classical theory of abelian tori. At the integral and absolutely summing map- Hilbert transform is used here. Integral beginning of the book, the author briefly pings, including the Dvoretsky-Rogers the- equations with logarithmic kernels with a reviews the classical facts on lattices and orem for operator spaces. In Chapter 4, polynomial are solved in ordinary and elliptic curves (complex tori, Weierstrass the central part of the text, the main topics generalised spaces of functions in Chapter function, divisors, theta functions, the of nuclearity, exatness and local reflexivity 7. In Chapter 8, the classical Wiener-Hopf Riemann-Roch theorem and moduli are presented. The final chapter is devot- equation with absolutely integrable kernel spaces of elliptic curves). Taking these as ed to the algebraic applications of operator is solved. Finally, Chapter 9 investigates motivation, the author presents a discus- space theory (non-commutative harmonic dual integral equations. The book con- sion of many questions concerning com- analysis, including quantised Banach alge- tains instructive examples and exercises plex abelian varieties in higher dimen- bras and Fourier algebras on locally com- for each particular class of integral equa- sions. An abelian variety is a complex pact groups). An appendix summarises tions. It should be very useful for engi- torus that admits a holomorphic embed- elementary results from functional analysis neers and students. (šs) ding in a projective space: characterising (Banach and Hilbert spaces, C*-algebras, abelian varieties is the central problem in von Neumann algebras, together with a M. Flexor, P. Sentenac and J.-C. Yoccoz this book. To answer it, the author uses brief list of operator algebras). The (eds.), Géometrie complexe et systèmes modern tools – holomorphic line bundles, authors claim that their ‘goal in this mono- dynamiques, Astérisque 261, Société cohomologies with values in a sheaf and graph has been to explain the deep analo- Mathématique de France, Paris, 2000, 443 Chern classes. This part of the book is gy between linear spaces of bounded func- pp., FRF 450, ISBN 2-85629-081-7 quite elementary, and requires only a very tions and linear spaces of bounded opera- This volume consists of a representative EMS December 2001 37 RECENT BOOKS collection of fifteen papers on dynamical plex analysis); the second third, which can complemented by its historical and systems, presented at a meeting held in still be partly covered in an undergraduate humanistic impact. The Mátraháza meet- 1995 on the occassion of Adrien Douady’s course, consists of selected topics such as ing was one of the last meetings in which sixtieth birthday. Most of the papers con- the Poisson integral and hyperbolic geom- Paul Erdõs took part. This famous twenti- cern various aspects of iterations of real etry; in the last third, the author presents eth-century mathematician was well polynomials, especially quadratic ones topics that have applications. The final known, not only for his immense contribu- (Julia and Mandelbrot sets, invariant and chapters cover the necessary background tions to mathematics (and in particular to Sinai-Ruelle-Bowen measures, Douady- for passing PhD qualifying exams in com- discrete mathematics), but also for his Hubbard theory, and denseness of systems plex analysis. unusual life style. It is very appropriate with finitely many attractors of special Surprisingly the book does not need that a volume dedicated to this unforget- properties). Also studied are hyperbolic much background: apart from high-school table personality should be edited by his rational maps, Lampert maps, the one- basics, one needs some general under- former students, colleagues and friends. A parameter generalisation of the Lorenz standing of the methods of mathematical long foreward of over ten pages describes model and holomorphic foliations in the analysis and some knowledge of multivari- his broad work in combinatorics, the complex plane. These proceedings are able calculus. The author considers the importance of his research, and his way of accessible to experts in dynamical systems, course to be a good opportunity for stu- thinking of mathematics as a whole. In and the lengthy introductions of most dents to develop and consolidate previous- addition to the professional line, the fore- papers may also make them available to a ly covered material, and to learn its active word gives a rich flavour of Paul Erdõs’ life, wider mathematical community. (jmil) use in calculations. The preface contains with many stories that reveal his character useful hints for both instructors and stu- and help us keep in our minds a picture of L. E. Fraenkl, Introduction to Maximum dents. More than 800 well-chosen exercis- a brilliant and unique mathematician, and Principles and Symmetry in Elliptic es with 20 pages of hints and solutions, at the same time a warm and charitable Problems, Cambridge Tracts in Mathematics together with clear and concise expositions human being. This book contains two con- 128, Cambridge University Press, Cambridge, of many results, makes this book enjoyable tributions by Erdõs, one of them being the 2000, 340 pp., £45, ISBN 0-521-46195-2 even for specialists