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. 43 Building 303 DK-2800 Kgs. Lyngby, Denmark March 2002 e-mail: [email protected] KRZYSZTOF CIESIELSKI Mathematics Institute EMS Agenda ...... 2 Jagiellonian University Reymonta 4 Editorial ...... 3 30-059 Kraków, Poland e-mail: [email protected] Executive Committee Meeting – Brussels ...... 4 KATHLEEN QUINN The Open University [address as above] e-mail: [email protected] EMS News ...... 7 SPECIALIST EDITORS INTERVIEWS EMS-SIAM Conference ...... 8 Steen Markvorsen [address as above] SOCIETIES Aniversary - Niels Henrik Abel ...... 12 Krzysztof Ciesielski [address as above] EDUCATION Interview - Sir John Kingman...... 14 Tony Gardiner University of Birmingham Birmingham B15 2TT, UK Interview - Sergey P. Novikov ...... 16 e-mail: [email protected] MATHEMATICAL PROBLEMS Union of Czech Mathematicians and Physicists ...... 20 Paul Jainta Werkvolkstr. 10 Mathematicians’ Careers ...... 22 D-91126 Schwabach, Germany e-mail: [email protected] ANNIVERSARIES Forthcoming Conferences ...... 29 June Barrow-Green and Jeremy Gray Open University [address as above] Recent Books ...... 36 e-mail: [email protected] and [email protected] and CONFERENCES Designed and printed by Armstrong Press Limited Kathleen Quinn [address as above] Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK RECENT BOOKS telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134 Ivan Netuka and Vladimir Sou³ek Published by European Mathematical Society Mathematical Institute ISSN 1027 - 488X 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 May 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 e-mail: [email protected] Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, OPEN UNIVERSITY Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e- PRODUCTION TEAM mail: ([email protected]). Please include the name and full address (with postal code), Liz Scarna, Kathleen Quinn telephone and fax number (with country code) and e-mail address. The annual subscription fee (including mailing) is 65 euros; an invoice will be sent with a sample copy of the Newsletter.

EMS March 2002 1 EMS NEWS EMS Committee EMS Agenda EXECUTIVE COMMITTEE 2002 PRESIDENT (1999–2002) 19-21 April Prof. ROLF JELTSCH EMS ‘brainstorming’ meeting at Berlingen (Switzerland) Seminar for Applied Mathematics ETH, CH-8092 Zürich, Switzerland 22-26 April e-mail: [email protected] EMS Lectures by Prof. Gianni Dal Maso (SISSA, Trieste, Italy): VICE-PRESIDENTS Neumann problems in domains with cracks and applications to fracture mechanics Prof. LUC LEMAIRE (1999–2002) Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany). Department of Mathematics Contact: Prof. Stefan Müller, e-mail: [email protected] Université Libre de Bruxelles C.P. 218 – Campus Plaine Bld du Triomphe 13-17 May B-1050 Bruxelles, Belgium EMS Lectures by Prof. Gianni Dal Maso (SISSA, Trieste, Italy): e-mail: [email protected] Neumann problems in domains with cracks and applications to fracture mechanics Prof. BODIL BRANNER (2001–2004) Laboratoire d’Analyse Numérique, Université Paris VI. Department of Mathematics Contact: Prof. François Murat, e-mail: [email protected] Technical University of Denmark Building 303 15 May DK-2800 Kgs. Lyngby, Denmark Deadline for submission of material for the June issue of the EMS Newsletter e-mail: [email protected] Contact: Robin Wilson, e-mail: [email protected] SECRETARY (1999–2002) Prof. DAVID BRANNAN 19-31 May Department of Pure Mathematics EMS Summer School in Craiova (Romania): The Open University Mathematical and numerical methods in computational quantum chemistry Walton Hall Contact: Yvon Maday, e-mail: [email protected] Milton Keynes MK7 6AA, UK e-mail: [email protected] 31 May TREASURER (1999–2002) Executive Committee meeting in Oslo (Norway). Prof. OLLI MARTIO Department of Mathematics 1-2 June P.O. Box 4 EMS Council Meeting, Oslo. FIN-00014 University of Helsinki Finland 3-8 June e-mail: [email protected] Abel Bicentennial Conference, Oslo. ORDINARY MEMBERS Prof. VICTOR BUCHSTABER (2001–2004) 21-26 June Department of Mathematics and Mechanics EURESCO Conference: Moscow State University Discrete Painlevé Equations and the Solvability of Difference Equations 119899 Moscow, Russia in Giens, near Toulon (France) e-mail: [email protected] webpage: http://www.esf.org/euresco/02/ Prof. DOINA CIORANESCU (1999–2002) Laboratoire d’Analyse Numérique 1-5 July Université Paris VI 4 Place Jussieu Congrès de Mathématiques Appliquées à la mémoire de Jacques-Louis Lions 75252 Paris Cedex 05, France Collège de France, Paris (France) e-mail: [email protected] e-mail: [email protected] Prof. RENZO PICCININI (1999–2002) webpage: http://acm.emath.fr/congres-jllions Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca 15 August Via Bicocca degli Arcimboldi, 8 Deadline for submission of material for the September issue of the EMS Newsletter 20126 Milano, Italy Contact: Robin Wilson, e-mail: [email protected] e-mail: [email protected] Prof. MARTA SANZ-SOLÉ (2001-2004) 28-29 September Facultat de Matematiques Executive Committee meeting in Stockholm, at the invitation of the Swedish Universitat de Barcelona Mathematical Society Gran Via 585 E-08007 Barcelona, Spain 31 December e-mail: [email protected] Deadline for bids for the Fifth European Mathematical Congress, 5ecm, in 2008 Prof. MINA TEICHER (2001–2004) Contact: EMS Secretariat, e-mail: [email protected] Department of Mathematics and Deadline for Raising Public Awareness Article Competition Computer Science Contact: Vagn Lundsgaard Hansen, e-mail: [email protected] Bar-Ilan University Ramat-Gan 52900, Israel 2003 e-mail: [email protected] 10-13 February EMS SECRETARIAT EMS-SMAI-SMF Meeting in Nice (France). Ms. T. MÄKELÄINEN Mathématiques Appliquées - Applications des Mathématiques (Applied Mathematics - Department of Mathematics Applications of Mathematics) P.O. Box 4 Contacts: Doina Cioranescu, e-mail: [email protected] FIN-00014 University of Helsinki and Mireille Martin-Deschamps, e-mail: [email protected] Finland webpage: http://acm.emath.fr/amam/ tel: (+358)-9-1912-2883 fax: (+358)-9-1912-3213 1 March telex: 124690 Deadline for proposals for 2004 EMS Lectures e-mail: [email protected] Contact: David Brannan, e-mail: [email protected] website: http://www.emis.de 2 EMS March 2002 EDITORIAL The co-presidents of AMAM 2003 are Rolf Jeltsch, Michel Théra and Michel Waldschmidt. The Scientific Committee is Editorial co-chaired by Pierre Louis Lions (France) Editorial and Sergey Novikov (Russia), and its mem- bers are Lucien Birgé (France), Jean- and AMAM 2003 Announcement Michel Coron (France), Marie-Françoise Doina Cioranescu and Mireille Martin-Deschamps Coste-Roy (France), Alain Damlamian (France), Nicole El Karoui (France), Antonio Fasano (Italy), Olivier Faugeras departments of several of the French (France), Andras Frank (Hungary), Grandes Ecoles and universities. Aside François Golse (France), Michael Gromov from its lobbying on behalf of the applied (France), Eugene Ya. Khruslov (Ukraine), mathematics community, the SMAI is Peter Alexander Markowich (Austria), involved in the publication of journals Michel Merle (France), Jean-François (ESAIM series with EPS Science Mestre (France), Etienne Pardoux Publishing) and a lecture notes series (France), Olivier Pironneau (France), (Mathématiques et Applications with Frédéric Poupaud (France), Dirk Roose Springer), and in the organisation of many (Belgium), Zeev Schuss (Israel), J.Trevor meetings, including the yearly Congrès Stuart (UK), Eitan Tadmor (Israel and d’Analyse Numérique and the SMAI Congres USA) and Vladimir V. Vasin (Russia). The (every 4 years). It has four special interest Organising Committee is co-chaired by groups (concerned with numerical analysis Doina Cioranescu and Mireille Martin- in industry; statistical methods and applied Deschamps, and also contains Jacques probability theory; optimisation and oper- Blum, Denise Chenais and Charles Walte ational research; function approximation) from the University .of Nice. which hold their own yearly meetings. Relations with other scientific societies The conference is structured according to Doina Cioranescu such as the SMF, the Societé Française de the following list of topics: Statistics and the Société Française de 1. Applications of number theory, includ- French mathematicians are grouped into Physique are well developed. The SMAI ing cryptography and coding two learned societies, the Société was a founding member of the 2. Control theory, optimisation, opera- Mathématique de France (SMF) and the International Council for Industrial and tional research and system theory Société des Mathématiques Appliquées et Applied Mathematics, and organised the 3. Applications of mathematics in biology, Industrielles (SMAI). first ICIAM Congress in Paris in 1987. including genomics, medical imaging, The SMF (http://smf.emath.fr/) is a non- The existence of the two societies does models in immunology, modelling and profit organisation, founded in 1872, not split the mathematical community, as simulation of biological systems whose purpose is to ‘defend and promote there are many joint members and the two 4. Scientific computation, including ab mathematics and mathematicians’. Today, societies have several joint projects and initio computation and molecular its membership reaches 2000, with most of activities. dynamics its members being in academics, but also Both societies are involved in interna- 5. Meteorology and climate, including including institutional members such as tional collaboration, particularly at the global change libraries and mathematics departments. European level, and they took part in the 6. Financial engineering Its headquarters are located within the World Mathematical Year 2000 project, 7. Signal and image processing Institut Henri Poincaré in Paris, and there from its onset. On this occasion they 8. Non-linear dynamics is also an Annex in Marseille on the launched the ACM 9. Other applications: probability and sta- Campus of the University in Luminy, The SMAI and the SMF were both tistics, inverse problems, fluid dynam- which deals with the storage and diffusion instrumental in the creation of the EMS, of ics and material sciences of the SMF’s publications. which they are both founding members. So, when the question was raised of how to There will be 12 plenary speakers, 30 mini- The activities of the SMF include: increase the role of applied mathematics in symposia, three round tables and two - publication of professional books and the EMS, they acted jointly and took part poster sessions. The following have already journals in the Berlingen meeting in May 2001. agreed to present a plenary lecture: Alfred - management of the CIRM (Centre In the recent past, mathematicians have M. Bruckstein (Israel), Robert S. Eisenberg International de Rencontres become aware of the broad needs of math- (USA), Roland Glowinski (USA), Leslie Mathématiques), located on the Luminy ematics in other sciences and in technolo- Greengard (USA), Eugenia Kalnay (USA), campus gy, and have responded positively. As Roland Keunings (Belgium), David - lobbying on behalf of mathematics with applications have become more sophisti- Levermore (USA), Pascal Massart (France), political authorities cated and complex, they have required the Marek Musiela (UK), René Schoof (Italy) - animation and reflection within the com- input of many branches of mathematics, and Enrique Zuazua (Spain). munity concerning teaching and some until recently considered as very fun- All EMS members are invited to partici- research in mathematics damental, thereby making the distinctions pate in AMAM 2003: why not propose a - popularisation of Mathematics – for between pure and applied mathematics minisymposium or a poster? example, via the d’Alembert prize less sharp. For information and registration please awarded every other year. refer to our website: http://acm.emath.fr AMAM 2003 /amam/ The SMAI (http://smai.emath.fr/) was found- After the Berlingen meeting, the EMS pro- ed in the early 1980s, when a large portion posed the organisation of a conference on Doina Cioranescu is Director of Research at of the applied mathematics community felt this subject. They suggested that the con- CNRS, Laboratoire Jacques-Louis Lions, the need to have specific representation. ference be organised jointly by the SMF Université Pierre et Marie Curie, 175 rue du Since then, the SMAI’s membership has and the SMAI, be held in Nice, and be Chevaleret, 75013 Paris, France. risen to close to 1400, including institu- called Applied Mathematics and Applications of Mireille Martin-Deschamps is Professor at the tional members, such as the research cen- Mathematics (AMAM 2003). It will be held Laboratoire de Mathématiques, Université de tres of some private or semi-public corpo- at the Palais des Congrès in Nice from 10 Versailles et Saint-Quentin, 45 avenue des rations, as well as the applied mathematics to 15 February 2003. Etats-Unis, 78035 Versailles Cedex, France. EMS March 2002 3 EMS NEWS EMSEMS ExecutiveExecutive CommitteeCommittee MeetingMeeting Brussels (Belgium), 9-10 February 2002

Present: Rolf Jeltsch (President, in the the following two events in Brussels: the spring 2002 it will include mathematics. Chair), David Brannan, Bodil Branner, Conference of the Belgian Presidency of AlphaGalileo is a collaboration between Victor Buchstaber, Doina Cioranescu, Luc the European Union’s Research Council Finland, France, Germany, Greece, Lemaire, Olli Martio, Marta Sanz-Solé, Event (creation of the European Research Portugal and the UK, with support from Mina Teicher. Apologies had been received Area) and a conference on International best the ESF and other European bodies. It was from Renzo Piccinini. practices in evaluation of research in public agreed to make positive contact with its In attendance by invitation: Carles institutes and universities. On both occasions organisers. Casacuberta (Publications Officer), Robin they were able to talk briefly to the On the Secretary’s suggestion, David Salinger was elected Publicity Officer for a further term of 2003-05. The Helsinki Secretariat reported on some membership matters that would hopefully be ready for Council, and there was a brief discussion of the need to regis- ter mathematical societies in Russia at the moment. At the request of certain member societies in need, a reduction in their EMS dues for specific years was agreed.

Scientific Meetings Mina Teicher reported on the Summer Schools in 2002 in Eilat and Craiova. Applications to the EU for summer schools in Spain, Porto and CIME had been sub- mitted for future years. There was a view that the EMS should select subjects for summer schools and then ask societies or active people to organise the schools. Wilson (Editor-in-Chief, Newsletter), David Commissioner Ph. Busquin. The EMS had A call had been circulated for sugges- Salinger (Publicity Officer), Saul Abarbanel pointed out that no mathematicians were tions for the 2003 EMS Lecturer, preferably (Chair of the Applied Mathematics on his Scientific Advisory Board of 45 per- in a more pure field. Professor Gianni Dal Committee), Ari Laptev (Chair of the Local sons. Maso of SISSA, Trieste, was the EMS Organising Committee of 4ecm), Thomas Rolf Jeltsch had attended an informal Lecturer for 2002, and would speak at the Hintermann (Managing Director of the meeting on digitising (in a searchable way) University of Paris VI and the Max Planck EMS Publishing House), Sir John mathematical literature during the Joint Institute in Leipzig. Kingman (nominee for EMS President for Mathematics Meeting of the AMS, MAA The Diderot Mathematical Forum 2003-06), Helge Holden (nominee for and SIAM in San Diego. DMF5 on Mathematics and EMS Secretary for 2003-06), and Tuulikki The Treasurer reported that the finan- Telecommunication had taken place in Mäkeläinen (Helsinki Secretariat). cial state of the EMS was sound. The Lausanne, Eindhoven and Helsinki. Much The President thanked the Université Financial Statements for the year 2001 of the scientific programme had been Libre de Bruxelles and the Belgian were accepted and signed by the Executive excellent, and the video conferencing had Mathematical Society for their invitation Committee members; it was noted that the been successful. There was a discussion of and generous hospitality, and welcomed Society currently has an Investment Fund the future of the Diderot Mathematical all participants. of 70K euro, in shares and investment Forums, and a feeling that the EMS should funds, together with some cash in hand. A think afresh about the DMF concept, in Officers’ Reports budget proposal for 2003 and 2004 was order to maximise the value of Society The President reported on the composition agreed for presentation to the Council in activities. of the Scientific Committee of amam03, the Oslo. There was some discussion of presi- Ari Laptev, President of the Organising By-Laws of the European Mathematical dential expenses, and the need not to limit Committee of the 2004 European Congress Foundation, MATHDI, the appointment the choice of President to people with their of Mathematics in Stockholm, reported on of Manuel Castellet as Chair of ERCOM, own sources of funding. the progress made for the Congress. The extension of the time for the EMS-RPA The Publicity Officer proposed that the 4ecm has now a home page at competition, and on the EMS Summer EMS prepare a letter to go in corporate http://www.math.kth.se/~4ecm. Lennart Schools. He reported that at the EMS- societies’ mailings to their members, and Carleson (Stockholm) will be Chair of the SIAM conference in Berlin there had been this was agreed; electronic distribution Scientific Committee and Björn Engquist 420 participants from 42 countries, includ- could be considered. The EMS would (Stockholm) its Vice-Chair; and other pos- ing 36 European countries and all EU and share a booth with Zentralblatt at ICM-2002 sible members of the Committee were dis- Associated States. in Beijing, would have a booth at the Abel cussed, including the need for balance in The Zentralblatt Consultative Committee Conference in Oslo until the Tuesday, and its composition. Only the Chair and Vice- meeting on 6 November 2001 in would have a booth at amam03 in Nice. It Chair will be made public. Heidelberg had been business-like and was agreed that contact should be made routine. The EMS is now trying to further with member societies whose number of There was a stimulating discussion of the the drive to make ZentralblattMATH a truly EMS members has not increased recently. EMS Prizes, and several recommendations European endeavour, starting with a brain- A new venture, the AlphaGalileo Project, is will be put to Council: storming weekend in Berlingen on 19-21 seeking to improve the communication of 1. Eligibility for an EMS Prize is open to April 2002. European research to the world’s media any European mathematician who has Luc Lemaire and Rolf Jeltsch attended (http://www.alphagalileo.org); from late not reached his/her 35th birthday on 30 4 EMS March 2002 EMS NEWS June of the year of the congress. In the There will be a conference, amam03, in Chairs of Committees in Oslo on 2 June event of a possible candidate having Nice on 25-27 June 2003 with the title 2002 from 2-4 p.m., chaired by Rolf had a broken career pattern, a corre- Applied Mathematics - Applications of Jeltsch. sponding increase in age will be accept- Mathematics, sponsored jointly with SMAI Saul Abarbanel reported his wish for the able at the discretion of the Prize and SMF. It will be chaired by Rolf Jeltsch, Applied Mathematics Committee to meet Committee, up to a maximum of three Michel Thera and Michel Waldschmidt. annually. It was decided to reconsider the additional years. By way of example The Scientific Committee Co-Chairs are role and future of the Databases Committee only, this provision is intended to cover Pierre-Louis Lions (Université Paris- in Berlingen. Manuel Castellet (2002-05) items such as military service, women Dauphine) and Sergei P. Novikov had succeeded Ole E. Barndorff-Nielsen having children, etc. (University of Maryland and Moscow), and (1998-2001) as Chair of ERCOM. Mina 2. A mathematician is defined to be the Scientific Committee Coordinator is Teicher had become Acting Chair of the ‘European’ in the context of EMS Prizes Alain Damlamian (Université Paris 12). Summer Schools Committee during the if they are of a European nationality or The Local Organising Committee consists absence abroad of Renzo Piccinini (2000- their normal place of work is within of: Doina Cioranescu (Université Paris VI) 03); it was decided to dissolve this Europe/substantial amount of their (Chair), Mireille Martin-Deschamps Committee, and to discuss the question of mathematical work done in Europe. (Université de Versailles) (Chair), Jacques how to organise summer schools in future 3. The Prize Committee will endeavour to Blum, Denise Chenais and Charles Walter (possibly via the planned Meetings ensure a fair balance of nominations, as (Université de Nice Sophia-Antipolis). Committee) in Berlingen in April. It was also regards the following criteria: speciality There will be a discounted conference fee agreed to discuss the future of the within mathematics, nationality, and for members of the EMS, SMF and SMAI. Publications Committee (Carles Casacuberta, geographical base. The Congress web address is: 1998-2001-02) in Berlingen. The 4. Following the identification of the Chair http://www.acm.emath.fr/amam. Executive Committee reminded itself that of the Prize Committee, their name, The EC agreed to give moral support to it had agreed previously to set up a address and e-mail address will be pub- a conference Janos Bolyai Commemorating Meetings Committee, to be initially lished in the EMS Newsletter, together Year 2002 on 8-12 July 2002 in Cluj. chaired by Luc Lemaire (2001-04) with an invitation from the Chair to all The next EMS Council meeting will be on The Education Committee had discussed mathematicians to send in suggestions 1-2 June 2002, starting on Saturday 1 June with EU a possible follow-up to the with reasons and one or two names of at 10 a.m., in Auditorium 2 of Georg Reference Levels Project for 16-year-olds, people who could be contacted with fur- Sverdrups Hus, on the University of Oslo to cover the group up to 18-year-olds. ther information on the nominee. The campus. The delegates representing indi- call should be published in the vidual members are: Giuseppe Anichini Publishing Newsletter, on EMIS, sent to societies (1996-99-03), Vasile Berinde (2000-03), The Board of Trustees of European and mentioned on the Congress web Giorgio Bolondi (1996-99-03), Alberto Mathematical Foundation (EMF) had page. Conte (2000-03), Chris Dodson (2000-03), approved the final version of the EMF By- 5. The ‘place of work’ in the rules is jean-Pierre Francoise (2000-03), Salvador Laws, which will now be registered with the intended to include place of study. S. Gomis (2000-03), Laurent Guillopé Chamber of Commerce in Zürich and with 6. Prizes are to be awarded for the scientif- (2000-03), Klaus Habetha (1996-99-03), Berne, after which the EMF will become a ic merit of the person’s work. Willi Jaeger (2000-03), Tapani Kuusalo legal body. The Statutes have been accept- 7. The Chair of the Prize Committee will (1996-99-03), Marina R. Marchisio (1998- ed by the Notary Public. suggest the members of the Prize 2001-05), Vitali Milman (1998-2001-05), There was an important and lengthy Committee for approval by the EMS László Márki (1996-99-03), Andrzej discussion of the business of the EMS Executive Committee. Their identities Pelczar (2000-03), Zéev Rudnick (2000- Publishing House, which (for commercial will not be made public until after the 03), Gérard Tronel (2000-03), Robin reasons) will not be set out here. EMSph Prizes are awarded. Wilson (2002-05), and Sebastià Xambó- business will be a topic for discussion at the Descamps (2002-05). Oslo Council meeting. The Committee The Prize Committee for the Felix Klein Committee Reports will be written, with agreed that, even simply by virtue of its Prize consists of three persons from the possibly a few minutes oral representation existence, EMSph should encourage com- EMS, two from the Kaiserslautern at the meeting, followed by a question and mercial publishers to ‘do a better job for Institute, and one from ECMI. answer session. Committee chairs will be mathematics’. A call for bids to hold the 2008 ECM invited to attend. There will be a presenta- It was agreed that all EC members who appeared in the December Newsletter and tion of 4ECM within the Council meeting. knew of a good article for the EMS will be repeated. The Executive Committee’s nomina- Newsletter should tell the Editor-in-Chief tions for the President (Sir John Kingman), about it, and those not in English might be Vice-President (Luc Lemaire), Secretary translated – subject of course to the (Helge Holden) and Treasurer (Olli author’s and publisher’s agreement. Robin Martio) had been decided earlier, and Wilson was appointed to a second term of there was a discussion on nominations for office (2002-04) as Newsletter Editor-in- the other vacancies. There was also a stim- Chief. It was again stressed that it was ulating discussion of essentially technical important to have the Newsletter on EMIS, changes to the Statutes and By-Laws that with a time lag of about six months being would be proposed to Council by the appropriate. Executive Committee. The EC noted that Bernd Wegner, The President was arranging an ad hoc Editor-in-Chief of Zentralblatt, would reach meeting Berlingen 2: Publishing, Meetings, his 60th birthday on 18 February 2002. It Integrated Initiatives, on 19-21 April 2002. expressed its unanimous congratulations Among the topics would be Zentralblatt to him on this auspicious day, and wished MATH, Digitalisation and EMS Publishing. him every happiness and many years to come! His contribution to mathematics for Society Committees a quarter-century as Editor-in-Chief of It was agreed to publish the remits of the Zentralblatt had been outstanding, and the committees on EMIS, to have a Vice-Chair whole mathematical community world- for each Committee, terms of office for all wide was greatly indebted to him. committee members, and an Executive The Publications Officer reported on a Committee member as a contact for each number of volumes in various stages of the Committee. There will be a meeting of the preparation and production process. EMS March 2002 5 EMS NEWS Relations with Mathematical Institutions should be phrased in terms of the underly- be followed by a meeting of the EMS Chairs There was a concerned discussion of the ing principles to be supported by the EMS, of Committees. lack of adequate representation of rather than get involved in details that At the invitation of the Swedish Mathematics at the European Science would vary from country to country. Mathematical Society, an EC meeting will Foundation (ESF), and it was agreed to be held on 28-29 September 2002 in make strong representations to ESF on a Future EC/Council Meetings Stockholm. The Local Organising more prominent position for mathemati- There will be an EC Meeting in Oslo on 31 Committee of amam2003 have invited the cians in ESF’s PESC [Physical and May 2002, to finalise preparations for the EC to meet in Nice on 9-10 February 2003. Engineering Sciences Standing Council meeting starting the following Committee] and its working groups. day. The meeting will be preceded by a And finally … Rolf Jeltsch will represent the EMS at meeting of the EMF Board of Trustees. The EC participants expressed their heart- the IMU General Assembly – the EMS is an There will be a Council Meeting in Oslo felt thanks to Luc Lemaire and his Affiliate Member of the IMU. on 1-2 June 2002, in Auditorium 2, in Université Libre de Bruxelles and Belgian Georg Sverdrups Hus. This building is the Mathematical Society colleagues for a well- new University Library, located on the run meeting in a congenial atmosphere. Oslo University Campus. The meeting will David A. Brannan

MeetingMeeting ofof thethe EMSEMS CouncilCouncil Oslo: 1-2 June 2002

The EMS Council meets every second bers of the Executive Committee shall be year. The next meeting will be held in elected for a period of 4 years. Committee Oslo, Norway, on 1-2 June 2002, before members may be re-elected, provided that the Abel Bicentennial Meeting in Oslo consecutive service shall not exceed 8 The EMS EC thanked the Norwegian which begins on 3 June. The first session years. No current member has served on Academy of Sciences and Letters for creat- of the Council meeting will start at 10 a.m. the Executive Committee for 8 years, so ing the Abel Prize for Mathematics, recog- on 1 June, and will run all day with a all existing Committee members are in nising it as a major event for mathematics. break for lunch. The second session will principle available for re-election. There are no restrictions on the subject probably start at 9 or 10 a.m. on 2 June, The Council may, at its meeting in area or age of prize-winners, and the selec- and may last most or all of the day with a Oslo, add to the nominations received tion process will be very open. There will break for lunch, depending on the volume and set up a Nominations Committee, dis- be an Abel Prize Committee as well as a and complexity of the business on the joint from the Executive Committee, to Scientific Advisory Panel working to sup- agenda. consider all candidates. After hearing the port the Prize Committee. report by the Chair of the Nominations It was agreed to publish a notice for the Membership of the EMS Executive Committee (if one has been set up), the J.-L. Lions Commemorating Conference in July Committee Council will proceed to the elections to in the EMS Newsletter. The Council is responsible for electing the the Executive Committee posts. President, Vice-Presidents, Secretary, If a nomination comes from the floor Any Other Business Treasurer and other members of the during the Council meeting, there must The EC had a stimulating and stimulated Executive Committee. The present mem- be a written declaration of the willingness discussion of the Bologna Declaration. On bership of the Executive Committee, of the person to serve, or his/her oral the one hand it was agreed that the long- together with their individual terms of statement must be secured by the chair of term autonomy of universities was impor- office, is as follows. the Nominating Committee (if there is tant; on the other hand, that universities President such) or by the President. It is recom- could not ignore that governments gener- Professor Rolf Jeltsch (1999-2002) mended that a statement of policy of the ally supply most university funding Vice-Presidents candidates nominated from the floor throughout Europe. Professor Luc Lemaire (1999-2002) should be available. Professor Bodil Branner (2001-04) Secretary Accommodation arrangements Professor David Brannan (1999-2002) Delegates to the Council meeting, who are Treasurer planning to attend the Abel Centennial Professor Olli Martio (1999-2002) Meeting, are advised that their accommo- Members dation arrangements should be made Professor Victor Buchstaber (2001-04) through the normal Abel Centennial Professor Doina Cioranescu (1999- Meeting organisation arrangements. For 2002) delegates to the Council who are not Professor Renzo Piccinini (1999-2002) attending the Abel Centennial Meeting, Professor Marta Sanz-Solé (2001-04) an address for accommodation arrange- Professor Mina Teicher (2001-04) ments will be provided later.

The President may serve only one term of Secretariat: Ms. Tuulikki Mäkeläinen office, so Rolf Jeltsch cannot be re-elected Department of Mathematics as President. David Brannan and Renzo P. O. Box 4 Piccinini have indicated that they do not FIN-00014 University of Helsinki wish to be re-elected. The Executive Finland Committee proposes the names of Sir e-mail: [email protected] John Kingman (Cambridge) for President It was agreed to draft a policy statement and Helge Holden (Trondheim) for David Brannan on the Bologna Declaration, which should Secretary Secretary of the EMS be discussed at Council in Oslo – this Under Article 7 of the Statutes, mem- e-mail: [email protected] 6 EMS March 2002 REPORT for Lausanne: mawww.epfl.ch/benarous Fifth Diderot Mathematical Forum /Recherche/diderot.html MATHEMATICS AND TELECOMMUNICATIONS Video-conferencing technology The three cities were connected to each Eindhoven, Helsinki, and Lausanne other using a star network, with external centre node located in the University of 22-23 November 2001 Oulu, Finland. Lausanne and Eindhoven were connected to Oulu using 384 kbps ISDN lines. Helsinki was connected to From a mathematical point of view, the In the Eindhoven Workshop : Oulu through Internet (over the 2.5 Gbps topic chosen, Mathematics and C.P.M. (Stan) Baggen (Philips Research, FUNET backbone network). Telecommunications: problems connected with Eindhoven): Coding for informed decoders It was interesting to share presentations cell phones, allowed the presentation of a Marc Moonen (Katholieke Universiteit between the sites, although this required a very wide variety of mathematical Leuven): Signal processing and mathematical relatively long broadcasting time. Some approaches: from probability theory to modeling challenges in ADSL/VDSL high-speed expected better technical quality in the harmonic analysis and algebra, several telephone line modems videolinks. areas of mathematics play, and will contin- Jean-Paul M.G. Linnartz (Philips ue to play an important role in the devel- Research, Eindhoven): A mathematical From Helsinki opment of the subject. It is patent though, framework for resource management in wireless There were 50 registered participants especially from what one heard during the networks (including the 11 invited speakers). On the Forum, that some of the mathematical Philippe Godlewski (ENST, Paris): first conference day, there were approxi- tools needed are yet to be developed (cer- Models, achievable performance and capacities mately 50 additional non-registered peo- tainly in the stochastics area and in alge- in cellular mobile networks ple attending the lectures given by Neuvo, braic coding, but somewhat more surpris- Richard J. Boucherie (University of Hagenauer, and Urbanke. The main ingly in more mature areas of mathematics Twente, Enschede): Mobility and channel speaker, Dr Yrjö Neuvo, reported that he such as one-dimensional harmonic analy- borrowing in mobile communications networks had been contacted afterwards by scientists sis), and that communications problems Frans M.J. Willems (Eindhoven both from Finland and from abroad and thus offer a very attractive area for mathe- University of Technology): Embedding infor- that this feedback had been rewarding. maticians. mation in data-streams The organisers were Paul Urbach Joergen Bach Andersen (Aalborg From Eindhoven (Philips Research Center Eindhoven), University): Electromagnetics and wireless There were approximately 85 registrations Olavi Nevanlinna (Helsinki University of communications for the Eindhoven site: not everybody Technology) and Gérard Ben Arous (École Alle-Jan van der Veen (University of showed up on both days, but all lectures Polytechnique Fédérale de Lausanne). Technology Delft): Use of factor analysis were well attended. The emphasis in analysis in array signal processing Eindhoven was on signal processing and The speakers were: A.J.E.M. (Guido) Janssen (Philips coding theory, but there was also a lecture For the lectures shared through the videolink: Research, Eindhoven): Gabor systems and on electromagnetics for wireless communi- (from Helsinki) Yrjo Neuvo (Helsinki): communication theory cations, by Bach Andersen. The level of the Mathematics for mobile communications, Luc Vandendorpe (Université presentations was well above average. (from Eindhoven) Joachim Hagenauer Catholique de Louvain): Signal processing Many who attended were very enthusiastic (Technische Universität München): aspects in CDMA systems. about the quality of the lectures and have Information and coding theory for mobile asked the lectures to be placed on the web, phones In the Lausanne Workshop: which has been done (see above). (from Lausanne) R. Urbanke (EPFL, Emre Telatar (EPFL): Application of random Lausanne): Low density parity check codes matrices in communications From Lausanne Alice Guionnet (CNRS-École Normale Attendance was reasonably large (40). The In the Helsinki Workshop: Supérieure de Lyon): Some mathematical conference was opened from there by the Samuli Aalto (Helsinki University of aspects of random matrix theory in communica- EMS President, Rolf Jeltsch. Most partici- Technology): Teletraffic analysis of multicast tions pants were obviously pleased by the quality networks Marina Monsurro (EPFL): Algebrico-geo- and diversity of the talks, as well as the Kaisa Nyberg (Nokia Research Center): metric codes depth of the mathematical problems Cryptography in UMTS Piyush Gupta (Bell Labs, Murray Hill, underlying the future progress of this Ioan Tabus (Tampere University of USA), The traffic-carrying capacity of ad hoc important area of engineering. Technology): On the use of the Hadamard wireless networks The forum was a true success on the sci- transform for index assignment over channels François Baccelli (INRIA, École entific side, and an exciting event on the with memory Normale Supérieure): Stochastic networks social side. Being jointly organised by peo- Savo G. Glisic (University of Oulu): and topical maps ple in communications (M. Hasler, M. Modelling and analysis of code acquisition Patrick Thiran (EPFL): Connectivity in Vetterli) and in mathematics (G. Ben process by using signal flow graph theory ad-hoc networks Arous), its scientific programme could real- Jyrki Lahtonen (University of Turku): Jean-Yves Le Boudec (EPFL): Network ly draw from both sides and show a very Algebraic geometry in error correcting codes calculus broad spectrum of the possible interfaces Jyri Hämäläinen (Nokia Networks): TX Hans-Andrea Loeliger (ETH Zürich): of maths and telecoms. There were ses- diversity feedback modes as a function of FB bits Graphical models and signal processing sions on Stochastic methods in communi- Tapani Ristaniemi (University of Martin Hasler (EPFL): Communications cations, Networking, and Signals and Jyväskylä): Independent component analysis using chaos Systems. and CDMA Martin Vetterli (EPFL and UCB): Pirkko Kuusela (Helsinki University of Sampling signals with finite rate of innovation Suggestion Technology): Internet congestion control delay It may be a good idea for the future to differential equation models Presentations organise a poster session. This would give Olav Tirkkonen (Nokia Research Some of the presentations are available on young people the opportunity to present Center): Clifford algebras and space time codes the following web sites: their work, and would make the conference Ilkka Norros (VTT Information for Helsinki: www.math.hut.fi/diderot2001 more lively. Of course, it would inevitably Technology): Internet traffic as a stochastic for Eindhoven: www.research.philips.com cause more work for the organisers. process /diderot2001 Jean-Pierre Bourguignon EMS March 2002 7 EMS NEWS AppliedApplied MathematicsMathematics inin ourour ChangingChanging WWorldorld First EMS-SIAM Conference in Berlin, 2-6 September 2001 Peter Deuflhard and Rolf Jeltsch

The Computer Science Campus of the Free University of Berlin with communication tent especially installed for the conference (left, ZIB; right, Computer Science building)

The First EMS-SIAM Conference (web One of the most recent areas where through the Gotthard tunnel, the location page: http://www.zib.de/amcw01) took mathematics comes into play is genomics. of a horrible accident shortly after. place on the attractive Science Campus of Michael Waterman gave an excellent The fact that new mathematics and the Free University of Berlin. The local short glimpse on algorithms for under- simulation tools are needed in materials host institution was the Zuse Institute standing DNA sequences, where a lot of science was demonstrated in two rather Berlin (ZIB), and the Co-Chairs were Rolf discrete mathematics is involved. The lec- different ways by Jon Chapman and Jeltsch (ETH), Gil Strang (MIT) and Peter ture of Pietro Perona showed that we can Michael Griebel. Jon Chapman derived a Deuflhard (ZIB); unfortunately, for sud- already do quite a bit using present math- thin-film model for superconducting den health reasons, Gil Strang was unable ematics, but still have a long way to go to materials by singular perturbation tech- to attend. More than 400 participants make automatic visual recognition really niques. from 42 countries (36 of them European) possible. Michael Griebel studied new nanotube attended this event, with about 41% from Alfio Quarteroni demonstrated that properties of certain carbon materials, by Germany and 8% from the US. The when classical computational fluid dynam- applying Hilbert’s space-filling curve to majority of participants were quite young. ics meets medical applications, new chal- the design of parallel adaptive multi-grid The idea of the Conference was to bring lenges come up – such as modelling the methods. It is here that mathematicians together applied mathematics from both cardiovascular system – for example, the may co-author materials patents. sides of the Atlantic. As indicated by its interaction of the walls of arteries with the Global models for the atmosphere cou- title, the focus of the conference was on blood flow. pled with ocean dynamics are known to be new areas where applied mathematics is a The challenges in the simulation of too large for today’s computers: Andrew coming main player, with a strong impe- traffic throughout a whole country were Majda investigated new mathematical tus from applications. impressively presented and discussed by possibilities of modelling such coupled Kai Nagel. With the help of his methods, PDE systems. The derived smaller models Scientific programme one can directly observe the bottlenecks. build bridges to the whole large-scale As is usual for such a large conference, the Unfortunately, the need for this kind of models, which are currently beyond our backbone was the invited plenary talks, simulation became apparent immediately computability horizon. and of the invited speakers half came after the Conference: He had, in fact, Martin Grötschel demonstrated the dif- from Europe and half from the US (see shown traffic flow simulations through ficulties of designing optimal telecommu- below). Switzerland, with one or two pipes nication networks. Even though integer 8 EMS March 2002 EMS NEWS