in the field. The book very last paper he worked on before he This book presents the basic theory of the is recommended for libraries, students, passed away in September 1996. symmetry of solutions to second-order and teachers of both undergraduate and The topics covered in the book also elliptic partial differential equations, by graduate courses. (jive) include applications of algebraic tech- means of the maximum principle. In niques in combinatorics and graph theory Chapter 0, the author sets up the basic J. J. Gray, The Hilbert Challenge, Oxford – in particular, polynomials and graph notation and termonology. The introduc- University Press, 2000, 315 pp., £20, ISBN 0- homomorphisms, combinatorial number tory Chapter 1 is then intended to moti- 19-850651-1 theory, discrete geometry and discrepancy, vate further investigation. Chapter 2 deals This book gives a fascinating account of structural graph theory, and specialised with maximum principles for sub-solutions Hilbert’s 23 problems, which he presented topics in random graphs. (jk) of elliptic partial differential equations of at the International Congress of the second order. In Chapter 3 the author Mathematicians in Paris in 1900. The Harish-Chandra, Admissible Invariant studies the behaviour of positive solutions author describes the life and mathematical Distributions on Reductive p-adic Groups, of the equation ∆u + f(u) = 0, in a bound- work of David Hilbert (1862-1943), his University Lecture Series 16, American ed symmetric set Ω with u = 0 on the influence on the development of mathe- Mathematical Society, Providence, 1999, 97 boundary of Ω. As a consequence of these matics, and his influence on the society of pp., US$20, ISBN 0-8218-2025-7 results, he shows the spherical symmetry of mathematicians. He describes all of The famous Harish-Chandra results on this solution in the case of a ball. In Hilbert’s problems and shows what they admissible invariant distributions were Chapter 4 the spherical symmetry of a pos- were, why they were proposed, how they presented in Princeton in 1973, and a itive solution of the equation ∆u + f(u) = influenced the nature of mathematics and short version of his lectures was published 0 in Rm is shown. Chapter 5 concerns the of mathematical thinking in the twentieth in his so-called ‘Queen’s notes’ in 1978. monotonicity of positive solutions of the century, how they were solved, and so on. Later, he asked P. L. Sally, Jr. to prepare a equation ∆u + b.grad u + f(u) = 0 in a The reader can enjoy the reactions of detailed version of these notes. This small bounded set. Each paragraph ends with mathematicians to the Hilbert problems booklet contains notes on this topic pre- exercices. and appreciate their efforts to solve them. pared by E. DeBacker and P. L. Sally, Jr., The text is accompanied by five appen- This book is written in a clear and lively which are based on Harish-Chandra’s own dices. Appendix A is devoted to the study manner, and can be recommended to versions of his lecture notes. The preface of the Newtonian potential as a solution of everybody interested in mathematics and also includes comments on later develop- the Poisson equation, and the behaviour of mathematicians. (mnem) ment in the field, after the publication of this potential and its gradient. Appendix the Queen’s notes. B gives rudimentary facts about harmonic E. Györi and V. T. Sös (eds.), Recent The main result of the book is the fact functions and the Poisson equation. The Trends in Combinatorics. The Legacy of that the character of an irreducible admis- subject of Appendix C is a construction of Paul Erdös, Cambridge University Press, sible representation of a connected reduc- the first of three comparison functions of a 2001, 192 pp., £35, ISBN 0-521-80170-2 tive p-adic group can be represented by a type introduced by D. Siegel. In Appendix This book is much more than just a pro- locally summable function on the group; D, the divergence theorem is proved. ceedings. It stems from the combinatorial the main tool used is the Fourier transform Appendix E presents the edge-point workshop, Some Trends in Discrete of distributions on the corresponding Lie lemma. (dm) Mathematics, held in Mátraháza, Hungary, algebra. This result by Harish-Chandra in October 1995. The editors have man- strongly influenced the later evolution of T. W. Gamelin, Complex Analysis, aged to gather surveys and research papers the subject. It is therefore excellent to Undergraduate Texts in Mathematics, on the really hot topics of recent discrete have a carefully prepared presentation of Springer, New York, 2001, 478 pp., mathematics. The style and quality of the this topic available in book form. (vs) US$49.95, ISBN 0-387-95039-1 and 0-387- contributions are such that the volume can 95069-9 serve as a textbook on special topics suit- M. Kamenskii, V. Obukhovskii and P. It is difficult to describe this textbook in a able for an advanced graph theory and Zecca, Condensing Multivalued Maps and short review. Among its many aims, the combinatorics seminar, while established Semilinear Differential Inclusions in author wishes to provide beginners with researchers will enjoy reading many of the Banach Spaces, De Gruyter Series in