Round table discussion with Martin Grötschel (Chair), Round-table discussion: Rolf Jeltsch, Tom Manteuffel, Joyce McLaughlin, Applied Mathematics in Europe Hilary Ockendon and Alfio Quarteroni. The round-table discussion was chaired by Martin Grötschel from ZIB. The panelists were Rolf Jeltsch (ETH Zürich, President of EMS), Tom Manteuffel (President of SIAM), Joyce McLaughlin (Rensselaer Polytechnical Institute), Hilary Ockendon (Oxford University and President of the European Consortium for Mathematics in Industry) and Alfio Quarteroni (Politecnico di Milano, Italy, and EPFL Switzerland). The discussion mainly focused on three points: – what research should be done in applied mathematics, trends and the future? programming is, in principle, well under- ed their latest results in 313 contributed – how should education at university stood, the sheer size of the problems still papers and 44 posters. These sessions level cater for applied mathematics, needs a lot of mathematical intuition for were arranged around the same topics as inclusion in a general mathematical the invention of good theoretically-based the mini-symposia, and were scheduled so education, and special curricula for heuristics. The profit of such calculations that participants in the mini-symposia applied mathematics and also for com- goes into millions of euros. could also attend the corresponding ses- putational science and engineering? sions of contributed papers. The idea was – the structure of learned societies in that international speakers coming from mathematics and applied mathematics different schools of thought could fruitful- in Europe. ly interact with the contributors. Not only did the panellists give excellent contributions, the discussion also benefit- Social programme ed greatly from the competence of the A communication tent had been especial- audience which included many leading ly installed on the campus for the applied mathematicians in Europe, head Conference. It turned out to be the par- of departments and presidents of soci- ticipants’ favourite meeting place over a eties. The EMS sponsored a reception cup of coffee or tea or during lunch after the round-table where the discussion breaks. Since all lectures were within walk- continued on a more informal level. ing distance, most of the participants During the Conference, the EMS and walked together in small groups to the SIAM discussed future joint conferences communication tent to continue their dis- that could focus on more specialised top- cussions. ics. The EMS recognised that conferences The evening before the conference, a on the same level as the one in Berlin get-together party took place in that tent, should continue, probably on a biannual and after the Mandelbrot tele-lecture Co-Chairs Peter Deuflhard and Rolf basis, but maybe with varying partner soci- there was a Barbecue Party which was Jeltsch with Erlinda Körnig, the ‘engine’ eties. The EMS Executive Committee has extremely well attended. The highlights of the conference office. already decided to organise the next con- of the party were the open-air Klezmer ference with the two French societies, Tom Hou studied microscale singulari- music from the balcony of the ZIB build- Société Mathématique de France (SMF) ties of three-dimensional vortex sheets, ing that could be heard down in the BBQ and Société de Mathématiques which may even be hard to detect in real area and an indoor classical string quartet Appliquées et Industrielles (SMAI). The life. The mathematical difficulty stems (Beethoven) in the greenhouse interior of Conference will be held in Nice, 10-13 from Kelvin-Helmholtz instabilities that the beautiful computer science building. Feb 2003 and the topic will be Applied make the problem ill-posed. For pictures, see the web page: Mathematics – Applications des Mathématiques For health reasons, Benoit Mandelbrot http://www.zib.de/amcw01/gallery/conf.html (for details, see page 3). The main idea is could not be physically present in Berlin Apart from these campus events, the ZIB to give young researchers in applied to deliver his lecture, but the organisers staff was extremely helpful. A cultural e- mathematics an opportunity to get to established a direct real-time connection guide was prepared and some footloose know new topics in applied mathematics to IBM Yorktown Heights: this connection tours were organised, which allowed par- and applications of mathematics, and to made it possible for Mandelbrot to deliver ticipants and their companions to enjoy give them a chance to network, exchange his lecture, which put the Black-Scholes Berlin and its surroundings. views and interact. formula under strong dispute. The impression was as though he were directly in the Berlin auditorium – certainly an interesting experience for all participants – and the satellite connection was so good that there was a lively discussion at the end of the lecture. A second backbone structure was the organisation of 45 mini-symposia. Most of them lasted for two hours with four speak- ers presenting their results. The topics of the mini-symposia, which had been partly solicited and all reviewed before, were chosen from the same areas as the plenary Queue during the BBQ party. lectures. In addition, researchers present-

EMS March 2002 9 EMS NEWS of these limit problems. These results have been extended, with different collab- EMS Lecturer 2002: Gianni Dal Maso orators, to the case of other linear and non-linear equations and systems. The 2002 EMS Lecturer will be Professor a student of the Scuola Normale of Pisa At present his main research interests Gianni Dal Maso (e-mail: [email protected]) from 1973 to 1977, and graduated in are in free discontinuity problems. These of the International School for Advanced Mathematics from the University of Pisa in are variational problems where the func- Studies (SISSA) in Trieste, Italy. 1977, with Ennio De Giorgi as his advisor. tional to be minimised depends on a func- He will visit two different locations in He was then a graduate student of the tion and on its discontinuity set, whose Europe to give the same series of lectures Scuola Normale di Pisa from 1978 to 1981, shape and location are not prescribed. In on Neumann problems in domains with cracks working with Professor De Giorgi on many many cases the discontinuity set can be and applications to fracture mechanics to audi- problems connected with the theory of considered as the main unknown of the ences in Leipzig and Paris (see details gamma-convergence, that was developed problem. Examples are given by the min- below), affording as many interested math- in those years. imisation of the Mumford-Shah functional ematicians as possible the opportunity to After serving as assistant professor of in image segmentation, and by the mini- attend, and to discuss the topics with him. Mathematical Analysis in the Faculty of mum problems that appear in many varia- Engineering of the University of Udine tional models for fracture mechanics, An abstract of his lecture series is as fol- from 1982 to 1985, he moved to the where the unknown crack is represented as lows: International School for Advanced Studies the discontinuity set of the displacement The first part of the course is devoted to the (SISSA) in Trieste. He worked there as vector, and the functional to be minimised study of solutions to non-linear elliptic equa- associate professor of mathematical analy- is the sum of the elastic energy and of an tions in Ω – K, where Ω is a two-dimensional sis from 1985 to 1987, and as full profes- integral on the discontinuity set, which smooth domain and K is a compact one-dimen- sor of calculus of variations since 1987. He represents the work done to produce the sional subset of Ω. The solutions are required was awarded the Caccioppoli Prize in 1991 crack. to satisfy a homogeneous Neumann boundary and the ‘Medaglia dei XL per la condition on K and a non-homogeneous Matematica’ of the Accademia Nazionale Selected list of publications Dirichlet condition on δΩ. The main result is delle Scienze detta dei XL in 1996. An introduction to gamma-convergence, Birkhäuser, the continuous dependence of the solution on K, At SISSA he has developed his research Boston, 1993. with respect to the Hausdorff metric, provided interests on gamma-convergence, Integral representation on BV(Ω) of Γ-limits that the number of connected components of K homogenisation theory, and free disconti- of variational integrals, Manuscripta Math. 30 remains bounded. Classical examples show that nuity problems, and has been the supervi- (1980), 387-416. the result is no longer true without this hypoth- sor of 19 Ph.D. students working on these Asymptotic behaviour of minimum problems esis. subjects. He currently serves as the head with bilateral obstacles, Ann. Mat. Pura Appl. (4) Using this stability result, the second part of of the Sector of Functional Analysis and 129 (1981), 327-366. the course develops a rigorous mathematical for- Applications of SISSA. Some necessary and sufficient conditions for mulation of a variational quasi-static model of the convergence of sequences of unilateral con- the slow growth of brittle fractures, introduced Research interests vex sets. J. Funct. Anal. 62 (1985), 119-159. by Francfort and Marigo. Starting from a dis- Professor Dal Maso started his research (with U. Mosco) Wiener criteria and energy crete-time formulation, a more satisfactory con- work in Pisa while Ennio De Giorgi was decay for relaxed Dirichlet problems, Arch. tinuous-time formulation is obtained, with full developing the new notion of gamma-con- Rational Mech. Anal. 95 (1986), 345-387. justification of the convergence arguments. vergence to deal in a systematic way with (with G. Buttazzo) Shape optimization for EMS members and others interested in the following kind of phenomena: the Dirichlet problems: relaxed formulation and attending one of these series of lectures solutions of variational problems depend- optimality conditions, Appl. Math. Optim. 23 are warmly welcomed to do so, and to talk ing on a parameter may converge to the (1991), 17-49. informally with Professor Dal Maso on solution of a limit problem, even if the (with J. M. Morel and S. Solimini) A varia- related topics. However attendees are integrands of the functionals to be min- tional method in image segmentation: existence strongly encouraged to contact the local imised do not converge in any reasonable and approximation results, Acta Math. 168 organisers of the series that they plan to sense, or converge to a limit integrand that (1992), 89-151. attend in advance, so that the necessary is different from the integrand of the func- (with A. Garroni) New results on the asymp- practical arrangements can be made (for tional minimised by the limit of the solu- totic behaviour of Dirichlet problems in perfo- example, having a lecture room of suffi- tions. Gamma-convergence is a very effi- rated domains. Math. Mod. Meth. Appl. Sci. 3 cient size for everyone coming). cient tool to tackle these kinds of prob- (1994), 373-407. lems. (with L. Ambrosio and A. Coscia) Fine prop- Local arrangements In his work in Pisa and Udine he stud- erties of functions with bounded deformation, Location 1: Max Planck Institute for ied several problems related to gamma- Arch. Rational Mech. Anal. 139 (1997), 201-238. Mathematics in the Sciences, Leipzig convergence. In particular he developed, (with F. Murat) Asymptotic behaviour and Dates of the lectures: 22-26 April 2002 with Giuseppe Buttazzo, several tech- correctors for Dirichlet problems in perforated Local contact: Prof. Stefan Müller, Max niques for proving, under different domains with homogeneous monotone opera- Planck Institute for Mathematics in the hypotheses, that the gamma-limits of inte- tors, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 Sciences, Inselstr. 22-26, D-04103 gral functionals are still integral function- (1997), 239-290. Leipzig, Germany (e-mail: [email protected]) als, and he studied, by gamma-conver- (with A. Braides) Non-local approximation of Location 2: Université Paris VI, gence techniques, the asymptotic behav- the Mumford-Shah functional, Calc. Var. Partial Laboratoire d’Analyse Numérique iour of solutions to minimum problems Differential Equations 5 (1997), 293-322. Dates of the lectures: 13-17 May 2002 with strongly oscillating obstacles. Using (with F. Murat, L. Orsina and A. Prignet) Local contact: Prof. François Murat, the notion of capacity, he also gave a com- Renormalized solutions of elliptic equations Université Paris VI, Laboratoire d’Analyse plete characterisation of the sequences of with general measure data, Ann. Scuola Norm. Numérique, Boite courrier 187, 75252 obstacle problems whose variational limit Sup. Pisa Cl. Sci. (4) 28 (1999), 741-808. PARIS Cedex 05, France (e-mail: is still an obstacle problem. (with G. Alberti and G. Bouchitte) The cali- [email protected]); telephone: +33-1- He later used these techniques to study, bration method for the Mumford-Shah func- 44274299; fax: +33-1-44277200 with Umberto Mosco, the asymptotic tional, C. R. Acad. Sci. Paris Ser. I Math. 329 behaviour of the solutions of Dirichlet (1999), 249-254. Brief biography problems for the Laplace equation in per- (with R. Toader) A model for the quasi-stat- Professor Dal Maso was born in Vicenza in forated domains, and to determine the ic growth of brittle fractures: existence and 1954; in 1955 his family moved to Trieste, general form of their variational limits, as approximation results, Arch. Rational Mech. where he had his basic education. He was well as the fine properties of the solutions Anal., to appear. 10 EMS March 2002 EMS NEWS EMSEMS lecturlectureses forfor 20032003 CallCall forfor prproposalsoposals

For some years the European tions, in order to give as many people as ite) for the lecture series, the sites, and the Mathematical Society has been running a possible the opportunity to attend. The organisers of the schools will vary from successful series of EMS Lectures. In 2000 EMS will give some preference to lecturers year to year, to cover a wide range of the G. Papanicolau gave a series of lectures on who visit institutions that might not nor- subject. Time Reversed Acoustics at the University of mally attract prominent lecturers or semi- The Society now invites proposals for at least Crete (Heraklion) and on Financial nar speakers, and would prefer the geo- one Lecture Series for 2003. Proposals should Mathematics at ETH in Zürich, and the graphical locations of the lectures to be sig- contain at least the topic (title and short 2001 EMS Lecturer, M. Vergne, spoke on nificantly distant from each other (for description), the name of the proposed lec- Convex Polytopes at the University of Malta example, North and South Europe, or East turer, the sites, the timing at each site, con- and at the Universita Degli Studi Roma, and West Europe), in order to maximise ditions for participants, and the name and Tor Vergata. The 2002 Lecturer is G. Dal the impact of the lectures. address of the organiser submitting the Maso (SISSA, Trieste), whose research The costs of participation should be proposal. Some preference will be given to interests include gamma-convergence, kept low, and (if possible) grants should be applications that involve the writing-up of homogenisation theory, and free disconti- available to people from countries that the Lecture Notes into a volume suitable nuity problems cannot afford any financial support. The for publication. The EMS Lectures may be in pure or EMS will guarantee its moral support to Please send proposals for series of EMS applied mathematics, or may span both the selected lecture series, and will pay for Lectures in 2003, to: areas; however, for 2003 the Society would the lecturer’s travel costs and for posters Professor D. A. Brannan, Faculty of prefer to appoint at least one lecturer in advertising the lectures within the Mathematics and Computing, The Open pure mathematics, in order to retain a rea- European mathematical community. It will University, Walton Hall, Milton Keynes sonable balance. With this activity, the also do its best to help the organisers to MK7 6AA, UK. Society aims to encourage European math- raise funds, and is likely to offer some Fax: +44 1908 652140; e-mail: d.a.bran- ematicians (especially young ones) to meet financial support to organisers for partici- [email protected] and study together current developments pants who are young or come from Please send your proposals by 30 September in mathematics and its applications. The European countries with financial difficul- 2002 if possible; the Society would hope to lectures should take place over several days ties. decide on proposals within a month or so. (up to 5 days) in each of at least two loca- Topics (which may be single or compos- David A. Brannan, Secretary

NewNew deadlinedeadline forfor ArticleArticle CompetitionCompetition

Last year the European Mathematical a general audience were published Articles (translations) may, however, also Society announced a competition to throughout the world, and many valuable be submitted in French, German, Italian inspire the writing of articles with a math- ideas for articles popularising mathematics or Spanish. The English (or alternative ematical theme addressing a general audi- were generated. The Committee for language) version should be submitted ence. The deadline for submissions was Raising Public Awareness of Mathematics both on paper and electronically. originally set as 31 December 2001. In of the European Mathematical Society There will be prizes for the three best response to comments, and to give more (acronym RPA) believes that it is vital that articles, of 200, 150 and 100 euros, and the time for suggestions of a wider range of such articles be written. In order to inspire winning articles will be published in the articles, the Society has decided to accept future articles with a mathematical theme EMS Newsletter. Other articles from the submissions in any European language and to and to collect valuable contributions, which competition may also be published, if extend the deadline for submission of articles to deserve translation into many languages, space permits. Furthermore, it is planned 31 December 2002. the EMS wishes to encourage the submis- to establish a web-site containing English The advertisement of the competition sions of articles on mathematics for a gen- versions of all articles from the competi- is repeated below, with the appropriate eral audience, through a competition. The tion approved by the RPA Committee. changes incorporated. EMS is convinced that such articles will By submitting an article for the compe- Vagn Lundsgaard Hansen contribute to raising public awareness of tition, it is assumed that the author gives Chair, Raising Public Awareness of mathematics. permission to translation of the article Mathematics Committee (RPA) The RPA-committee of the EMS invites into other languages, and for possible mathematicians, or others, to submit man- inclusion in a web-site. Translations into Articles in many ways, uscripts for suitable articles on mathemat- other languages will be checked by per- math displays, ics. sons appointed by relevant local mathe- says, To be considered, an article must be matical societies and will be included on the EMS committee of RPA: published, or be about to be published, in the web-site. A competition surely may, a daily newspaper, or some other general Articles should be sent before 31 inspire to the way, magazine, in the country of the author, December 2002 to the Chairman of the RPA in which to pay, thereby providing some evidence that the Committee of the EMS: as we say, article does catch the interest of a general Professor Vagn Lundsgaard Hansen, attention to public awareness! audience. Articles for the competition Department of Mathematics, Technical shall be submitted both in the original University of Denmark, Matematiktorvet, During World Mathematical Year 2000, language (the published version) and Building 303, DK-2800 Kongens Lyngby, many articles on mathematics addressing preferably also in an English translation. Denmark. e-mail: [email protected]

EMS March 2002 11 ANNIVERSARY ReadRead thethe Masters!Masters! ReadRead Abel!Abel! Otto B. Bekken