standard material in a rather flexible papers describing recent progress in com- Nonlinear Analysis and Applications 7, Walter course. About one third of material repre- binatorics and giving a collection of inter- de Gruyter, Berlin, 2001, 231 pp., DM 196, sents nineteenth-century mathematics (a esting open problems. ISBN 3-11-016989-4 standard part of any basic course in com- The scientific quality of the book is well This monograph gives a self-contained 38 EMS December 2001 RECENT BOOKS presentation of the theory of condensing ed in the origins and deeper context of Lecture Series 14, Cambridge University Press, multivalued (= set-valued) mappings, and their science. (jnes) 2000, 311 pp., £24.95, ISBN 0-521-77968- applies it to semi-linear differential inclu- 5 sions in Banach spaces. The adjective E. Kaszkurewicz and A. Bhaya, Matrix As the title of the book suggests, the ‘condensing’ (with respect to a certain Diagonal Stability in Systems and Kurzweil-Henstock theory of integration is measure of non-compactness) means that Computation, Birkhäuser, Boston, 2000, 267 dealt with. Introductory topics are includ- the multivalued mapping in question does pp., DM 168, ISBN 0-8176-4088-6 ed to the first chapter, while in the second, not increase the specified measure of non- In this book, the authors discuss a special the basic defintion of the integral is given, compactness; a (regular) measure of non- class of stability results for dynamical sys- with its important basic properties. More compactness says, roughly speaking, how tems described by a system of difference or sophisticated topics are given in Chapter 3, much a given set violates the property ‘to ordinary differential equations. The book including the convergence theorem for be relatively compact’. starts with a chapter that gives an overview Kurzweil-Henstock integrals, based on the Chapter 1 summarises the basic proper- of several applications where the stability concept of equi-integrability of a set of ties of multivalued mappings as far as con- of systems can be investigated using diago- functions, and the McShane integral, tinuity and measurability are concerned. nal-type Lyapunov functions. In the sec- which is equivalent to the Lebesgue inte- Chapter 2 then introduces abstract mea- ond chapter, the reader can find a thor- gral and can be also defined by using sures of non-compactness, with special ough introduction to the concepts of diag- Riemann-type integral sums for certain attention to Hausdorff measure of non- onal stability and D-stability in the frame- partitions of an interval. In Chapters 4 compactness in separable Banach spaces work of matrix theory. The next chapter and 5, the strong Luzin integral is defined (and, in particular, in spaces of continuous deals with certain classes of dynamical sys- and is shown to be that it is equivalent to functions), and introduces basic definitions tems that admit the diagonal-type the Kurzweil-Henstock integral. This part and properties of condensing mappings. Lyapunov functions and gives the basic sta- of the book mentions more advanced con- Topological degree theory for condensing bility results. The authors discuss the cases cepts concerning real controlled conver- both convex-valued and non-convex-val- of non-linear systems, systems continuous gence results, including AC* and BV* func- ued multifields forms Chapter 3; the theo- and discrete in time, and systems with tions, as we know them from the classical ry is briefly illustrated also by applications time-varying delays in the state. In the book of S. Saks and P. Y. Lee. In Chapter to optimal control of neutral functional remaining three chapters, these methods 6, the integration of functions over n- differential equations. Chapter 4 then are applied to certain problems introduced dimensional intervals is presented, with gives basic facts from the theory of C0- in the first chapter – namely, the problem Fubini-type theorems and change of vari- semigroups of linear operators, with spe- of convergence of an asynchronous itera- ables (substitution). At this point, the cial attention to condensing operators. tive method, stability of the neural net- authors mention that, because the Measures of non-compactness in Banach- works, circuits, ecosystem models and Kurzweil-Henstock integral is a non- space-valued functions are also addressed. large-scale systems. absolutely convergent integral, the inte- Semi-linear differential inclusions of the The book is self-contained, includes both gration over n-dimensional sets causes dif- type x’(t) ε Ax(t) + F(t, x(t)), arising in (for classical and new results presented in an ficulties that can be overcome by looking example) hybrid systems with dry friction unified way, and includes a great variety of for absolutely Kurzweil-Henstock inte- or in feedback control, are studied in useful references. (jhr) grable functions. The last chapter of the Chapter 5 (initial value problems) and book is devoted to some applications of the Chapter 6 (periodic problems). To this S. B. Kuksin, Analysis of Hamiltonian previous theory to problems in analysis aim, the multivalued part F is assumed to PDEs, Oxford Lecture Series in Mathematics (line integrals, Green’s theorem, Dirichlet be condensing with respect to a special and its Applications 19, Oxford University problem, Fourier series, etc.). measure of non-compactness. Press, 2000, 212 pp., £39.50, ISBN 0-19- The book is well written, is suitable for Reading this book from the beginning is 850395-4 use in elementary courses as well as for recommended, because there is no list of The aim of this book is to present the fol- graduate studies, and can be recommend- notation and a rather poor index. The lowing form of the proof of Kolmogorov- ed for a wide audience of students and spe- book will serve excellently as a self-con- Arnold-Moser (KAM) theorem: most of the cialists in the theory of integration and real tained introductory text, as well as a state- space-periodic finite-gap solutions of a analysis in general. (šs) of-art survey for researchers and advanced Lax-integrable Hamiltonian partial differ- students interested in this branch of non- ential equations (PDE) persist under a S. Morosawa, Y. Nishimura, M. linear analysis. (trou) small perturbation of the equation as time- Taniguchi and T. Ueda, Holomorphic quasiperiodic solutions of the perturbed Dynamics, Cambridge Studies in Advanced S. Kangshen, J. N. Crossley and A. W.-C. equation. This theorem provides an Mathematics 66, Cambridge University Press, Lun, The Nine Chapters on the important tool for an effective study of 2000, 338 pp., £45, ISBN 0-521-66258-3 Mathematical Art. Companion and non-linear PDEs. This book is a comprehensive introduction Commentary, Oxford University Press, 1999, In Chapter 1, the theory of Hamiltonian to holomorphic dynamics, induced by iter- 596 pp., £110, ISBN 0-19-853936-3 PDEs is developed. The presentation of ations of holomorphic maps. It is well This book is a scholarly English translation abstract Lax-integrable equations is given known that even iterations of a quadratic of the Chinese Nine Chapters on in Chapter 2. The properties of classical polynomial can produce very complicated Mathematical Art, which is considered as the Lax-integrable PDEs are discussed in next fractals. The first part of the book Eastern counterpart of Euclid’s Elements. It two chapters. The following three chap- (Chapters 1-5) is devoted to dynamics on is an anonymous text of more than 2000 ters contain a description of normal forms domains in the Riemann sphere, while the years old. It served as a textbook not only for Lax-integrable PDEs in the vicinity of rest (Chapters 6-9) treats the case of two in China, but also in neighbouring coun- manifolds, formed by finite-gap solutions. complex variables. tries, until around 1600 when Western sci- The final three chapters contain the proof In Part I, Chapter 1 summarises the ence was introduced. This book contains a of the main theorem. A number of techni- basic facts on iterations of a polynomial modern translation of the text, together cal details are explained in the Addendum. near a fixed point. A dichotomy with with historical commentaries which are The book is devoted to global aspects of respect to the dynamics of a given rational also very old – the best known of these the KAM theorem for PDEs, and does not or entire function (Fatou and Julia sets) is commentaries is by Liu Hui (263 AD): the include two local theories, perturbations of investigated in Chapter 2, where impor- Sea Island Mathematical Manual which is linear equations and small oscillations in tant properties of both sets are explained. translated in full in Chapter 9. The amaz- non-linear equations. (pso) Chapter 3 describes phenomena typical for ingly complex history is told with rigour entire functions. Chapter 4 starts with the and elegance. P. Y. Lee and R. Výborný, The Integral: Newton iterations for zeros of a meromor- This book is of interest to historians of An Easy Approach after Kurzweil and phic function and continues with the science and to all mathematicians interest- Henstock, Australian Mathematical Society Fatou-Julia-Sullivan theory of iterations of EMS December 2001 39 RECENT BOOKS rational functions and Shishikura’s esti- This two-volume set is recommended both the Haar measure on locally compact mate. The last chapter of the first part is for graduate students and experts in the groups, algebras L1(G),L∞(G) and Beurling devoted to the so-called ‘conformal field of *-algebras. (jl) algebras. The fourth chapter deals with dynamics’ (group actions of Kleinian locally compact abelian groups and their groups) and to the Sullivan dictionary of M. M. Postnikov, Geometry VI. duality theory. Further chapters are devot- analogies between iterations of holomor- Riemannian Geometry, Encyclopaedia of ed to functions on locally compact abelian phic functions and actions of a Kleinian Mathematical Sciences 91, Springer, Berlin, groups, an extension of the Wiener theo- group; this chapter also contains several 2001, 503 pp., DM 199, ISBN 3-540-41108- rem for groups, and Segal algebras. The recent conjectures related to the main one: 9 notion of the spectrum of a bounded mea- structurally stable rational functions are This book is a more-or-less standard intro- surable function and its properties are hyperbolic. duction to Riemannian geometry, includ- explained in Chapter 7. The final chapter Part