It appears to me that if one wants to make absorbed by it, and I decided to devote myself to progress in mathematics one should study the mathematics ... [7, p.104]. masters and not the pupils. Weierstrass’s first publication was on This quotation from Abel was presented ‘Abelian functions’. He was very much a by his first biographer Carl Anton Bjerknes follower of Abel, and according to Mittag- in 1880 [5]. The extract above is from Leffler [9] (see also [12]), he often gave the Edwards [6], who continues: advice to his students: It is as good an idea to read the masters now Read Abel, read Abel! as it was in Abel’s time. The best mathematicians For the Weierstrassian rigorous analysis know this and do it all the time. Unfortunately, of today, a good starting point is a detailed students of mathematics normally spend their study of some of Abel’s letters. We will early years ..., and make little or no reference to return to this, but to get the appropriate the primary literature of the subject. The stu- setting we need some highlights on Abel’s dents are left to discover on their own the wis- mathematical life. dom of Abel’s advice. In this they are being cheated [6, p.105]. Without Holmboe, no Abel! Edwards further develops his answer to Niels Henrik Abel was born on 5 August ‘why should we read the masters?’ He 1802 near Finnøy in Norway, but his math- weakness in his methods, so a short paper quotes André Weil as saying: ematical life really started in 1818. After was sent to Professor Degen in As a young normalien I had studied spending some school years without show- Copenhagen for publication as a Danish Riemann, and later Fermat. I was persuaded ing any particular distinction, he got a new Science Academy memoir. Degen could very early that diligent attention to the great mathematics teacher. The young Bernt not point to anything wrong either, but he mathematicians of the past is a source of inspi- Michael Holmboe, from 1815 also an assis- asked Abel to elaborate it more by giving ration ... Having had the benefit of such experi- tant of Prof. Christoffer Hansteen at the details of an example: x5 – 2x4 + 3x2 – 4x + ence, I naturally found myself led to include his- University, was only seven years older than 5 = 0. As we know, Abel himself found his torical commentaries to put in proper perspective Abel. Through Holmboe’s new approach mistake. the expositions, which were in danger of falling to teaching, giving the pupils appropriate In 1824 he published his first proof that into excessive dogmatism ... [6, p.107] problems to work on in addition to the reg- it was generally impossible to solve equa- We refer to Edwards for more details of ular chores, Abel’s creative talent was real- tions of degree 5 in the Cardano-Bombelli his arguments on why we should listen to ly fired. Soon Holmboe had to give him manner. Problems involving equations Abel’s advice today. The full passage con- more. continued to be his favorite theme, as Abel cerning this advice in Ore’s biography of Together Abel and Holmboe worked wrote to Holmboe from Paris in October Abel reads: through Euler’s three books on the calcu- 1826. Degen’s reply contained further “I have bought what I believe we do not have lus, which were university texts. Library important advice for Abel ‘... to study ellip- at home, and still have more here, which I will records show Abel borrowing Newton’s tic transcendentals’. send in the spring... Among the books is the fifth Arithmetica Universalis and Principia This started Abel on his second main volume of the Mécanique Céleste. Perhaps you Mathematica, Gauss’s Disquisitiones contribution to mathematics. His work will be good enough to deliver it to Hansteen Arithmeticae, Lagrange’s Calcul de Fonctions, with integrals and elliptic functions, which with my regards ... anyone who has composed and other works of the masters. It is really led to the famous ‘Paris Memoir’ and the such a work can look back upon his scientific amazing which books and journals were ‘race with Jacobi’. The mathematical career with satisfaction.” Abel confirms his great available at the University Library of this details of this area are no longer in current admiration for Laplace in a marginal observa- young institution, founded only in 1813. standard curriculas. Here we concentrate tion in his mathematical notebook: “It is readily Abel himself commented upon this, com- on the third area in which Abel was inter- seen that any theory written by Laplace will be paring his library to those in Copenhagen ested, and where he is often mentioned as superior to all produced by mathematicians of a and Berlin. a founder and forerunner of what was to lower standing. It appears to me ...” [11, Holmboe continued to be his closest come, the theory of analysis. But first we p.138] friend, to whom Abel opened up both need a few more details on Abel’s life. Searching Abel’s Paris notebook, we mathematically and personally throughout found the marginal comment in French [2, his life. Mathematically, Abel moved at a To Berlin and Paris p.79]. Laplace himself, however, is quoted pace that Holmboe, of course, could not The Bergen bishop Pavel met Professor by Kline [8, p.436], saying: follow – and neither could his university Hansteen in the western part of Norway, Read Euler, read Euler! He is the master of teachers, the professors Hansteen and and wrote in his diary for July 1821: us all ... Rasmusen. ... told me about a son of the Pastor Abel of Euler certainly belonged among the Typical is the story of the quintic equa- Gjerstad, who now goes to school in Christiania masters that the young Abel had read dili- tion – to prove or disprove the existence of [Oslo], and who is one of the greatest mathe- gently. a general formula for solving polynomial matical geniuses. When he has passed his exam- For the ‘Nouvelle Edition’ of Abel’s equations of degree 5. Through his read- en artium, we plan to put together a grant for Works, Weierstrass helped to obtain some ing, Abel became acquainted with Cardano him to travel abroad. We expect to see in him material from Berlin. After its publication, and Bombelli’s presentation of formulas one of the world’s best mathematicians ... in a letter to Sophus Lie from April 1882, for cubic and quartic equations. He quick- The rumour spread. Holmboe, we find: ly started to make his own research notes, Hansteen and Rasmusen understood that ... as I learned to know him from Crelle’s Mathematiske Udarbeidelser, his first note- they had a jewel in their custody, and they Journal during my student years, this has book from 1818-20, where we find lived up to the responsibilities. On their become of the greatest importance to me ... The ‘Equations of third degree and solutions strong recommendation the young representation given by Abel ... became the first (by Cardan)’ (see [1, p.139]). Norwegian university (opened 1813) and important mathematical problem ... which I In 1821 he thought he had solved the the Parliament (created 1814) gave Abel a luckily could solve. In the 7th semester of my problem of the quintic equation. Holmboe, two-year fellowship to go abroad. original political science studies I became Hansteen and Rasmusen could find no Abel’s first stop was Copenhagen, and 12 EMS March 2002 ANNIVERSARY theorem reached through so simple con- asked him, if possible, to overcome my aversion siderations’ (see [7, p.63]). It was present- against mathematics which had resulted from my ed to the Academy on 30 October 1826. long and fruitless efforts. During a three Cauchy should have read it and given his months’ period he proceeded so far that I got into judgement to the Academy before print- my head algebra, function theory, ... It is unnec- ing, but he never did. A long and exciting essary to say that I found his instruction clear story can be told about the Memoir, ending and his methods very useful. [11, p.243] with the rediscovery of Abel’s original in Thus, Abel was also worth listening to, 1953 in Biblioteca Moreniana in Florence as a teacher! by Viggo Brun (see [11]). The fate of his greatest memoir trou- bled Abel for the rest of his life, until on 6 January 1829, from his sickbed at Froland he wrote a two-page note on his ‘addition theorem’. The note was published by Crelle in the Journal, and it made Jacobi ask for the Memoir, which was finally print- ed in 1841. Without this note from Froland it probably would have remained in Cauchy’s drawer. Abel also spent some happy days at Froland. From his notebook during his summer visit there in July- August 1828, we quote, as his ‘manifesto’: ... The situation was that one tried to solve the equations without knowing that this was pos- Vigeland Sculpture of Abel in Oslo sible at all ... and if it then was impossible, one would search for ever without finding the solu- then, with recommendations from the tion ... Instead of searching by trying or guess- Danish Professor von Schmidten, he went ing how to integrate functions, one should to August Leopold Crelle in Berlin. Crelle rather investigate if it is at all possible to do so was a famous construction engineer of in some specified way. If the problem is posed in German railroads and highways, but was this way, it contains the seed for the solution ... also very much up to date on current math- I have treated many branches of the analysis in ematical research. Meeting Crelle became this way, and even though I often have posed a new turning point of Abel’s life, and they problems that have exhausted my abilities, I developed a life-long (sic!) intense friend- have obtained results throwing light on the ship. As we know, Crelle and Abel created nature of quantities which belong to the task of the first German Journal für die Reine und mathematics to study. References Angewandte Mathematik. Almost all Abel’s 1. Niels Henrik Abel, Mathematiske works were published here in the first years Epilogue Udarbeidelser, Notebook from 1818-20, Oslo 1826-29 of the Journal’s existence (see [10, In November 1826 Abel returned to University Library. p.20]). Berlin, and in June 1827 was back in 2. Niels Henrik Abel, Memoirs de Mathématique, Abel stayed in Berlin for only five Christiania without job or income. He had Paris Notebook dated 6 August 1826, Oslo months – very important months for our offers from Crelle to remain in Berlin, but University Library. story. Here he read Cauchy’s 1821 Analyse he had to return home! Abel was in love 3. Niels Henrik Abel, Oeuvres Complètes (ed. B. Algébrique, and developed further his with his country – always and everywhere M. Holmboe), 1839. strong admiration for Cauchy’s work. He thinking of how to serve his university and 4. Niels Henrik Abel, Oeuvres Complètes, had already used Cauchy’s results on per- his friends at home. This is shown by many Nouvelle Edition, 2 vols. (ed. L. Sylow and S. mutations in his 1824 paper on the quintic. passages from his letters. Lie, Christiania, 1881. In July 1826 Abel arrived in Paris, his next Abel had no job. He had a chance in 5. C. A. Bjerknes, Niels Henrik Abel: en skildring mathematical stop. His tragic personal 1825-26 when Rasmusen became Chief av hans liv og arbeide, Aschehoug 1929 (1st ed. acquaintance with Cauchy is illustrated Cashier of The National Bank, but the job Stockholm, 1880). through a letter to Hansteen in August went to Holmboe. The University adminis- 6. Harold M. Edwards, Read the Masters! in 1826: tration wrote (see [7, p.43]): Mathematics Tomorrow (ed. L. A. Steen, Finally I have arrived at the focus of all my he was not considered so easily able to adjust Springer-Verlag, 1981, pp. 105-110. mathematical wishes, to Paris ... Above all I himself to the students’ ability. 7. Elling Holst, Carl Størmer and Ludwig would like to have my memoir completed ... to be In 1828 he finally got to substitute for Sylow, Festskrift ved 100-aarsjubilæet for Niels presented to the Institute ... I have the hope that Hansteen, when Hansteen went to Siberia Henrik Abels fødsel, Kristiania, 1902 (an edi- the Academy will print it ... [7, p.39]. to research on magnetism. The University tion also exists in French ). and in one to Holmboe in October 1826: administration now wrote that they were 8. Morris Kline, Mathematical Thought from I showed it to Cauchy, but he scarcely would extremely satisfied with the ‘easy-to-understand’ Ancient to Modern Times, Oxford, 1972. look at it. Without bragging I dare say it is way with which he organises and presents his 9. Gösta Mittag-Leffler, Niels Henrik Abel, Ord good. I am curious to hear the verdict of the lectures ... och Bild, Stockholm, 1903. Institute. ... Cauchy is ‘fou’, and he is unap- In the meantime, Abel advertised in the 10.MA 290: Topics in the History of proachable, but he is the mathematician who newspaper for pupils in mathematics – Mathematics, Unit 14, Algebra and the these days best knows how to present mathemat- both for laggard students and for school- Profession of Mathematics, by Jeremy Gray, ics ... He is now publishing a series of memoirs boys preparing for the examen artium. Open University, 1987. entitled Exercises des Mathématiques. I buy After Abel’s death at Froland on 6 April 11.Øystein Ore, Niels Henrik Abel: Mathematician them and read them diligently. 1829, one of these students wrote a beauti- Extraordinary, Chelsea 1974 (original in Abel’s Paris Memoir was later described ful obituary [11, p.242]: Norwegian, Oslo, 1954). by Jacobi as ‘the most important discover- Many who have been tutored by Abel have ies done in mathematics in this century’, by declared that his presentation was very intelligi- A more recent extensive biography of Abel is: Legendre as ‘monumentum aere peren- ble, and personally I have the same experience. Arild Stubhaug, Niels Henrik Abel and his Times. nius’, and by Picard as ‘there is maybe in After having tried in vain to profit from a not Called Too Soon by Flames Afar, Springer-Verlag, the history of science no such important a very gifted teacher’s lectures, I went to Abel and 2000 (originally in Norwegian, 1996). EMS March 2002 13 INTERVIEW InterviewInterview withwith SirSir JohnJohn KingmanKingman Interviewer: Tom Körner (Cambridge)

mathematics, and probability seemed to me to combine the best of deep pure math- ematics and real-world applications.

Who did you do your PhD under? I had planned to work with Lindley, but he left Cambridge just as I started PhD work in 1960 and I was supervised by Peter Whittle. After a year he left too, and sug- gested that rather than following him to Manchester I should go to Oxford to work with David Kendall. I spent a year in Oxford, at the end of which David was elected to a new chair in Cambridge, and I returned with him as a member of the teaching staff. So I never finished my PhD.

Did switching supervisors mean that you had to switch problems? My work on queueing theory had led me to more fundamental problems in Markov chain theory, and to what became the the- ory of regenerative phenomena. There was certainly a change of emphasis, and I was very much influenced by David Kendall, in mathematical style and taste as well as in substance. Although I was no longer his student, I worked closely with him until I left Cambridge for the new University of Sussex in 1965.

Did you enjoy a new university untram- melled by tradition? Sussex in the 1960s was a very exciting place, alive with new ideas and opportuni- ties. My wife was teaching history there, and we made many friends across the whole range of subjects. Sir John Kingman is the Director of the Isaac Were there any teachers at school or uni- Newton Institute for Mathematical Sciences. A versity whom you particularly remember? In 2002 the new universities of the 1960s Cambridge graduate, he was, successively, I had several very good teachers at school, are often difficult to distinguish from their Professor at the new University of Sussex, and received a lot of encouragement in my older brethren. Have they added anything Wallis Professor in Mathematics at Oxford ambition to study mathematics. At permanent to the system? University. In 1985 he became Vice-Chancellor Cambridge I had a number of lucky All British universities were affected by the of Bristol University, where he stayed until breaks. In my second year Michael Atiyah new departures taken by Sussex, Warwick 2001. He has been Chair of the Science and joined the College and supervised my pure and the other new universities. Many of the Engineering Research Council, President of the mathematics: an education in itself. When things we now take for granted in tradi- London Mathematical Society, and President of I told him of my interest in probability and tional universities were pioneered by these the Royal Statistical Society. statistics, he arranged for me to be taught universities, especially in new subjects and He is the EMS Executive Committee’s nominee by Dennis Lindley, perhaps the best interdisciplinary collaboration. for EMS President from 2003-06. teacher of the subject of his generation. There were also a number of quite dread- After four years at one of the newest uni- What sort of background do you come from? ful lecturers in Cambridge at that time, versities you went as professor to the oldest My father’s family come from Somerset in who had better remain nameless. in England. How did Oxford contrast? the West of England, where his father was Statistics in Oxford in 1969 was frankly a a coal miner. My grandfather was adamant There was very little probability in the mess. There was no professor of statistics, that his two sons should not go down the Cambridge course when you did it. How did the only chair having been abolished some mine, and my father got to the nearby you come to choose to work in probability years before. The only statistician who held University of Bristol and became a PhD in theory? a chair was Maurice Bartlett, who was chemistry. He eventually moved to In my summer vacations I worked in the Professor of Biomathematics and was sup- London to a scientific job with the Post Office Engineering Research Station posed to concentrate on advising biologists Government and married my mother from on problems in what we would now call about their statistical and mathematical a London family. My brother and I were applied probability, especially on conges- problems. I was appointed Professor of brought up in the suburbs of London, tion in telephone systems. I was fascinated Mathematics to raise the profile of proba- where I attended a small grammar school. by the mathematical problems that arise bility theory (but not statistics) in the From there I won a scholarship to read from stochastic models. In those days Faculty of Mathematics. Of course, mathematics at Pembroke College, Cambridge mathematics was rigidly divid- Maurice (and his successor Peter Armitage) Cambridge. ed between pure and traditional applied and I conspired to persuade Oxford to 14 EMS March 2002 INTERVIEW take statistics seriously, and now there is a and I should be surprised if this were neg- INI, you see that most of them are in uni- proper statistics department teaching atively correlated with mathematical abili- versity teaching positions to which they mathematicians and non-mathematicians. ty. Of course, an affectation of incompe- return mathematically refreshed. tence can be a useful defence mechanism. The local problems in Oxford do reflect a Even if the Newton Institute works on an more global problem in integrating mathe- A modern vice-chancellor not only has to international scale does it work at a British matics and statistics. Statisticians often feel take a lot of hard decisions but acts as a level? Can ordinary lecturers at a British hard done by in traditional mathematics focus of resentment for many members of university really find the time and resources departments and press for separate depart- the university. Did you find it hard to take to join one of your programmes? ments, courses and degrees. What do you the personal animosity? We have asked this question, and the evi- feel about this? It is no good becoming a vice-chancellor if dence so far is that they can. If we find evi- Remember that statistics is not a subset of you want to be loved. On the other hand, dence to the contrary, we shall approach mathematics, and calls for skills and judge- you can be respected as someone with the our funders to seek resources to improve ment that are not exclusively mathemati- interests of the university at heart, and as the situation. cal. On the other hand, there is a large someone whose decisions are seen to be intersection between the two disciplines, fair and considered. In practice, I found it You are Chairman of the Statistics statistical theory is serious mathematics, possible to get on well with people with Commission set up by the UK Government and most of the fundamental advances, whom I disagreed about important issues. to keep official statistics honest. Is this task even in applied statistics, have been made necessary? Can the Commission succeed in by mathematicians like R. A. Fisher. It is Which decisions that you took as vice-chan- it? And should this be its main task? important to expose students of mathe- cellor are you most satisfied with? Which do There is a job to be done, both in ensuring matics to statistics, which many will choose you most regret? the integrity of Government statistics, and as a career. There is no easy way to achieve My best and my worst decisions had to do in countering widespread scepticism along the right structure in a university, and no with the appointment of particular profes- the lines of the sneer (attributed by Mark single optimal solution. sors. It is the most important job of a vice- Twain to Disraeli) “Lies, damned lies and chancellor to appoint the best possible aca- statistics”. Only time will tell whether we Which of your mathematical results are you demic leaders: there can be no good uni- can succeed, but I am hopeful. proudest of? versity without good professors. The one that has given me most satisfac- Finally I would like to ask about the tion, and which I think lies deepest, is the Was it possible for you to keep up your European Mathematical Society itself. Why characterisation of diagonal Markov tran- mathematical interests as vice-chancellor? do you think it is necessary? sition probabilities. It is part of the theory Yes, but not as much as I would have liked. Because we live in a world in which increas- of regenerative phenomena which I intro- ingly decisions affecting the mathematical duced, although it was inspired by David You have now moved to be Director of the community are made at a European level. Kendall, and which is I think an important Isaac Newton Institute in Cambridge. Is it There is a pressing need to raise the pro- area of the theory of random processes. an easier job? file of mathematics with those who take The result which has been most influen- A very different job, but very challenging. these decisions. There is much else that the tial is undoubtedly the subadditive ergodic The success of the Institute depends on EMS can and will do, but its most impor- theorem, conjectured by John choosing the most exciting fields of pure tant job is to argue the case that mathe- Hammersley and Dominic Welsh. They and applied mathematics several years matics is essential and must be supported. rightly saw that it would have a wide range ahead, and then attracting the best mathe- If we do not hang together, we shall hang of applications, and I was lucky enough to maticians from all over the world. My pre- separately. find a proof. decessors Michael Atiyah and Keith In terms of applications outside mathe- Moffatt have set me a very high standard. Some people see the EMS as a child which matics, my early work on queues in heavy People sometimes fear that the mathe- will grow up to be something like the AMS. traffic is now a standard part of opera- matical world will become divided into an What do you think? tional research. Some biologists believe élite group of researchers jetting every six The American Mathematical Society is a that some of my results in population months from one research institute to very successful operation in the US con- genetics, especially a Markov process on another and a lumpenproletariat of teach- text. The EMS can certainly learn from the equivalence classes of finite sets called the ers. AMS, but Europe is not America. For coalescent, are important for the under- instance, many countries have their own standing of genetic diversity. Do you think this is likely to happen? successful mathematical societies which the No. If you look at the lists of visitors to the EMS must complement, not try to replace. How did you move into administration? I got involved in the peer review work of the Science and Engineering Research Council, first in mathematics and then more widely, and in 1981 was invited to become its Chairman. I enjoyed the prob- lems of research funding across a broad range of subjects, and when in 1985 I was asked to head the University of Bristol I welcomed the opportunity to lead a great research university.