II starts with a brief introduction to ing its global aspects. It has strong inter- describes functions on general locally com- the analysis of several complex variables. sections with some well-known textbooks pact groups, including the Mackey-Bruhat Chapter 6 explains the behaviour near a (Gromoll-Klingenberg-Meyer, Kobayashi- theorem on the existence of quasi-invari- fixed point (including stable and unstable Nomizu, Helgason, etc.). What is non- ant measure. The appendix contains manifolds). Chapter 7 studies polynomi- standard here is the order of the chapters, proofs of the Domar and Malliavin theo- als, especially complex Hénon maps. The where the really introductory chapters are rems, additional material on Segal alge- last two chapters are devoted to a measure- put at the end of the book. bras and the notion of difference spec- theoretic treatment of dynamics which is Two chapters are of particular interest: trum. The book ends with notes and addi- based on the so-called ‘pluripotential theo- Chapter 5 about symmetric spaces, where tional references to each of the chapters. ry’. the algebraic approach of O. Loos is The monograph is designed to serve Since complex dynamics is a modern explained, and Chapter 24 on four-dimen- both as a general survey and as a detailed subject, the book contains many recent sional manifolds, which is a real master- exposition of the topics it treats. It should results. Even though the text is almost self- piece that includes many global results. be accessible to graduate students and contained and very carefully written, the Many interesting and non-trivial exercises researchers interested in harmonic analysis reader needs a good background knowl- are included in every chapter. and understandable with a basic knowl- edge of the classical geometric theory of a On the other hand, this monograph has edge of functional analysis and measure complex variable (e.g., from Ahlfors’ some weaknesses. First, even though the theory, together with a background of real books) and some experience of topology author refers to many famous names and complex analysis. (jl) and measure theory. (jmil) throughout the book, he never gives stan- dard references: instead of usual list of ref- J. Rossmann, P. Takáè and G. T. W. Palmer, Banach Algebras and the erences he gives only a short list of ‘sug- Wildenhain (eds.), The Maz’ya General Theory of *-Algebras, Vol. II: *- gested reading’ at the end of the book. Anniversary Collection, Vols. 1, 2, Operator Algebras, Encyclopedia of Mathematics and its This seems rather unusual for an ‘encyclo- Theory Advances and Applications 109, 110, Applications 79, Cambridge University Press, pedia’ book. Secondly, in some places, the Birkhäuser, Basel, 1999, 364 and 352 pp., 2001, 822 pp., £75, ISBN 0-521-36638-0 information is so fragmentary that it DM 238 and 238, ISBN 3-7643-6203-0 and This is the second volume of a two-volume becomes useless. For instance, on page 54 3-7643-6202-2 set on Banach algebras and *-algebras; the there is a special paragraph called ‘Semi- The contributions to these volumes are first volume appeared in 1994, also in the symmetric spaces’, which includes only a dedicated to V. G. Maz’ya, and are partly Encyclopedia of Mathematics and its definition and the trivial statement that all based on talks given at the conference Applications series. It provides a modern locally symmetric spaces are semi-symmet- ‘Functional Analysis, Partial Differential account of basic Banach algebra theory ric. Perhaps the author has no idea about Equations and Applications’ held in and deals with *-algebras. the recent developments in this highly Rostock in September 1998. Vladimir G. It is difficult to describe in detail the con- non-trivial topic, starting with the funda- Maz’ya is the author and co-author of more tents of this voluminous monograph. The mental paper by Z. Szabó (J. Differential than 300 publications and more than a author starts with a chapter devoted to *- Geometry, 1982). This paper shows, in fact, dozen books, and he made significant con- algebras, emphasising their structure and that the locally symmetric spaces form a tributions to many fields of mathematics, exploring the algebraic results (*-repre- ‘subset of measure zero’ in the class of all extending to the theory of Sobolev spaces, sentations, linear maps, irreducible *-rep- semi-symmetric spaces. (ok) capacity theory, boundary integral meth- resentations and hermitian and symmetric ods, qualitative and asymptotic methods of *-algebras) that underlie the theory of H. Reiter and J. D. Stegeman, Classical analysis of linear and non-linear elliptic Banach algebras and *-algebras. The next Harmonic Analysis and Locally Compact boundary value problems, the Cauchy chapter deals with special *-algebras (G*- Groups, London Mathematical Society problem for elliptic and hyperbolic equa- algebras, BG*-algebras, T*-algebras, S*- Monographs New Series 22, Clarendon Press, tions, the theory of multipliers in spaces of algebras, Sq*-algebras, U*-algebras, her- Oxford, 2000, 327 pp., £60, ISBN 0-19- differentiable functions, maximum princi- mitian U*-algebras and γS*-algebras). In 851189-2. ples for elliptic and parabolic systems, and the subsequent chapter the author extends The original book, Classical harmonic analy- boundary value problems on domains with nearly all the results previously known for sis and locally compact groups, by H. Reiter singularities. Banach *-algebras and hermitian Banach appeared in 1968. Reiter died in 1992, A major part of the first volume consists *-algebras (which include C*-algebras as a and his former student Jan Stegeman was of four surveys of his work in various fields very special case) to *-algebras with various asked by Oxford University Press to pre- of mathematics, while other articles in this algebraic restrictions (including automatic pare a new edition. He decided to stay volume have their origin in his joint work continuity for Banach *-algebras and close to the original text whenever possi- with their authors. The first contribution, results for Hilbert and Tomita algebras). ble, but nevertheless, the new edition has by L. I. Hedberg, deals with Maz’ya’s early The final chapter is devoted to locally com- expanded and additional material has results in the theory of function spaces, pact groups (including the study of con- been appended. potential theory and partial differential nected groups, Lie groups, totally discon- The text starts with classical harmonic equations, including his counter-examples nected groups and group representations) analysis (Fourier transforms, the Wiener to the regularity theory, which in a sub- and *-algebras related to them. approximation theorem, and subalgebras stantial way extend the results of E. De This second volume of the set is accom- of L1(Rn)). The next chapter introduces Giorgi and E. Giusti, and M. Miranda. In panied by a wealth of historical remarks certain topological algebras (Wiener alge- the second survey article, N. G. Kuznetsov and examples. At the end, an extensive bras) and an abstract version of the Wiener and B. R. Vainberg discuss results concern- bibliography is attached. The volume also theorem; Ditkin sets, ideals in function ing the unique solvability of two funda- contains unpublished results with com- algebras and sets of spectral synthesis are mental problems of steady-state surface- plete proofs at a graduate student level. also studied. The next chapter concerns wave theory: the problems of time-har- 40 EMS December 2001 RECENT BOOKS monic water waves and of a wave pattern lines’. Such a Stokes phenomenon is a ous way. Through a large number of caused by a body in uniform forward deep-lying characteristic of the given dif- examples and exercises, it is shown that motion in calm water. In the third part, J. ferential equation. A quite complete theo- the Laplace transform is an extremely use- Elschner describes Maz’ya’s work on inte- ry is available in the case of one variable. ful tool in solving linear problems, includ- gral and pseudodifferential operators, The topic treated in the book is the ing ordinary differential equations with while in the fourth, J. Rossman reviews asymptotic theory of holonomic linear dif- constant coefficients or time delay, or time- Maz’ya’s results in the theory of boundary- ferential equations for two complex vari- dependent coefficients, integro-differen- value problems on non-smooth domains; ables with irregular singularities. The tial equations, difference and partial dif- the domains considered here can have problem is formulated in the language of ferential equations, and problems with point singularities, edges or polyhedral flat connections for a meromorphic vector Dirac distribution (via the Riemann- vertices. The contributions based on joint bundle on a complex analytic surface. In Stieltjes integral). All assertions are work with V. G. Maz’ya include papers the first chapter, the key notion of a good proved. written by V. Havin, G. Schmidt, R. Cooke, formal structure for a meromorphic vector This clearly written undergarduate text- A. Grigoryan and T. Shaposhnikova. bundle with a flat connection is introduced book can be recommended to students and The second volume contains most of the and discussed. The second part is devot- teachers of this subject, both in a mathe- invited lectures, as well as a few con- ed to a study of the Stokes phenomenon matical and engineering context. (jmal) tributed papers. There are nineteen con- for connections that admit a good formal tributions, ranging from function spaces structure. The third part of the book stud- J. C. Simo and T. J. R. Hughes, (the Hardy inequality, maximal operators ies analogues of Turrittin’s theorem from Computational Inelasticity, Interdisci- and multipliers in Lizorkin-Triebel space), dimension 1, concerning the existence of a plinary Applied Mathematics 7, Springer, New via the qualitative theory of differential good formal structure for a meromorphic York, 1998, 392 pp., DM 129, ISBN 0-387- equations (maximum and anti-maximum connection (on the pull-back by a sequence 97520-9 principles for certain classes of systems, of complex blowing-up) and their conse- This book deals with numerical simulation perturbation of trajectory attractors for quences. The existence proof is given for for classical non-controversial elastoplas- dissipative hyperbolic equations, and sym- bundles of rank at most five. Throughout, ticity