Most mathematicians claim both to despise administration and to be bad at it. Why do you differ? There are plenty of counterexamples to your assertion. In Britain alone Peter Swinnerton Dyer was in charge of the whole university system, and Michael Atiyah was a very successful President of the Royal Society. In my experience many mathematicians have proved good leaders, Isaac Newton Institute for Mathematical Sciences

EMS March 2002 15 INTERVIEW InterviewInterview withwith SerSergeygey PP.. NovikovNovikov (part(part 2)2)

Interviewer: Victor M. Buchstaber (Moscow)

Part 1 of this interview appeared in the previ- cles, the community of physicists thirsted of the 1960s. Experts in theoretical ous issue. to study modern mathematics. In turn, I physics heard something about topology also had the desire to study these branches and wanted to get acquainted with it. After Tell us about how you took your first steps of theoretical physics. a period of study I faced the same problem into new areas. I started with statistical mechanics and as that at the end of the 1950s: how should The lack of serious interaction between quantum field theory and quickly under- I start? mathematicians and mechanicians in mod- stood that no success can be achieved this ern theoretical physics was a failure of the way: it is necessary to learn the material What was your first work in these new Moscow State University Department of step by step from simple ideas to compli- areas? Mechanics and Mathematics in the 1950s cated ones. In due time, this scheme was I was interested in Einstein’s general rela- and 1960s. thought through by Landau. Together tivity. I was deeply impressed by the fun- I had the opportunity to get acquainted with Lifshits they wrote a series of text- damental discovery in this area that our with the foundations of mechanics and books forming a high road for studying universe is far from being eternal, living with the theory of incompressible fluid at theoretical physics (though it is useful to only 10-20 billion years, while continuous- seminars by friends of mine, and this was study some parts by using textbooks of ly expanding. all I could get in this direction at the other authors): it is necessary to begin with Khalatnikov asked me to give a careful perusal of their researches devoted to the state of the universe in the vicinity of a sin- gularity. Together with my disciple Bogoyavlenskii, I wrote a series of papers devoted to anisotropic perturbations of the standard model of the universe. We man- aged successfully to apply the technical tools of working with many-dimensional dynamical systems: I took the ideas of these tools from my participation in the seminars of my friends at the Department of Mechanics and Mathematics in the 1960s. However, the mathematicians in our department chose only things that could be rigorously proved, while we had to extend these limits. It soon became clear that it is senseless to consider the cycle of compression that preceded the current expansion because, after a small perturbation, an isotropic compression achieves a Belinskii-Lifshits- Khalatnikov complicated regime with a complicated singularity that cannot be extended anywhere. We found out that the observable isotropy of the expanding uni- verse does not follow unambiguously from the laws of the Einstein classical general relativity, in any natural statistical setting with initial data at an early stage if the mat- ter is in some state accessible to the under- standing of modern physics. However, modern astronomical obser- vations lead to the conclusion that the uni- verse had already become isotropic at a very early ‘inflationary’ stage in which the substance was in a mysterious condition. This certainly decreased the value of works devoted to non-isotropic cosmological models. S.P. Nonikov I stopped my work in this area, although friends and colleagues Department of Mechanics and Mechanics, then to proceed with Field theory (Zel’dovich, Khalatnikov, I. D. Novikov, Mathematics. and Quantum mechanics, and only after that and others) invited me to turn to quantum I heard in Gelfand’s circle that quantum should one study Statistical mechanics and gravity with them, because I could not mechanics conceals beautiful mathematics. Quantum field theory. It is also good to learn believe that a quantisation of the Einstein I also heard from my brother [the physicist Hydrodynamics, Elasticity theory, Physics of gravity is really necessary: the scales at Leonid Keldysh] that quantum field theory continuous media, and Kinetics. which this quantisation must take place are was of great importance. Following this path for some years, I too fantastic and unattainable. In the mid-1960s, influenced by the decided to begin an active interaction with progress in the theory of elementary parti- physicists of the Landau school at the end How did you change to soliton theory, where 16 EMS March 2002 INTERVIEW tion), the situation turns out to be very and in which methods of algebraic geome- interesting. The development of this try were intensively applied. method, which was realised in this case by Krichever (1976-77), required the total What about your conjecture giving a solu- algebraisation of the procedure to release tion of the classical Riemann-Schottky it from both the Hamiltonian systems and problem by soliton methods? the self-adjoint operators: you obtain solu- For some years in the late-1970s I closely tions of the Kadomtsev—Petviashvili equa- examined the formulas of Its-Matveev type tion by using only data from algebraic for solutions of the KdV equation and of geometry.. Krichever type for solutions of the KP This was a decisive step in understand- equation. They are of the form u(x, y, t) =2 ing the connections between solitons and ∂2/∂x2 log θ(Ux + Vy + Wt + Z; B) + const. complex algebraic geometry. At the same I asked myself: ‘Is this expression an effec- time, the method presents difficulties: we tive formula, as is the case in classical face the problem of singling out real solu- analysis?’ I decided that it isn’t. tions having physical sense: for example, We do not know in which cases the for the famous sine Gordon equation, the matrix B is determined by a Riemann sur- problem of the theory of real periodic solu- face, and this is precisely the Riemann— tions have remained open. Problems of Schottky problem. Moreover, the vectors this kind can be solved readily and effec- U, V, and W must be connected with the tively only within the framework of the the- matrix B by complicated relations that Victor Buchstaber with Sergey P. Novikov ory of self-adjoint operators, but this is not nobody understands. so many important results are due to you? the case for the sine Gordon equation. How one can make such formulas effi- Working in a circle of physicists in 1973, I Grinevich and I are now making serious cient? My idea was that one should initial- got acquainted with the remarkable math- progress here. ly regard the matrix B and the vectors U, ematical ideas of soliton theory – namely, Later on, many works devoted to the V, and W as independent variables. All with the method for the inverse scattering development of these ideas were complet- relationships among them must follow problem, which had been discovered as a ed at my seminar. Krichever, Dubrovin, from the requirement that the entire result of the joint activity of experts in the- Veselov, Bogoyavlenskii, Taimanov and expression satisfies the simple universal oretical physics and mathematicians in the Grinevich took part in it. KP equation. If this is the case, then we θ 1960s. This method worked successfully obtain a significant effectivisation of the - for solitons – that is, for solutions of the What were the most fundamental directions functional calculus and of the solution of well-known KdV (Korteweg-de Vries) equa- that you developed here? the Riemann-Schottky problem. tion with rapidly decreasing initial data. I would like to mention the following The first important result in this direc- Is it possible to develop the correspond- directions: tion was obtained by Dubrovin in 1981; it ing periodic analogue? Since 1974 I have The inverse problem for a two-dimensional was considerably strengthened by devoted my energies to this very problem. Schrödinger operator for a fixed energy. We Arbarello and De Concini (1984). My con- My discovery consisted in the close unity started developing this direction with jecture was completely proved by Shiota between the following branches of mathe- Manakov, Dubrovin, and Krichever in (1986). This approach, starting with matics: the spectral theory of operators 1976, but the most interesting soliton sys- Dubrovin, was repeatedly used in soliton θ with periodic coefficients on the line, the tems were found by Veselov and me later theory for practical effectivization of - theory of completely integrable on, in 1984 (the Novikov-Veselov hierar- function formulas. An analogue of this Hamiltonian systems, and analysis on chy). conjecture was investigated by Taimanov θ Riemann surfaces (that is, algebraic geom- The problem of classifying the commuting oper- for Prym -functions. In this case the KP etry). The main role in the construction of ators with rank greater than 1 and the defor- hierarchy must be replaced by the so- exact solutions of the KdV equation is mations of holomorphic bundles over algebraic called Novikov-Veselov hierarchy related played by the Hill operators or curves (Krichever-Novikov equations and the to a two-dimensional Schrödinger opera- Schrödinger operators on the line with the solutions of the KP equation of high rank). tor. remarkable finite-zone property. This theory was created in 1978-80 in col- As I proved, this property of the spec- laboration with Krichever, and Grinevich How about methods of Riemannian geome- trum follows from a purely algebraic and Mokhov also took part in it. try in the theory of systems of hydrodynamic assumption – that a periodic differential Difference analogues of this theory were type. What are the Dubrovin-Novikov operator is ‘algebraic’: this means that developed quite recently by Krichever and brackets? there is another differential operator that me: by the way, Krichever has beautifully Since the early 1980s, I was interested in commutes with the given one. applied these ideas to the investigation Poisson brackets in hydrodynamics under The theory of finite-zone operators was and generalisation of the so-called Hitchin the influence of a circle of Landau disci- soon completed by me and my disciple systems. ples, Dzyaloshinskii and Khalatnikov. It Dubrovin, and also by Matveev and Its, Universal approach to the Hamiltonian formal- turned out that Landau already knew these who actively joined the development of ism of systems integrable by methods of algebra- brackets by 1940 when trying to quantise a these ideas after my first work on this ic geometry – that is, the so-called ‘algebro-geo- fluid. Two directions of my scientific works topic. Soon, in 1975, a part of these ideas metric Poisson brackets’. This direction was actually arose from this source of ideas: the was independently found in USA by Lax, developed by Veselov and me in 1982-84. many-valued calculus of variations and the McKean, and van Moerbeke. As Krichever and Phong indicated several theory of systems of hydrodynamic type. Already, by 1974, Shafarevich had years ago, similar symplectic structures Quasi-linear homogeneous systems of brought my attention to the fact that these mysteriously arise in Seiberg and Witten’s first-order differential equations (systems constructions lead to new results, even in works on the supersymmetric Yang-Mills of hydrodynamic type) have been studied algebraic geometry per se, giving an explic- theory (for N = 2). since Riemann, in connection with hydro- it rational realisation of the entire space of Analogues of the Laurent-Fourier bases on dynamics of compressible fluid. Dubrovin modules of hyperelliptic Jacobians. These Riemann surfaces – namely, Krichever-Novikov and I investigated the following problem: methods can be transferred without any bases and algebras, and the operator quantisa- when is such a system Hamiltonian? modification from the Korteweg-de Vries tion of a bosonic string. This direction was Physical systems of this kind usually arise equation to all one-dimensional systems developed by Krichever and me in 1986- when describing an inviscid fluid, and it is integrable by the method of solitons. 90. natural to expect that they must be For spatially two-dimensional systems This is the list of directions in soliton Hamiltonian. (We should not mix up this (such as the Kadomtsev-Petviashvili equa- theory that I developed with my disciples problem with the possibility of represent- EMS March 2002 17 INTERVIEW ing a system as a subsystem or quotient sys- fixed point – can also be represented in a case of those above, but saw no analogy tem of a Hamiltonian system, because this similar form. I noted that this system can with the Dirac monopole and carried out is always possible.) be reduced to the motion of a charged par- no topological analysis. Some physicists – In 1983 we introduced a class of ‘brack- ticle along the surface of the two-dimen- Deser, Jackiw, Templeton (1982), and ets of hydrodynamic type’ which gives a sional sphere (with some metric) in an Witten (1983) – arrived at related ideas in natural answer to the question: these external magnetic field with non-zero flow diverse examples soon after me. brackets are based on Riemannian geome- through the sphere. This situation is like a (2) It turned out that there is a many-val- try. For diverse reasons, our discovery had ‘Dirac monopole’! Certainly, the physical ued analogue of Morse theory for closed 1- many consequences. Many new important magnetic field is absent here; however, forms on finite-dimensional manifolds; systems of hydrodynamic type arose in the mathematically, a magnetic field turns out however, instead of usual CW complexes, 1970s and 1980s from soliton theory – to be equivalent to the correction of the gradient of a 1-form generates com- Whitham (1971), Flashke-Forest- Poisson brackets (symplectic structure) that plexes over specific rings, which were later McLoughlin (1980), etc. – to solve asymp- occurs in the reduction of the system. on called Novikov rings and used for the totic problems by using the scheme of Intending to develop something similar homology theory of Floer type, where the ‘non-linear semi-classics’, successfully to Morse theory for finding periodic orbits analysis is more complicated but the heart applied by physicists (Gurevich-Pitaevskii, on the sphere (that is, 2-tori of an initial of the problem is the same – namely, 1- 1973). When proving my conjecture, the system), I understood that the mechanical forms occur instead of functions. postgraduate Tsarev successfully applied action of the above system on the sphere is (3) In collaboration with my disciples our Hamiltonian formalism and construct- not defined as a single-valued functional: (Taimanov and Grinevich), I also obtained ed a scheme for exact integration of only its variation is correctly defined as a a series of results on periodic orbits in a Hamiltonian systems of hydrodynamic closed 1-form on the space of closed paths. magnetic field. Some deeper observations type on the basis of differential geometry I was amazed by this simple fact, and are still insufficiently justified; here there (1985). Later, in the second half of the immediately understood its fundamental are interesting mathematical problems. 1980s, as a result of a numerical and ana- role in mathematics and theoretical lytical researches in which Avilov, physics. Neither the calculus of variations What scientific and pedagogical ideas Krichever and Potemin worked with me, nor field theory discussed this possibility. underlay the book series ‘Modern geome- we combined this technique with analysis As a corollary, I came to the following con- try?’. Is this programme complete, or do on Riemann surfaces and analytically clusions: you plan a further development of this exactly solved the problem of the dis- (1) In quantum mechanics and quantum series? persed analogue of a shock wave, whose field theory, a ‘topological quantisation of Many years ago, in the 1960s, I formulated study was begun by physicists in 1973. the coupling constant’ arises, based on the a plan to present ‘modern’ topology, creat- In our works in the 1980s, a lot of beau- requirement that some 1-form, the so- ed since the early 1950s, in the education- tiful mathematics appeared, both algebra called ‘variation of action’, defines an inte- al literature: in my opinion, this is a great and geometry, which was used by Dubrovin gral 1-cohomology class of the space of achievement of 20th-century mathematics. in the 1990s in the topological two-dimen- fields (under appropriate normalisation). Until the second half of the 1960s, the best sional quantum field theory. These ideas This is necessary for the Feynman ampli- achievements were reasonably presented have recently been successfully applied in tude to be a single-valued functional. It is in the original works, such as those by the classical problem of orthogonal coordi- interesting that Dirac’s idea was different: Pontryagin, Serre, Cartan, Thom, Milnor, nates on flat spaces (Dubrovin, Zakharov, he started from the Schrödinger formalism Smale, Atiyah, Hirzebruch,… I always and Krichever). and (in modern language) required that tried to follow their example, to write large Very interesting non-local extensions of the magnetic field must be the Chern class works that are as clear as possible. The Poisson brackets, whose investigation was of a bundle whose fibres give the Hilbert topological achievements of that time started by Mokhov and Ferapontov (also space of states. The new approach is much could be learnt from these works. participants at my seminar) have increased more convenient for generalising the Dirac However, a formalised abstract style the abilities of the method. These exten- monopole to quantum field theory. I gave that unnecessarily complicated the exposi- sions still attract our attention. I note that, a classification of all local Lagrangians of tion for algebraic formalism had already generally, the appearance of a lot of field theory that lead to non-trivial 1- appeared during this period. It is very dif- diverse important Poisson brackets, the forms. It later emerged that, when evalu- ficult to understand the core of the subject knack of using them, and the understand- ating anomalies in the Yang-Mills theory from such texts. This style gradually began ing of their role in modern science are several years earlier, Wess and Zumino had to appear in topology, and not only topol- among the achievements of soliton theory. obtained a Lagrangian that was a special ogy. Besides, starting from the late-1960s, After this theory it became clear that the local Poisson structure is the major prima- ry object in theoretical physics, while the symplectic structure is preferable in pure geometry.

What is the many-valued calculus of varia- tions (the Morse-Novikov theory and the Novikov ring)? How is it related to the Wess-Zumino-Novikov-Witten quantum field model? The many-valued calculus of variations is also rooted in my Hamiltonian researches. Examining textbooks in hydrodynamics, I observed in 1981 that the so-called ‘Kirchhoff equation’ for the free motion of a rigid body in an ideal incompressible fluid is a Hamiltonian system on the Lie algebra of the isometry group of three- dimensional Euclidean space. Apparently, this fact was not mentioned earlier. Mechanicians soon pointed out that the equations of motion of a top – that is, a rigid body in a gravity field with a Sir Michael Atiyah and S.P. Novikov 18 EMS March 2002 INTERVIEW several of the best papers remained Geometry (English translation in the However, the study of this subject requires uncompleted by their authors, but this was Encyclopaedia, Vol. 4) are devoted to other very serious preparation, and one should- not understood by a wide community – at areas; their major problem is a rather n’t begin with it. Many people do not least, no publicity was given to this fact. It broad introduction into a new technique understand this rule: everybody knows, for became clear that there can be no serious developed with my disciples: the solution instance, that it’s impossible to build a development in an area that cannot be of periodic problems of soliton theory and house starting from the tenth floor, but learnt, and in which one cannot separate the spectral theory of operators that comes some people still do not apply this analogy known facts from unknown ones. from the analysis on Riemann surfaces and to science. It is also absurd to try to pre- For many years, I brought up good dis- algebraic geometry is one of the main sent this totality of knowledge in a super- ciples. They developed in seminars at examples. Algebraic geometers aspire to formal algebraised language, since the which training problems were solved and convert it into something abstract, while material would become so complicated the key ideas of topology were investigat- scientists who effectively use classical analy- that nobody could learn it. ed. I gave a series of courses whose mate- sis cannot study it without difficulty, and rial was carefully repeated. Besides, my thus the process of assimilation is very For more than ten years (1985-96) you were joint work with mechanicians and physi- complicated. President of the Moscow Mathematical cists in the 1970s, and the study of these Society, whose role in the creation of the areas, induced me to think deeply about What are your views on contemporary famous Moscow mathematical school of the the creation of courses that could serve physics and mathematics education? Many 20th century has been written about many both communities, mathematicians and people have heard that you speak about a times. What can you can tell us about this, experts in theoretical physics. Fomenko crisis of physical and mathematical com- and what is the role of the Society now? helped me to introduce the elements of munity. Yes, the Moscow Mathematical Society, geometry and topology to mechanicians. I My experience, my long-term connection which is the mathematical face of the drew up a plan for a series of books whose with education, tells me that an active Department of Mechanics and beginnings we had already, and also process of reducing the level of physics and Mathematics, is the main scientific arena recruited Dubrovin. In collaboration, we mathematics education began in the last for the mathematicians of the Moscow wrote a series of books Modern Geometry in school, whatever they work on. three parts. According to the plan, Part I Our society was founded in the 19th (geometry to topology) should accustom century, but it progressed as a consequence mathematicians to the elements of natural of the development of the Moscow mathe- sciences, create bridges with theoretical matical school in the 1910s and 1920s, physics, and accustom them to geometry especially when the presidents were and the ideas of field theory. Part II (the Zhukovskii and Egorov, the founders of differential approach to topology) should outstanding schools of mechanicians and be an understandable and useful course of mathematicians. The Egorov-Luzin school topology, both for physicists and mathe- became famous all over the world and maticians working in different areas of determined the face of Moscow mathemat- analysis, and a unification of topology with ics in the 20th century. In Moscow, all a world of other areas of science that are mathematical activity in the 1920s and less abstract. Part III contained the ele- 1930s was concentrated around the ments of modern algebraic topology. The Society, being interrupted sometimes by series should have been continued, and periods of hunting by the Soviet system for Part IV should be written to fulfil the plan, intellectuals – for example, during 1929- but we had neither strength nor time to do 33. So it was till the mid-1950s. Since the so. mid-1960s, after passing through a diffi- Later on, it turned out that the commu- cult period, the Society has won back its nity of topologists and geometers was not position as a central forum for Moscow too much interested in unification with the mathematicians, and has successfully kept natural sciences: Part I was spread insuffi- this ever since. ciently widely among mathematicians. decade (and possibly earlier). Such an Let me list some recent Presidents: P. Taimanov and I are now writing a new education no longer produces scientists Aleksandrov (1933-64), Kolmogorov textbook that greatly modernises the ideas with a broad profile. The process gears up. (1964-66 and 1973-85), Gelfand (1966- of Modern Geometry I. I hope it’s a good I wrote some papers on the subject. It is 70), Shafarevich (1970-73), Novikov (1985- time for this topic to be studied by a broad possible to speak even about a deep crisis 96) and Arnold (1996-…). community of mathematicians. Part II was in our areas of science. Recently I wrote a In the late Bolshevic period of the more successful, and quite broad collec- new paper (in Russian) about this crisis: it 1970s, marked by severe anti-Semitism as a tions of mathematicians, experts in mathe- is not published yet, but can be found on state policy and persecution of liberal matical physics, and students have studied the internet. intellectuals, our Society faced great diffi- this book. As to Part III, it should be noted It is a very serious problem that cannot culties. In the 1980s, the connection with that education in the area of ‘high’ topolo- be elucidated in two words. Theoretical MGU was weakened, where an anti-scien- gy had generally declined badly in the last physics declines most rapidly. Pure math- tific approach had prevailed, especially at thirty years, and currently the potential ematics turns out to be steadier for now: the Department of Mechanics and readers of Part III form a rather limited though it also declines, it has more chances Mathematics – the more so, since the lead- community of very particular experts. to survive and stay at the same high level. ership of MGU began unskilfully to dis- With Fomenko, I also wrote an elemen- It is possible that some fundamental prove Einstein’s general relativity, etc. tary textbook, and an encyclopaedic book achievements of the second half of the However, we managed to keep our scien- Topology I (English translation in the 20th century that are mathematical in tific face. Encyclopaedia of Mathematical Sciences, Vol. essence and made by experts in theoretical After the disintegration of the USSR in 12, Springer, 1996), which, in my opinion, physics – for example, modern quantum the early 1990s, we reorganised and transparently and clearly presents the field theory – will be saved for the future as strengthened our connection with the entire cycle of ideas of classical topology parts of mathematics. However, mathe- Steklov Institute, where a process of up to the early 1970s. My other educa- maticians must at first study these achieve- renascence took place; much was done by tional books (Soliton Theory, written with a ments. us at this time to create and stabilise the group of physicists, and a volume of the Based on this assumption, I would like Independent University. This work has Encyclopedia under the title Dynamical to write manuals to prepare mathemati- proceeded quite successfully in the last few Systems, Integrable Systems, and Symplectic cians in the elements of this area. years. EMS March 2002 19 SOCIETIES The Union of Czech Mathematicians and Physicists Luboš Pick