models, avoiding any problems aris- metry and asymmetry of positive solutions the author freely uses the modern lan- ing from pattern formation or material to a class of semilinear equations), the guage of sheaves, D-modules and corre- instabilities. However, large-strain elasto- spectral theory of differential operators sponding functors. plasticity is covered. The ideas of linear (eigenfrequencies of fractal drums and the The book presents a systematic treat- elastoplasticity are clearly explained, first discreteness of the spectrum for the ment of the results published or in one-dimensional setting. Then the Schrödinger operator on certain mani- announced by the author in the last ten models are generalised to three dimen- folds) to results coupling a continuous years. (vs) sions. This is followed by a very clear and description with discrete models and detailed explanation of time (backward numerical results (coupling of finite and P. L. Sachdev, Self-Similarity and Beyond. Euler) and finite element (mixed formula- boundary element methods for the time- Exact Solutions of Nonlinear Problems, tion for displacements, stresses and strains) harmonic Maxwell equations, and hybrid Monographs and Surveys in Pure and Applied discretisations. Next, the authors proceed methods for boundary value problems via Mathematics 113, Chapman & Hall/CRC, to large-strain models and their numerical boundary energy). Boca Raton, 2000, 319 pp., £63.99, ISBN 1- approximations, completed by numerical This is a useful publication giving a good 58488-211-5 tests. This is followed by the objective overview and many interesting results in As its title suggests, the main aim of this finite-difference approximations of the this vast field. (jsta) monograph is to find exact solutions for frame-invariant time derivative of tensors. problems described by non-linear partial Finally, linear viscoelasticity models are C. Sabbah, Equations différentielles à differential equations (PDEs). For this treated. points singuliers irréguliers et phénomène purpose, several techniques and approach- This book is well written, is easy to fol- de Stokes en dimension 2, Astérisque 263, es are considered. Starting from self-simi- low, and contains much useful material for Société Mathématique de France, Paris, 2000, lar transforms that are useful in finding the researchers and graduate students in vari- 190 pp., FRF 150, ISBN 2-85629-085-X asymptotic behaviour of solutions, a con- ous branches of engineering and applied The study of systems of linear differential struction of a blow-up solution and a better mathematics. (jmal) equations in one complex variable around understanding of the structure of the prob- a singular point is an old classical subject lems, the author presents the systematic C. Truesdel and K. R. Rajagopal, An that goes back to Riemann and Fuchs. In group transform approach and the direct Introduction to the Mechanics of Fluids, the case of a regular singularity (the Fuchs Clarkson-Kruskal method for finding such Modeling and Simulation in Science, condition), the solutions have at most poly- self-similar solutions, and also provides Engineering and Technology, Birkhäuser, nomial growth near the singularity. The such further techniques as travelling wave Boston, 2000, 277 pp., DM 148, ISBN 0- higher-dimensional analogues of equa- solutions, exact linearisation (as the hodo- 8176-4012-2 and 3-7643-4014-2 tions with regular singularities are well graph method) of non-linear partial differ- This textbook acquaints the reader with developed using the language of flat con- ential equations, the infinite series continuum equations of fluid motions, in nections on vector bundles, and far-reach- method, and embedding special solutions an elementary but precise way. The ing beautiful generalisations of classical into a more general class in order to obtain authors restrict themselves to isothermal results are available describing the appro- solutions of non-linear PDEs of a more processes. Although compressible Euler priate Riemann-Hilbert correspondence. general character than self-similar ones. equations are also treated, the main The situation is much more complicated The methods iand their limitations are emphasis is on incompressible fluids: the in the case of equations with irregular sin- clearly explained, and are complemented book deals with general simple fluids gularities. This case includes a lot of inter- by a number of solved examples focusing under the incompressibility constraint, the esting examples, such as the Bessel equa- on equations in fluid mechanics and non- linear (Navier-Stokes) fluid, the inviscid tion, the Whittaker equation, the Airy linear diffusion. (jmal) (Euler) fluid, and some second- and third- equation, and many others. The solutions degree examples of non-linear fluids. The of such equations no longer have polyno- J. L. Schiff, The Laplace Transform: equations are correctly derived and enor- mial growth near the singularity, and for- Theory and Applications, Undergraduate mous simple flows for these fluids are mal solutions are almost always divergent. Texts in Mathematics, Springer, New York, introduced, computed and analysed. Analytic solutions are defined only in a sec- 1999, 233 pp., DM 79, ISBN 0-387-98698- Among other topics, monotonous motions, tor with its vertex at the singularity point, 7 viscometric flows, and flows in simple and their asymptotic relation to formal The book introduces the Laplace trans- geometries (both steady and unsteady) are solutions changes when the boundary of form and the related complex variable the- considered. Each section contains several the sector crosses the so-called ‘Stokes ory in a beautiful, pedagogical and rigor- valuable exercises; readers can verify their EMS December 2001 41 RECENT BOOKS solutions with those provided in an appen- have chosen a wide selection of articles, so manifolds, the computer-aided discovery dix. as to present the most important and sur- of new embedded minimal surfaces, hyper- This book will be appreciated by those prising mathematical ideas. The articles bolic geometry, and moduli spaces of desiring a better understanding of fluid are divided into seven groups. Riemann surfaces). The final part, History motions. (jmal) The first part, Interviews and of Mathematics, includes six articles that Reminiscences, contains two interviews with describe the everyday life of mathemati- J.-L. Waldspurger, Intégrales orbitales leading figures from today’s mathematics, cians (their lives, work, interaction, and nilpotentes et endoscopie pour les groupes three reminiscences and memoirs, and one collaborations); these articles are devoted classiques non ramifiés, Astérisque 269, article with mathematical anecdotes. The (for example) to Kurt Gödel, Hilbert and Société Mathématique de France, Paris, 2001, second part, Algebra and Number Theory, Brouwer, and the history of the Bieberbach 449 pp., FRF 400, ISBN 2-85629-096-5 shows in six articles some of the most conjecture. (mnem) Let F be a finite extension of Qp, let G be important and significant problems in the an unramified classical group (orthogonal, field (for example, the proof of the List of reviewers for 2001 symplectic or unitary) over F, and let g be Mordell conjecture, the representation The Editor would like to thank the following for G the Lie algebra of G. Denote by D nil the theory of finite groups, and quaternionic their reviews this year: space of invariant distributions supported determinants). The third part, Analysis, J. Andìl, J. Antoch, M. Nìmcová-Beèváøová, in the nilpotent set on g(F), and by DG,st the also has six articles, describing some inter- L. Bican, M. Brzezina, J. Bureš, E. Calda, M. space of stably invariant distributions on esting discoveries (including the Banach- Dont, A. Drápal, J. Dupaèová, A. Elashvilli, E. g(F). Let H be an elliptic unramified endo- Tarski theorem, Painlevé’s conjecture and Fašangová, M. Feistauer, T. Fürst, J. Hron, M. scopic group of G. The main results of a geometrisation of Lebesgue’s space-fill- Hušková, V. Janovský, J. Ježek, O. John, A. this work (assuming that p is large enough) ing curve). Five articles in the fourth part, Karger, J. Kofroò, O. Kowalski, J. Kratochvíl, are an explicit description of the intersec- Applied Mathematics, demonstrate that P. Kùrka, P. Lachout, M. Lichá, J. Lukeš, J. G G,st tion of D nil and D , and an explicit physics remains at the core of applied Málek, J. Malý, M. Markl, J. Matoušek, D. description of the transfer map from the mathematics; in particular, a combination Medková, J. Milota, J. Mlèek, K. Najzar, J. H H,st G intersection of D nil and D to D nil. The of interesting topics and new kinds of Nekováø, J. Nešetøil, I. Netuka, B. Novák, Š. proofs use earlier results of the author, mathematics contribute to the current Porubský, D. Pražák, P. Pyrih, M. Rokyta, T. G relating D nil to distributions with integral revival of applied mathematics. The fifth Roubíèek, Š. Schwabik, J. Slovák, P. Somberg, support, and detailed calculations based part, Arrangements and Patterns, contains V. Souèek, J. Stará, Z. Šír, J. Štìpán, J. Trlifaj, on the Springer correspondence and the five articles devoted to questions of collab- V. Trnková, J. Tùma, J. Vanžura, J. Veselý, J. Lusztig Fourier transform. (jnek) oration between modern artists and math- Vybíral, M. Zahradník, K. Zimmermann. ematics; here, readers can enjoy a rich All of these are on the staff of the Charles R. Wilson and J. Gray (eds.), mixture of mathematical, artistic and cul- University, Faculty of Mathematics and Mathematical Conversations. Selections tural themes, including articles on Celtic Physics, Prague, except M. Markl, D. Medková from the Mathematical Intelligencer, knotwork, mathematical art, and the pave- and J. Vanžura (Mathematical Institute, Czech Springer, New York, 2001, 488 pp., DM 119, ment of the Baptistery of San Giovanni in Academy of Sciences), M. Nìmcová-Beèváøová ISBN 0-387-98686-3 Florence. The sixth part, Geometry and and Š. Porubský (Technical University, This book contains forty articles that were Topology, explains in six articles some of Prague), J. Nekováø (Cambridge University, published in The Mathematical Intelligencer the most famous discoveries since the England) and J. Slovák (Masaryk University, during its first eighteen years. The editors 1960s (instantons and the topology of 4- Faculty of Natural Sciences, Brno).

42 EMS December 2001