The Union of Czech Mathematicians and were Filip J. Kulík (1793-1863), Ernst Mach Physicists is one of the oldest learned soci- (1836-1916) and Augustin Seydler (1849- eties in the Czech Republic. It will cele- 91). The logo of the Union. brate 140 years of its existence in 2002. In 1863, Professor Kulík donated to the Society a good part of his enormous math- lishing and selling books, purchased a History ematical library; the remaining part was printing house and established its own Let us start with a brief survey of the devel- inherited by the Society after his death. In Publishing House and bookshop. opment of the activities in mathematics and 1868, Professor Mach offered the Society The establishment of Czechoslovakia in physics in the region that is now occupied his lecture theatre for meetings and his lab- 1918 brought important changes in mathe- by the Czech Republic. oratory for physical experiments. In 1869, matics and physics. In 1921, the Faculty of The eldest educational institution in the the Austrian police headquarters registered Sciences separated from the Faculty of area is the Charles University, which was the society (having by this time 69 mem- Humanities. The Prague Polytechnic was founded by the Holy Roman Emperor bers) under the new name Union of Czech reorganised and called the Czech Charles IV in 1348. However, teaching of Mathematicians. Technical University. In the same year, the mathematics and physics of significance In the first years of its existence the Union changed its name to the one it bears began only around the middle of the 18th Union made a significant contribution to today. century. At that time, polytechnic institu- the creation of mathematical and physical During the twenty years of independent tions were founded in Bohemia, and the so- terminology in the Czech language, and on called Royal Czech Learned Society was estab- 5-6 August 1870, it organised the first con- lished. (We recall that Bohemia was an gress of Czech physicists and mathemati- integral part of the Austrian – later Austro- cians. Hungarian – Empire until 1918.) In 1872, on the 10th anniversary of the Several outstanding scientists lived and establishment of the Society, the first num- worked in Prague in those times – in par- ber of a new journal was issued. The journal ticular, Stanislav Vydra (1741-1804), was called Èasopis pro pìstování matematiky a Bernard Bolzano (1781-1848) and fysiky (Journal for the Cultivation of Christian Doppler (1803-54). With the Mathematics and Physics), and was pub- growing interest in activities and teaching lished continuously (with a forced break of mathematics and physics, demand during World War II) until 1951, when it increased for a society that would support was split into Èasopis pro pìstování matematiky the developments of research and teaching (Journal for the Cultivation of Mathematics in these sciences, in particular among stu- – in 1991 renamed as Mathematica dents. As a result, on 28 May 1862, the Bohemica) and Èeskoslovenský èasopis pro Society for Open Lectures in Mathematics and fyziku (Czechoslovak Physics Journal). Physics in Prague was founded, and on this In 1873 the Union began to publish day our Union came into existence. Soon, textbooks in mathematics and physics, and the Union obtained support from universi- in 1892, a Supplement for High-School ty teachers, the most important of whom Students, was included in the membership journal: at that time, this was quite an inno- vative idea. At the beginning of the 20th century, there was a further blossoming of mathe- matics and physics. The Union was a cen- tre for discussions, sparked by a strong movement towards the reform of education in mathematics and the other sciences. The number of Czech secondary schools began to grow in Bohemia and Moravia, and some of the founders of the Union gained recognition for this. The Union’s branches outside Prague soon began to grow. The most important of these were those in Brno and Bratislava, established in 1913 and 1929, respectively. In 1911, departments of theoretical physics were opened at both parts of the University, which since 1882 had been divided into Czech and German parts. Albert Einstein (1879-1955) was living and The house in Žitná Street 25, bought by the working in Prague during the years 1911- Union in 1930. At the rear, the Union erected 12. a modern building, housing the bookshop and After World War I the Union became later the library of the Union. The house now practically the only publisher of textbooks, monographs and journals in mathematics, has one more floor (built in the early 1990s) Postage stamps released in and is occupied by the Mathematical Institute of physics and related sciences. In 1919, the the Academy of Sciences of the Czech Republic. Union obtained a license for printing, pub- 1962, 1987 and 2000. 20 EMS March 2002 SOCIETIES Czechoslovakia, the number of members of Commemorative Medal that has been used rary mathematics and physics, discussions the Union rapidly increased, as did the ever since. of pedagogical topics, and information scope of its activities. In 1933, the Union’s In 1990 the Union became a foundation about current activities of the Union. Publishing House merged with Prometheus, member of the European Mathematical Among the journals published by the the Publishing House of mining engineers, Society, through the representation of the Union we further find Matematika-fyzika- thereby establishing a publishing centre for Mathematical Research Section, and in informatika (Mathematics-Physics-Inform- technical literature. In 1935, the Union 1992 the Union became a reciprocity mem- atics), aimed at the theory and practice of started to run a society for the production ber of the American Mathematical Society. teaching of the three subjects, Uèitel matem- of tools for science and education. In 1938 In 1993 the Union attempted (without atiky (Teacher of Mathematics), dedicated the house in Žitná 25 was built, and the success) to regain its confiscated property. to the didactic side of mathematical prob- Union moved its headquarters there; the In 2000, the Mathematical Research lems, Školská fyzika (Physics in School), building currently houses the Mathematical Section organised a number of propaganda devoted to the teaching of physics, and Institute of the Academy of Sciences of the events commemorating the World Year of finally Èeskoslovenský Èasopis pro fyziku Czech Republic. Mathematics 2000; another postage stamp (Czechoslovak Physics Journal) and During World War II the Czech univer- was released by the Czech Mail. Informace MVS (Mathematical Research sities were closed by the Nazis. In this dif- Section Newsletter), providing information ficult period the Union did the best it could Structure and organisation for members of the respective sections. to convey information of new results to the The Union has about 2500 members, more In the field of education the Union sys- younger generation by organising various than half of them being secondary school tematically studies the current state of the courses and publishing monographs writ- teachers. The supreme body of the Union teaching of mathematics and physics and ten in a generally understandable manner, is the Union Congress, which is convened suggests ideas for its improvement. even though the publication of the mem- every three years. In between Congresses, For more than 40 years the Union has bership journal was forbidden by the Nazis. the activities are supervised by the Central been organising various competitions for In 1948, the Communist regime took Committee, headed by the President of the gifted young students at all levels – in par- over power in Czechoslovakia. One of its Union. The past presidents of the Union ticular, mathematics Olympiads, physics first steps was a forced ‘nationalisation’ – or have been significant scientists and impor- Olympiads or the Student Research tant personalities in Czech or Slovak scien- Competition, traditionally attended in tific life, including Bohumil Bydžovský, great numbers by the most brilliant stu- Vladimír Koøínek, František Záviška, dents. Miroslav Valouch, Josef Novák and Ivan The Union awards a Commemorative Úlehla, to name just a few. The current Medal to outstanding scientists, both from President of the Union is a distinguished the Czech Republic and abroad, usually to Czech mathematician, Professor Jaroslav those who gained recognition for the devel- Kurzweil. opment of mathematics or physics in the The Union has 15 branches in all Czech Republic. regions of the Czech Republic. Aside from the branches, the Union is divided into four sections – the Mathematical Research Section, the Physical Research Section, the Mathematical Pedagogical Section and the Physical Pedagogical Section. Each section Two sides of the has its own structure and bodies, and also Commemorative its own membership bulletin providing the Medal, released members (and others) with information at the occasion of Jaroslav Kurzweil about the life of the section, as well as infor- the Union’s mation about new developments in the 125th anniver- rather, confiscation of all private property. respective sciences. sary in 1987. As a result of this process, the Union lost its The Union is a member of important Publishing House, library and bookshop. international organisations, including the In the early 1950s the Czechoslovak European Mathematical Society, the Academy of Sciences was established, and European Physics Society, and is also a rec- the Union became a learned society iprocity member of the American attached to the Academy. The Union’s Mathematical Society. property was transferred to the Academy; in particular, the mathematical part of the Present Activities Union library became the basis for the During the 140 years of its existence, the Most of the material presented in this library of the Mathematical Institute of the Union of Czech Mathematicians and article was taken from [1]. Up-to-date Academy, where it has been taken care of Physicists has dedicated an enormous effort information was collected with the help of ever since. to maintain and improve the teaching and several colleagues – in particular, Jiøí In 1962, the Union convened its research in mathematics and physics in all Rákosník and Bøetislav Novák. Centenary Congress: a commemorative types of educational and scientific institu- postage stamp was released by the tions. In the field of science, either inde- Reference Czechoslovak Mail on this occasion. pendently or jointly with other institutions 1. L. Pátý and J. Veselý (eds.), Union of In 1968, the Physical Research Section of higher learning or research, it organises Czechoslovak Mathematicians and was established, and through its represen- national and international conferences, Physicists, JÈSMF, Polygraphia, branch tation the Union became a member of the symposia, seminars and various seasonal Prometheus, Praha, 1984. European Physics Society. schools. It assists in the publication of text- In 1969 a federalisation process took books and monographs, closely cooperates The author is an Assistant Professor at the place in Czechoslovakia. As a consequence, with the Publishing House Prometheus, Faculty of Mathematics and Physics of the the Union of Slovak Mathematicians and Ltd., and takes part in the preparation of Charles University in Prague. e-mail: Physicists began. national basic research projects. [email protected] In 1987, the 125th anniversary of the The Union publishes the journal Pokroky Address: Department of Mathematical Analysis, Union was celebrated in Prague. The matematiky, fyziky a astronomie (Advances in Faculty of Mathematics and Physics, Charles Czechoslovak Mail released three postage Mathematics, Physics and Astronomy), spe- University, Sokolovská 83, 186 75 Praha 8, stamps, and the Union released a cialising on survey papers from contempo- Czech Republic. EMS March 2002 21 FEATURE Mathematicians’Mathematicians’ CarCareerseers Analysis of a Questionnaire Ina Kersten and Emilia Mezzetti

The main issue of the EMS Committee for Women and Here are some tables summarising the answers. Mathematics in the last two years has been to distribute in the European mathematical community a questionnaire on the careers of mathematicians and to try and analyse it. The ques- tionnaire (which follows) contains questions about progression in the career (age, age of Ph.D., age of first permanent position, number of temporary positions, etc.), about family (job of parents and of partner, number of children, etc.), about scientific activity (age when wrote best paper, possible gaps in mathematical pro- duction, and reasons for these gaps). Our aim was to check whether it is true, and in what measure, that there are differences between the Curricula Vitae of men and women, and in particular whether it is true that the scientific career of women is generally slower, mainly because of family duties, especially children. Were these hypotheses confirmed, we would have a basis to start some concrete action, for instance against age limits in announcements for grants and prizes, which seem to be particularly discriminat- ing to women.

The questionnaire Are you male or female? How old are you? What is your nationality? How many children do you have? At what age did you complete your Ph.D.? How many countries have you studied/worked in? What is your mother’s job? What is your father’s job? Do you have a permanent job? How many years after your PhD did you obtain your first permanent job? How many temporary mathematical jobs have you had? At what age did you write the paper of which you are most proud so far? Age when Completed Ph.D. and when Wrote Best Paper Have you had any gaps in your mathematical career? If so, how long were those gaps? In your opinion, what were the reasons for those gaps? Comments: In some versions, the following questions were added: What is your partner’s job? Did you choose your place of residence motivated by your career or by that of your partner? Did the problem of the residence play a role in your professional life?

The questionnaire was distributed during the 3rd European Congress in Mathematics in Barcelona and its satellite meeting New women in mathematics. It was also published in the EMS Newsletter and the newsletters of some other mathematical asso- ciations in Europe, and personally distributed by members of the committee. We have collected 109 answers, 52 by women and 57 by men: not a big number. This shows, in our opinion, that unfor- tunately mathematicians have no wish to fill out questionnaires, and are not really very interested in the problem. Many respondents obtained a permanent job before complet- Almost one half of the respondents (45%) were from Norway: ing their Ph.D. indeed the questionnaire was distributed in a capillary way in On average, the female respondents are 6 years younger than Norwegian mathematical departments, and the answers collected the male respondents. This obviously affects the answers when by secretaries. So the picture of the situation in Norway is rather the best paper was written: female age 32 and male age 36. The faithful. Of the other respondents, 15 were German, 13 Italian, mean age of a Ph.D. is however the same for men and women. but other countries were still less represented. There were a few answers from Russia and Romania, but none from other East Gaps in Mathematical Career European countries. 46 respondents (26 female and 20 male) said that they had gaps 22 EMS March 2002 FEATURE in their mathematical career. Mother’s job

Frequency of reasons given by the respondents for gaps in their mathematical career:

Father’s job

(*) mathematician in several cases Number of respondents with a permanent job: 87/109 (female: 35/52, male: 52/57) Other questions, for example the one about number of temporary jobs, appear not relevant at all. How many years after your Ph.D. did you obtain your first permanent job? SUMMARY In conclusion, we have to admit that the sample we have collected is too small to allow us to draw any meaningful conclusion. The results of this questionnaire have been illustrated during the 10th international meeting of European Women in Mathematics (EWM) in Malta, 24-30 August 2001, where several members of our committee were present. An interesting and lively discussion followed. Particularly inter- esting was the contribution of Doris Janshen, a sociologist from the University of Essen. She gave us several suggestions. We should start again from the beginning, with a new well-thought- out questionnaire, taking into account as a basis the results of the previous one. We should concentrate on a few countries only, and try and collect a representative sample, as in Norway last time. Before distributing the new questionnaire, we should make some samples, testing it on some selected EWM members, for example. This is what we plan to do. For example, mathematicians of Eastern Europe did not show much interest in this kind of statistics, maybe because it is not dif- ficult to obtain a permanent job after a Ph.D. in these countries. A group in Ukraine, coordinated by Polina Agranovich, has now prepared another series of questions and is currently distributing it in two universities in Kharkov. It is mainly devoted to under- standing the reasons for choosing mathematics and possible gaps in the career. To conclude, we quote three recent articles that are somehow related to our work. The first one is a report, written by A. Abele, H. Neunzert, R.Tobies and J. Krüsken, about the interdisciplinary project enti- tled Women in mathematics: factors determining mathematical careers from a gender comparative perspective, and supported by the The question of possible gaps in the mathematical career had Volkswagen Foundation. The article appeared in the Newsletter rather surprising answers: more women than men had gaps, but of the German Mathematical Society, DMV-Mitteilungen, 2-2001, the percentage is high also among men: 36%. For women the p.8-16. It has recently been translated into English and will more frequent reason is family, but there are also academic appear in the EMS Newsletter. It contains several very interesting duties or personal problems as depression or stress. Among data and an analysis of the development of the situation of women men, all these reasons appear and moreover military service. mathematicians in Germany. Among other things, it confirms the sometimes questioned fact that women and men have the same Partner’s job potential capability of doing research. Women who succeed in Answers to the question about job of partner and parents are concluding Ph.D. studies in Germany obtain completely satisfac- rather interesting, but maybe not really related to our aim: the tory results and get the same marks as their male fellows. mother is often a housewife, the father an engineer, or a school or The second article is by Michèle Audin (Sur les étudiantes en university professor, often in a scientific topic. mathématiques, Gazette des mathématiciens 87 (2001), 41-49, Newsletter of Société Mathématique de France). She analysed the 33 respondents (26 female and 7 male) percentages of girls among first- and second-year students of mathematics in her university in the 1990s and compared the results of the exams. She concluded that girls choosing to study mathematics are much more motivated than boys and get better results. Once more, this convinces us that a stronger female pres- ence would be of great advantage to the mathematical communi- ty, that could enjoy big unexploited potentialities. The last one is a recent article by Reuben Hersh, published in EMS March 2002 23 FEATURE The Mathematical Intelligencer: Mathematical menopause, or, a young man’s game? (Math. Intelligencer 23 No.3 (2001), 52-60). It deals with the theme of the presumed incapacity of doing reasearch in mathematics after a certain age. On the basis of EurEuropeanopean WWomenomen inin research carried out among his friends and acquaintances (about 65), the author concludes, among other things, that if it is true that creativity decreases with age, then it is replaced by experience MathsMaths WWeb-basedeb-based and the capacity to coordinate the work of other people. So it is possible to continue a good level of scientific activity after having MentoringMentoring SchemeScheme crossed the famous threshold of 40 years, sometimes considered as a limit age. In August the EU agreed to fund a project proposed by the A short report on this questionnaire programme, by Ina organisation European Women in Mathematics to provide web- Kersten and Emilia Mezzetti, will appear in the Proceedings of the based mentoring to women in mathematical sciences in Europe. EWM conference in Malta, to be published by World Scientific. Recent reports have highlighted (yet again) the lack of women Ina Kersten, Mathematisches Institut, Universität Göttingen, in higher positions in academia across scientific disciplines. The Bunsenstrasse 3-5, D-37073 Göttingen, Germany, e-mail: kersten@uni- EU is committed to improving the human potential across math.gwdg.de Europe, and in particular, to realising the talent of the female Emilia Mezzetti, Dipartimento di Scienze Matematiche, Università degli population, so this project has been given the go-ahead as a Studi di Trieste, Via Valerio 12/1, 34127 Trieste, Italy, e-mail: step towards encouraging women to progress in their mathe- [email protected] matical science careers. The funding period for the EU scheme is 2 years and the scheme will be operated from Oxford Brookes University in the UK.

Aim and scope of project The aim of the web-based mentoring scheme is to enable new TheThe women mathematical scientists (for example, graduate stu- dents, those considering graduate work, postdoctoral students) to find mentors amongst the mathematical science community HumanHuman FFrrontierontier who can advise them on academic issues and also on issues such as how to apply for grants and how to prepare work for publi- cation. Mentors can also advise on broader gender-related issues faced by women in a mainly male-dominated environ- ScienceScience PPrrogramogram ment. Using the web to facilitate the mentoring scheme will The Human Frontier Science Program promotes world-scale enable women to form links with mentors across Europe. research in the life sciences through Research Grants, Similar schemes are now starting up across the world – for Fellowships and Workshops. example that run by the American Women in Mathematics The aim of the HFSP is to support basic research focused on organisation. We hope to link with them to provide mentors for complex mechanisms of living organisms; fields supported European women, and also to provide US mentors for those range from brain functions to biological functions at the mole- considering studying in the US. We hope that schemes of this cular level. Particular emphasis is placed on bringing scientists nature will contribute to the support network for women in from fields such as physics, mathematics, chemistry, computer mathematical sciences and encourage women to progress in science and engineering together with biologists, to open up their mathematical science careers. new approaches to understanding complex biological systems. HFSP previously supported two scientific programmes Further information focused on neuroscience and molecular biology. With the dis- If you are interested in joining the web-based mentoring project solving of boundaries separating traditional biological fields, as a mentor, or if you would like to use the scheme to find your and the need to involve disciplines outside biology in life sci- own mentor, please get in touch. We shall be actively seeking ence research, these separate programmes have been unified mentors soon and, when the project is up and running (later into a single scientific program by the HFSP Board of Trustees. this year we hope), we will be inviting those who require men- Henceforth, a single committee will review all grant applica- tors to visit the site. tions, while a second committee will review all long-term fel- lowship applications. Both committees are composed of leading Contact: Dr Cathy Hobbs, School of Computing and Mathematical international scientists. Sciences, Oxford Brookes University, Gipsy Lane, Headington, Oxford Research grants are awarded for projects that involve exten- OX3 0BP, UK. sive collaboration among teams of scientists working in differ- e-mail: [email protected] ent countries. The emphasis is on novel collaborations that bring together scientists from different disciplines. Fellowships are available to scientists who wish to work in foreign laborato- ries, with emphasis on individuals early in their careers. Further information can be found on the web site: Addendum to Obituary of http://www.hfsp.org Jacques-Louis Lions (issue 42) Journal of the European In addition to the series that Jacques-Louis Lions edited, there is one more: Studies in Mathematics and its Applications (with H. Fujita, H.B. Mathematical Society Keller and G. Papanicolaou), 30 vols., North-Holland, 1976- 2001. The author’s contact details are: The next issue of JEMS (Vol. 4, No. 1) contains just one paper Philippe G. Ciarlet, Laboratoire d’Analyse Numérique, of 114 pages: Université Pierre et Marie Curie, 4 Place Jussieu, F-75005 Andreas Knauf, The n-centre problem of celestial mechanics for PARIS, France. e-mail:[email protected] large energies tel: (33)1.44.27.51.13; fax: (33)1.44.27.72.00

24 EMS March 2002 EMS NEWS Norway Introduces Grant Major International Prize There is no Nobel Prize for Mathematics, but now Programme for The Abel Prize has come into being Niels Henrik Abel (1802-29) is one of the Mathematics, following the model of the world’s most notable mathematicians. He Nobel prizes. the Abel left deep tracks behind him in many The Abel Prize has been well received fields. His points of view and his internationally, as attested to by The approaches were new and had decisive International Mathematical Union Bicentennial significance for the development of (IMU): mathematics as a science. Abel solved The Executive Committee of IMU in its problems that mathematicians had been recent annual meeting, that took place at the struggling with for centuries, and he Institute for Advanced Study, in Princeton, Conference posed approaches to problems with which considered the creation of the Abel Prize as the mathematicians are still working. most important project in many years for the The year 2002 will be the 200th development of mathematics worldwide, in fact Oslo, anniversary of the birth of Niels Henrik as capable of greatly changing the scenario Abel, the leading man of science in the within a few years of its establishment. Of history of Norway. To mark this occasion course, the question of having an award 3-8 June 2002 the Government of Norway, at the similar to the Nobel Prize for Mathematics is a suggestion of the Department of century old, and its lack is a perpetually Mathematics at the University of Oslo has discussed feature of the scientific work of our The European Mathematical Society has undertaken to establish an Abel Prize in community. been informed that the Norwegian Government has given a grant to cover travel and other expenses for a number of young mathematicians from Eastern Europe and the Former Soviet Union to attend the Abel Bicentennial Conference in Oslo from 3-8 June 2002. The Abel Bicentennial Conference will be the occasion to introduce the newly established Abel Prize to a wide international audience, and this Grant Programme is intended as a part of this launch of the Prize. The EMS has been asked to nominate 15 young mathematicians for a travel grant to attend the Abel Bicentennial Conference. The EMS Executive Committee has decided that its Committee for the Support of Mathematicians from Eastern European Countries should make these nominations. Applicants are hereby invited from among mathematicians from Eastern Europe and the Former Soviet Union, who are not older than 35 years. Applications should include a short CV of the candidate (including contact details), brief information on their research interests, a list of their most important publications, and a letter of recommendation from an appropriate person (such as a senior colleague or collaborator). Please send applications to the Chair of the Committee, preferably by electronic mail to the following address: , or by mail to Professor Andrzej Pelczar, Instytut Matematyki, Jagiellonian University, Reymonta 4, 30-059 Krakow, Poland), together with an electronic copy addressed to Ms Tuulikki Makelienen in the EMS Secretariat (makelain@kantti. helsinki.fi). Applications should be received not later than 20 April. Successful candidates will be informed as soon as possible (preferably by electronic mail), and hopefully by 6 May.

Andrzej Pelczar EMS March 2002 25 PROBLEM CORNER Problem Corner: Back to Normality

Paul Jainta

Croatian mathematics competitions at school Croatia is recovering from the troubles of the 1990s – in particular, its educational set-up seems to have remained intact. Željko Hanjš, a lecturer at the Department of Mathematics, University of Zagreb, gives us a brief insight behind the scenes of mathematical talent spotting in Croatia. Hanjš was himself a contestant in the International Mathematical Olympia in 1977, and later acted as the leader of the Croatian IMO team in 1985 and from 1993 till 1999. Here is his account. Our country has about 5 million inhabitants and an area of 56000 km2, so it is astonishing that mathematics competitions in this small area have survived for more than 40 years. Initially, they were aimed at students who attended secondary schools, but from 1965 on they have been expanded to primary schools too, including classes from ages 4 up to 8. The hierarchy of competitions that existed in Croatia unrevised since 1992 is as follows. The first rather loose selection of mathematically gifted youngsters is carried out at school every January and February. The scene for this stage is thus provided by the intimate atmosphere of the educational institution before the competition jumps across school boundaries.

Municipal competition Municipal competitions are organised in the larger towns with a total of about 8000 pupils in primary schools and approximately 2000 students in secondary schools. For the young participants these occasions represent stirring events, especially if they are involved for the first time. The municipal stage takes place at the beginning of March. The problems are chosen and prepared by separate subcommissions, responsible for entrants from primary school and secondary schools, respectively. These commissions are full of enthusiastic teachers and lecturers who pick all the questions with great care, and they grade the written papers and decide which students are permitted to enter the second stage.

District decision Croatia is divided into 20 regions, with the capital Zagreb as a separate unit. The second stage includes all districts, and usually takes place in the middle of April. Again, each regional host town accommodates its own board to judge the results and pass them on to the national commission. The most successful competitors are awarded a price for the first time in the contest cycle.

National round The members in the national board have the responsibility of deciding which contestants will be invited to attend the national competition. To this final stage only 7-formers from secondary schools and 8-formers from primary schools are admitted. The place of the final competition changes whenever possible. About 180 contestants and roughly 60 teachers and 40 members of the national contest board are travelling there separately. As a rule, this spectacle lasts for four days. On the second day when students are pondering on their solutions, lectures for the unoccupied teachers and coaches are given, split into subjects adequate for primary or secondary school curricula. Some topics sound good: the Euler and Fermat Theorem, the resolution of irrational equations, how can trigonometry help in solving algebraic n n problems? or an examination of a class of functions of the form fn(x) =cos x + sin x. The third day is usually reserved for a picnic with the entrants. Soon after the results have been announced, we have to choose the team that will represent our country at the International Mathematics Olympiad. If the final round does not produce clarity in the line-up of this national team, further examinations follow to give additional information about the individual mathematical abilities of supplementary candidates. This ‘screening’ is scheduled for the afternoon of the third day, and as a rule roughly 15-20 entrants have to undergo this extra ‘treatment’. Finally, the team is put together. In the evening of the same day the results are announced to the contestants. And in the morning of the day of departure, the assembled staff meet together to discuss how working with mathematically talented youngsters could be improved in future, or what topics the indigenous journals Matka, which is enjoyed by students at primary schools, and Matematičko- fizički, which attracts pupils from secondary schools, should pick up next.

Regional contest Shortly after the final display is over, the time has come for students who visit fourth to sixth classes. They compete in regional contests that are organised in each of the four subregions of Croatia.

PROBLEM CORNER

Summer school for young mathematicians In summer, ever since 1972, a summer school is offered for young mathematics adepts, and a similar institution for primary school students opened its doors a few years ago. Meanwhile, about 100 young ace mathematicians amuse themselves with geometrical figures and numbers year by year. All these enumerated measures are under the auspices of the Croatian Mathematical society with support of the Ministry of Education and Sports.

Our thanks go to Željko Hanjš, who acted from 1991 onwards as Editor-in-Chief of the secondary school students’ journal Matematičk- fizički List and is thus a proficient reporter. The people of Croatia, especially the residents of Istria and Dalmatia, are traditionally growers of grapes or olives, or fishermen and seafarers. But in those regions, too, some ticklish maths problems are cultivated. Here is a sample.

134 Prove that there are at least 2000 triples of positive integers (a, b, c) such that a15 + b15 = c16. (Municipal competition for secondary schools, 2000, II class)

135 Let a and b be real numbers that satisfy both a3 – 3ab2 = 44 and b3 – 3a2b = 8: determine a2 + b2. (County competition for secondary school students 2000, I class)

136 A given rectangle with sides a and b is circumscribed by another rectangle of area m2: determine all possible values of m. (County competition for secondary school students 1999, III class)

137 Given a right triangle with angles α and β, legs a and b and hypotenuse c. Prove the inequality: cos2(α – β)/2 ≥ (2ab)/c2 . (County competition for secondary school students 2000, II class)

138 You have coins worth 1, 2, 5, 10, 20, 50 lipa and 1 kuna (= 100 lipa). Prove that if you can pay a bill for M lipa with N coins, then you can pay another bill for N kuna with M coins. (National competition 2000, I class)

139 A square is given in the plane with vertices T1 (1, 0), T2 (0, 1), T3 (–1, 0), T4 (0, –1). For each n, let Tn+4 be the midpoint of the line segment TnTn+1. If the sequence of points {Tn} has a limit point, what are its coordinates? (County competition for secondary school students 1999, IV class)

Solutions to some earlier problems

122 Let A1A2A3A4A5A6A7 be a regular heptagon. Prove that 1/A1A2 = 1/A1A3 + 1/A1A4.

Solution by Gerald A. Heuer, Concordia College, Moorhead (USA); also solved by Niels Bejlegaard, Copenhagen (Denmark); Pierre Bornsztein, Pontoise (France); Knut Dale, Telemark College, Bø (Norway); Pietro Fanciulli, Porto S. Stefano (Italy); J.N. Lillington, Dorchester (UK); Dr Z Reut, London (UK). Since A1A2 = 2r sin (π/7), A1A3 = 2r sin (2π/7) and A1A4 = 2r sin (3π/7), where r is the radius of the circumcircle, the equation to be proved is equivalent to 1/sin (π/7) = 1/sin (2π/7) + 1/sin (3π/7). (1) Adding the fractions on the right side of (1) and clearing of fractions, we obtain the equivalent equation sin (π/7) sin (3π/7) + sin (π/7) sin (2π/7) = sin (2π/7) sin (3π/7). (2) Using the formula sin a × sin b = ½[cos (a – b) – cos (a + b)], and simplifying, we find that (2) is equivalent to cos (2π/7) + cos (5π/7) = cos (3π/7) + cos (4π/7), which is obviously true because cos (π – x) = – cosx.

123 The sequence {xn} satisfies √(xn+2 + 2) ≤ xn ≤ 2 for all n ≥ 1. Find all possible values of x1986.

Solution by Dr Z Reut, London. Assuming that the square root is positive, the sequence {xn} is positive. 1/2 The system of inequalities: (xn+2 + 2) ≤ xn ≤ 2, gives by successive elimination: 1/2 1/2 1/2 (…(((xn+2m + 2) + 2) + … + 2) ≤ xn ≤ 2, where there are m nested square roots on the left-hand side. If xn = 2, for all n, the double inequality is satisfied. Let us assume that the sequence {xn} is decreasing, that is: 0 < xn+2m < xn, and the difference is: 1/2 1/2 1/2 1/2 1/2 1/2 (…(((xn+2m + 2) + 2) + … + 2) – xn+2m < (…(2 + 2) + … + 2) , PROBLEM CORNER which is less than the difference 2 – xn+2m . 1/2 1/2 1/2 It follows that 0 < xn+2m < 2 – (…(2 + 2) + … + 2) = 0, on letting m go to infinity. Thus the only possible value of x1986, which is obtained for n = 2, m = 992, is 0.

124 Find the real numbers x1, x2, … ,xn satisfying 2 2 2 √(x1 −1 ) + 2 √(x2 −2 ) + …+ n √(xn− n ) = (x1 + x2 + …+ xn)/2.

The following is a combination of similar solutions by Pierre Bornsztein, Pontoise, (France) and Dr Ranjeet Kaur Sehmi, Dept. of Applied Sciences, Punjab Engg. College, Chandigarh (India); also solved by Niels Bejlegaard, Knut Dale, , Gerald A. Heuer, J.N. Lillington and Dr Z Reut. 2 2 2 Let √(xi – i ) = yi for each i, so that xi = yi + i for each i, and the given equation reduces to 2 2 2 2 2 2 y1 + 2y2 + … + nyn = (y1 + 1 + y2 + 2 + … + yn + n )/2 2 2 2 2 2 2 or (y1 – 2y1 + 1 ) + (y2 – 4y2 + 2 ) + … + (yn – 2nyn + n ) = 0 2 2 2 or (y1 – 1) + (y2 – 2) + … + (yn – n) = 0, which is satisfied only when y1 = 1, y2 = 2, … , yn = n. 2 2 2 2 2 2 2 That is, x1 = 1 + 1 = 2×1 , x2 = 2 + 2 = 2×2 , … , xn = 2n .

125 Prove that there is a perfect cube between n and 3n, for any integer n ≥ 10.

Solution by Pierre Bornsztein; also solved by Niels Bejlegaard, Knut Dale, Gerald A. Heuer, Oren Kolman, Jerusalem (Israel), Dr Ranjeet Kaur Sehmi, J. N. Lillington, and Dr Z Reut. Suppose first that 10 ≤ n < 27; then n ≤ 33 ≤ 3n, trivially, and the result follows. If n ≥ 27, there exists a unique number x ≥ 3 such that x3 ≤ n < (x+1)3. To get the conclusion, it suffices to prove that (x+1)3 < 3n. Let n = x3 + k, where 0 ≤ k ≤ 3x2+3x. Then 3n = 3x3 + 3k = (x + 1)3 + 2x3 – 3x2 – 3x – 1 + 3k. But one can easily see that the function f(x) = 2x3 – 3x2 – 3x – 1 is increasing and positive for x ≥ 3. Thus f(x) > 0, for every integer x ≥ 3, and so 2x3 – 3x2 – 3x – 1 + 3k > 3k > 0. It follows that n < (x+1)3 < 3n, as required.

126 Show that if √7 − m/n > 0 for the positive integers m, n, then √7 − m/n > 1/mn .

Solution by J. N. Lillington, Dorchester; also solved by Niels Bejlegaard, Pierre Bornsztein, Knut Dale, Gerald A. Heuer, Oren Kolman and Dr Z Reut. If m = 1, then √7 − 1/n > 2 – 1/n ≥ 1 ≥ 1/n, and the result follows; so assume that m > 1. Consider the congruences of m ≡ 0, 1, 2, 3, 4, 5, 6 (mod 7); then m2 ≡ 0, 1, 4, 2, 2, 4, 1 (mod 7). Now given √7 − m/n > 0 ↔ 7n2 > m2, we have 7n2 ≠ m2 + 1, 7n2 ≠ m2 + 2 and 7n2 ≥ m2 + 3. Then 7m2n2 – (m2 + 1)2 ≥ m2 (m2 + 3) – (m2 + 1)2 = m2 – 1 > 0. This leads to √7 mn > m2 + 1, so that √7 > m/n + 1/mn or √7 − m/n > 1/mn.

127 Find all positive integers x, y, z satisfying 1+ 2x 3y = z2 .

Solution by Knut Dale, Bø; also solved by Niels Bejlegaard, Pierre Bornsztein, Pietro Fanciulli J. N. Lillington, Erich N. Gulliver, Schwäbisch Hall (Germany), Dr Z Reut, London. Suppose that 1 + 2x 3y = z2; then z must be odd, z = 2k+1, and we get 2x-2 3y = k (k+1). With k = 1, 2, 3, we obtain the solutions (x, y, z) = (3, 0, 3), (3, 1, 5) and (4, 1, 7), but the first one is not possible because y > 0. The next value of k giving a solution is k = 8, leading to (x, y, z) = (5, 2, 7). Now assume that k ≥ 9 and let r = x–2. Since k and k + 1 have no prime factors in common, we have to consider two cases: (1) k = 2r , k + 1 = 3y (r ≥ 4, y ≥ 3). If y = 2t, then 2r = 3y – 1 = (3t – 1) (3t + 1). The only powers of 2 differing by 2 are 3t – 1 = 2 and 3t + 1 = 4; so t = 1 and y = 2, contradicting y ≥ 3. If y = 2t + 1, then 2r = (2 + 1)2t+1 – 1 = 4a + 2(2t + 1), for some a, by the binomial theorem. But this is impossible, since r ≥ 4. (2) k = 3y, k + 1 = 2r (r ≥ 4, y ≥ 2). If r = 2t, then 3y = 2r – 1 = (2t – 1) (2t + 1). The only powers of 3 differing by 2 are 2t – 1 = 1 and 2t + 1 = 3; so t = 1 and r = 2, contradicting r ≥ 4. If r = 2t + 1, then 3y = 2r – 1 = (3 – 1)2t+1 – 1 = 3b–2, for some b, by the binomial theorem. But this is impossible, since y ≥ 2. CONFERENCES submit a full paper for review by the programme committee. Articles by keynote lecturers, invited speakers and contributors will be published by Springer- Verlag in the book series Mathematics and FForthcomingorthcoming conferconferencesences Visualization. For preparation of papers please use the LaTeX templates for multi-authored books available from http://www.springer.de/math/authors/b-tex.html. Compiled by Kathleen Quinn For review papers should be submitted on-line, using the paper submission form at the workshop website. Participants will receive a volume of abstracts Sponsor: Deutsche Forschungsgemeinschaft (DFG) Please e-mail announcements of European level conference, where current research and latest Location: Harnack-Haus in Berlin-Dahlem conferences, workshops and mathematical meetings of results and developments in the field will be presented Deadlines: for submission of papers, 10 March; for final interest to EMS members, to [email protected]. by experts papers, 30 April; for on-line registration, 30 April Announcements should be written in a style similar to Organising committee: G. Lawler, C.M. Newman and Information: e-mail: [email protected] those here, and sent as Microsoft Word files or as text S.R.S. Varadhan (all USA) web site: http://www.math.tu-berlin.de/vismath files (but not as TeX input files). Space permitting, Location: the Abdus Salam International Centre for each announcement will appear in detail in the next Theoretical Physics, Strada Costiera 11, Trieste. 25-3 June: XXII International Seminar on Stability issue of the Newsletter to go to press, and thereafter Grants: a few financial grants are available for Problems for Stochastic Models (SPSM) and will be briefly noted in each new issue until the meeting applicants from, and working in, developing countries Seminar on Statistical Data Analysis (SDA), Varna, takes place, with a reference to the issue in which the only Bulgaria detailed announcement appeared. Deadline: already passed Information: web site: http://stabil.fmi.uni-sofia.bg Information: e-mail: [email protected] [For details, see EMS Newsletter 41] April 2002 web site: http://www.ictp.trieste.it/www_users/math/ maths2002.html 27-29: Spring School on Frobenius Manifolds in Mathematical Physics, Enschede, The Netherlands 1 April -30 June: Trimester on Algebraic Topology, 15-17: Fourth International Conference on Advances Information: e-mail: [email protected] Barcelona, Spain in Fluid Mechanics, Ghent, Belgium [For details, see EMS Newsletter 42] Information: web site: http://www.wessex.ac.uk/ 27-29: Frobenius Manifolds in Mathematical Physics, conferences/2002/afm02/index.html The Netherlands 29 April-12 July: Trimester on Financial Markets: [For details, see EMS Newsletter 42] Location: University of Twente, Enschede Mathematical, Statistical and Economic Analysis, Organising committee: G. Heckman, G. Helminck, R. Pisa, Italy 19-26: Symmetry and Perturbation Theory Martini, P. Kersten, J. van de Leur, E. Looijenga, J. Scientific committee: W. Brock, D. Duffie, P. (SPT2002), Cala Gonone, Sardinia, Italy Stienstra (all from the Netherlands) Embrechts, D. Farmer, H. Follmer Information: web site: Local organising committee: G. Helminck and P. Main visitors: K. Bach, M.M. Dacorogna, D. Duffie, J. http://web.tiscalinet.it/spt_spt/spt2002.html Kersten D. Farmer, C. H. Hommes, J. Karatzas, Y. Kabanov, D. Sponsors: Mathematical Research Institute (MRI), Madan, A. McNeil, T. Mikosch, M. Pagano, R.G. 22-24: Discrete Groups and Geometric Structures, NWO (Netherlands Organization for Scientific Payne, A.M. Rivlin, K. Singleton, N. Touzi with Applications (Crystallographic Groups and Research), University of Twente, Faculty of Location: Centro di Ricerca Matematica E. De Giorgi, their Generalizations III), Kortrijk, Belgium Mathematical Sciences of the University of Twente Scuola Normale Superiore, Pisa Information: web site: (Netherlands), FOM (Foundation for Fundamental Information: http://www.kulak.ac.be/workshop Research, the Netherlands) web site: http://www.crm.sns.it [For details, see EMS Newsletter 42] Speakers: R. Dijkgraaf (Netherlands), B. Dubrovin (Trieste), T. Eguchi (Tokyo), C. Hertling (Bonn), A. May 2002 22-25: International Workshop on Visualization and Morozov (Moscow), I. Krasil’shchik (Moscow), S.M. Mathematics 2002 Berlin-Dahlem, Germany Natanzon (Moscow), L. Takhtajan (New York) Aim: to provide an active forum for mathematicians and Information: e-mail: [email protected] 13-17: 34th Journées de Statistique, Brussels and computer graphics researchers on the fundamental (programme and registration), Louvain-la-Neuve, Belgium problems of visualization techniques, on applications in [email protected] (local managing director) Information: web site: www.stat.ucl.ac.be/JSBL2002 mathematics and on mathematical concepts in web site: http://www.math.utwente.nl/fa/springschool/ [For details, see EMS Newsletter 41] visualization. It is the third symposium in a series of workshops bringing together mathematicians and experts 27-31: 6th Congress of SIMAI (The Italian Society 13-31: School and Conference on Probability Theory, from computer graphics for Applied and Industrial Mathematics), Chia, Trieste, Italy Topics: visualization in differential geometry and partial Sardinia, Italy Scope: this School will concentrate on three areas of differential equations, algorithmic representation of Information: web site: http://www.iac.rm.cnr.it/simai probability: particle systems, combinatorics and random mathematical structures, computational aspects of (click on ‘simai 2002’) environment. Different biological and physical systems topology, discrete geometry of meshes, compression of [For details, see EMS Newsletter 42] can be modelled in terms of interacting particle systems large and time-dependent geometric models, virtual and a study of some specific models is very rewarding. laboratories for mathematics and applications, on-line 28-31: 2nd International Conference on Advanced Scaling limits of large systems result in considerable visualization and computational web services Computational Methods in Engineering (ACOMEN simplification of the description of the systems as they Keynote speakers: Rida Farouki, Markus Gross, Alfio 2002), Liège, Belgium evolve in time. The connection between probability and Quarteroni, Jurgen Richter-Gebert, Gabriel Taubin Information: web site: http://cage.rug.ac.be/~acomen combinatorics is undergoing a revolution at the moment. Invited Speakers: Phil Bowers, Mathieu Desbrun, [For details, see EMS Newsletter 42] Issues of conformal invariance of certain two- Gerald Farin, Joel Hass, Beau Janzen, Chris Johnson, dimensional models are just beginning to be understood. Ravi Malladi, Tom Wickham-Jones 30-2 June: Conference in Honour of Steven Percolation and random walks in a random environment Conference chairs: Christian Hege and Konrad Polthier Kleiman’s 60th Birthday, Oslo, Norway provide examples of the complexities that can result Programme committee: Helmut Alt, James Arvo, Theme: algebraic geometry and commutative algebra from being in a stationary but random environment, Chandrajit Bajaj, Thomas Banchoff, Ken Brakke, Peter Topics: motivic cohomology, moduli problems, whose spatial fluctuations can cause strange things to Deuflhard, Thomas Ertl, Gerald Farin, George Francis, intersection theory, enumerative geometry happen Hans Hagen, David Hoffman, Chris Johnson, Michael Speakers: Henning H. Andersen (Aarhus), Larry Breen Aim: the lecturers are researchers who have made Joswig, Leif Kobbelt, Heinrich Muller, Gregory Nielson, (Paris 13), Herb Clemens (Utah), Susan Colley significant contributions to the field. Their lectures will Ulrich Pinkall, Helmut Pottmann, Martin Rumpf, (Oberlin), Dan Edidin (Missouri), Eduardo Esteves provide an opportunity for the participants to learn first- Dietmar Saupe, Hans-Peter Seidel, John Sullivan, (IMPA/MIT), Dan Grayson (Illinois), Tony Iarrobino hand about some of the far-reaching recent Nobuki Takayama, Ross Whitaker, Luiz Velho, Jarke (Northeastern), Bernard Teissier (Paris 7), Israel developments in the field van Wijk, Gunter Ziegler Vainsencher (UFPE), Ravi Vakil (Stanford), Angelo Topics: interacting particle systems, scaling limits of Organisers: Sonderforschungsbereich Differential Vistoli (Bologna) particle systems, dimers and geometry, conformally Geometry and Quantum Physics (Sfb 288) at the Organising committee: Susan Colley (Oberlin), Dan invariant processes in the plane, percolation, random Technische Universität in Berlin, Department of Edidin (Missouri), Dan Grayson (Illinois), Ragni Piene walks in random environment Scientific Visualization at the Konrad-Zuse-Zentrum fur (Oslo) Main speakers: include L.R. Fontes (Brazil), R. Informationstechnik Berlin (ZIB) Sponsors: MIT Math. Dept., Norwegian Academy of Kenyon (France), C. Landim (Brazil), G. Lawler Format: keynote lectures, invited talks and contributed Sciences and Letters, Centre for Advanced Study (Oslo), (U.S.A.), T. Liggett (U.S.A.), V. Sidoravicius (Brazil), presentations. The time for keynote lectures, invited Research Council of Norway, NORDAG (NorFA) A.-S. Sznitman (Switzerland) talks and contributed talks will be 50, 40, and 30 Location: Norwegian Academy of Science and Letters, Programme: the first two weeks (13-24 May) will be minutes (respectively), including discussions. There will Drammensveien 78, Oslo, Norway devoted to expository lectures on the topics listed above, be possibilities for software demonstrations Information: e-mail: [email protected] while in the last week (27-31 May) there will be a high- Call for papers: interested contributors are asked to web site: http://www.math.uiuc.edu/~dan/Kleiman60/ EMS March 2002 29 CONFERENCES present an overview of the mathematical heritage of of Osaka, Tel Aviv University June 2002 Abel and, based upon this heritage, identify new Location: Vietri sul Mare (near Naples) mathematical trends for the 21st century Deadlines: abstracts, already passed; registrations, still 3-7: Conference dedicated to the 90th anniversary of Topics: there will be sections on the history of open B. V. Gnedenko, Kyiv, Ukraine mathematics, algebraic geometry, complex analysis, Information: web site: http://biocomp.unina.it Theme: probability theory and its applications differential equations, non-commutative geometry Aim: the focus will be on topics close to the wide range Invited speakers: Michel van den Bergh, Fabrizio 4-13: 3rd Linear Algebra Workshop BLED 2002, of scientific interests of B.V. Gnedenko. The aim is two- Catanese, Ciro Ciliberto, Herbert Clemens, Alain Bled, Slovenia fold: first, to highlight the contributions of B.V. Connes, Gerd Faltings, John Erik Fornæss, Günter Frei, Information: web site: Gnedenko in probability theory and its applications, William Fulton, Mark Green, Phillip Griffiths, Guenadi http://www.ijp.si/ftp/pub/STOp/law/ history of mathematics, problems of education, and, Henkin, Christian Houzel, Steven Kleiman, Igor M. [For details, see EMS Newsletter 41] second, to present the developments of his ideas as well Krichever, Hendrik W. Lenstra, Mark Melnikov, Roman as the current trends in the theory of probability and Novikov, Norbert Schappacher, Atle Selberg, Yum- 5-8: Free Boundary Problems, Trento, Italy related fields Tung Siu, Dennis Sullivan Topics: free boundary problems, phase transitions, fluid Topics: limit theorems for independent random Support: a few grants are available for young filtration, ferromagnetism, mechanics, materials science, variables; quality control, reliability theory, queueing mathematicians, including participants from third world biomathematics, image processing, computational theory; extremal statistics, random sums; parametric countries. Grants will be approximately 1000 euro each methods statistics, test of hypotheses; asymptotics of stable and should cover travel expenses and lodging Main speakers: L. Ambrosio, G. Bertotti, Z. Chen, P. processes; statistical change point analysis; issues in Sponsors: International Mathematical Union, The Degond, E. Di Benedetto, W. Dreyer, C.J. van Duijn, education; limit theorems for random fields; stochastics Norwegian Academy of Science and Letters, Ministry of M.E. Glicksman, N. Kenmochi, R. Kohn, S. Mueller, J.- and mathematical physics; statistical methods with Education, Research and Church Affairs, The M. Morel, R.H. Nochetto, F. Otto, O. Penrose, E. applications to insurance and finance; probabilistic Norwegian Agency for Development Cooperation Presutti, A. Quarteroni, F. Reitich, A. Schmidt, M. number theory; discrete probabilistic models; stochastic (NORAD) Soner, V. Starovoitov, J.J.L. Velazquez analysis Scientific committee: Michael Artin, Gerd Faltings, Focus sessions: free boundary problems in polymer Programme committee: A.V. Skorokhod (USA), Phillip A. Griffiths, Gennadi Henkin, Christian Houzel, science, image processing, grain boundary motion, Yu.V. Kozachenko (Ukraine), A.I. Martikainen (Russia), Olav Arnfinn Laudal, Jacob Palis optimal design for free boundary problems, numerical V.V. Petrov (Russia), Yu.K. Belyaev (Sweden), I.N. Information: web site: aspects of free boundary problems, free boundary Kovalenko (Ukraine), A.V. Ivanov (Ukraine), Yu.N. http://www.math.uio.no/abel/conference/index.html problems in biomathematics, modelling of crystal Lin’kov (Ukraine), J. Steinebach (Germany), N.Kh. growth, transitions with anisotropy Rozov (Russia), D. Vere-Jones (New Zealand), M.I. 3-8: Algebra Conference – Venezia 2002, Venice, Poster session: open to contributions by all participants Yadrenko (Ukraine), A.V. Bulinskii (Russia), N.N. Italy Programme committee: P. Colli , G. Dziuk, A. Fasano, Leonenko (UK), S. Albeverio (Germany), Yu.M. Topics: abelian groups, algebras and their M. Fremond, A. Friedman, S. Luckhaus, K.-H. Berezanskii (Ukraine), Yu.G. Kondratiev(Ukraine), representations, commutative rings, module theory, ring Hoffmann, M. Niezgodka, J. Ockendon, M. Primicerio, Yu.S. Mishura (Ukraine), A.G. Kukush (Ukraine), K.-H. theory, topological algebraic structures J.-F. Rodrigues, J. Sprekels, C. Verdi, A. Visintin Indlekofer (Germany), I. Katai (Hungary) Main speakers: S. Bazzoni (Italy), A. Facchini (Italy), Organising committee: P. Colli, G. Dziuk, A. Fasano, Organising committee: V.S. Korolyuk (Ukraine) and R. Farnsteiner (Germany), K.-H. Hoffmann, J. Sprekels, C. Verdi, A. Visintin Yu.V. Prokhorov (Russia) (co-Chairs), O.D. Borysenko R. Gilmer (USA), R. Goebel (Germany), W. Heinzer (local organiser) (Ukraine), V.V. Buldygin (Ukraine), S.S. Demidov (USA), H. Krause (Germany), K. Kunen (USA), I. Sponsors: University of Firenze, University of Freiburg (Russia), D.B. Gnedenko (Russia), I.A. Ibragimov Reiten (Norway), J. Trlifaj (Czech Republic), C. i. Br., University of Milano, University of Pavia, (Russia), V.I. Khokhlov (Russia), O.I. Klesov (Ukraine), Vinsonhaler (USA), R. Wiegand (USA) University of Trento, C.A.E.S.A.R. Institut Bonn, Yu.G. Kondratiev (Ukraine), Yu.V. Kozachenko Plenary speakers: R. Colpi (Italy), D. Herbera (Spain), W.I.A.S. Berlin, Deutsche Forschungsgemeinschaft, (Ukraine), Yu.S. Mishura (Ukraine), M.O. Perestyuk S. Kasjan (Poland), B. Olberding (USA), D. G.N.A.M.P.A., G.N.C.S., G.N.F.M. of I.N.d.A.M., (Ukraine), N.I. Portenko (Ukraine), Yu.A. Rozanov Shakhmatov (Japan), L. Struengmann (Germany) Project ‘Free Boundary Problems’ of M.I.U.R., Project (Italy), A.M. Samoilenko (Ukraine), V.V. Sazonov Scientific committee: D. Dikranjan (Italy), A. Facchini ‘Scientific Computing: Š’ of M.I.U.R., Project (Russia), B.A. Sevastyanov (Russia), A.N. (Italy), M. Fontana (Italy), L. Fuchs (USA), K. Fuller ‘Symmetries, Geometric Structures, Š’ of M.I.U.R. Shiryaev(Russia), Ya.G. Sinai (Russia), M.I. Skil’ (USA), R. Göbel (Germany), W. Heinzer (USA), C. Venue: Centro S. Chiara, via S. Croce 67, Trento (Ukraine), V.V. Skopenko (Ukraine), A.V. Skorokhod Ringel (Germany), D. Simson (Poland) Grants: for participants from weak currency countries, (USA), M.I. Yadrenko (Ukraine), O.K. Zakusylo Organising committee: F. Barioli, S. Bazzoni,, R. or born after 1 January 1967 (Ukraine), M.Z Zgurovskii (Ukraine), V.M. Zolotarev Colpi, S. Gabelli, E. Gregorio, C. Metelli, L. Salce, F. Information: e-mail: P. Colli [email protected] (Russia) Stumbo, A. Tonolo, P. Zanardo (Italy) web site: http://fbp2002.unitn.it/ Sponsors: Ministry of Education and Science of Site: Venice International University, Island of San Ukraine, Center for Science and Methodology of Higher Servolo, Venice 5-9: Conference in Honour of Hans Wallin, Umea, Education, Kyiv National Taras Shevchenko University, Deadlines: registration and abstracts, 31 March Sweden National Technical University of Ukraine (KPI), Proceedings: to be published by Marcel Dekker, Inc. Information: web site: National Pedagogical Dragomanov University, Lviv Information: e-mail: [email protected] http://www.math.umu.se/aktuellt/HWkonferens.htm Franko State University, Institute for Mathematics, web site: http://dm.unife.it/~venezia/ [For details, see EMS Newsletter 41] National Academy of Science of Ukraine, ‘Mathematica’ Foundation, Moscow State Mikhail 3-9: BIOCOMP2002, Vietri sul Mare, Italy 6-8: Zero Dimensional Schemes and Related Topics, Lomonosov University, Steklov Institute for Theme: mathematical biology and biocomputation Acireale, Sicily, Italy Mathematics, Russian Academy of Science, Bernoulli Programme: invited lectures, selected contributed [in honour of Tony Geramita on the occasion of his 60th Society, INTAS Conference papers and round-table discussions birthday] Abstracts: abstracts should be sent to Aim: to bring together specialists of various fields to Theme: algebraic geometry and commutative algebra [email protected], typeset for AMS TeX in focus on the relevant problems of mathematical biology Main speakers: Karen Chandler (Notre Dame), Luca amsppt style. If you are not familiar with AMS TeX, and biocomputation at the beginning of the third Chiantini (Siena), Aldo Conca (Genova), Alessandro please copy the template file at millennium Gimigliano (Bologna), Martin Kreuzer (Regensburg), http://ln.com.ua/~tbimc/gnedenko/ Topics: biomechanics and molecular motors; pattern Tony Iarrabino (Northeastern), Rosa María Miró-Roig Proceedings: papers for the Proceedings should be sent formation; spatial and non-linear dynamics in population (Barcelona), Uwe Nagel (Paderborn), Leslie Roberts to [email protected] or submitted upon biology and ecology; coding, computations and (Queen’s), Rosario Strano (Catania), Bernd Ulrich arrival, typeset for AMS TeX in amsppt style stochasticity in neurobiology and other excitable media; (Purdue) Location: Kyiv National Taras Shevchenko University biocomputing, bioinformatics and gene networks Organising committee: Eddy Campbell (Queen’s), (Volodymyrska, 60), Kyiv, Ukraine Programme committee: S. Amari (Japan), J.J. Collins Brian Harbourne (Nebraska), Juan Migliore (Notre Grants: restricted number of grants for participants (USA), P. Cull (USA), I. Eshel (Israel), M. Iannelli Dame), Ferruccio Orecchia (Napoli), Alfio Ragusa from the former Soviet Union and young (Italy), P. Lánský (Czech Republic), S.A. Levin (USA), (Catania), Lorenzo Robbiano (Genova) mathematicians Z. Ma (China), M. Mimura (Japan), R. Moreno Diaz Sr. Grants: limited funding available for young researchers Deadlines: for requests for a letter of invitation, 31 (Spain), K. Pakdaman (France), L. Peliti (Italy), F. Related conferences: the AMS-UMI meeting in Pisa, March; for abstracts, 30 April; for requests for a hotel Pichler (Austria), S. Sato (Japan), J.P. Segundo (USA), 12-16 June (http://www.dm.unipi.it/~meet2002/) has reservation, 10 May C.E. Smith (USA), A. Tesei (Italy), H.C. Tuckwell several special sessions in commutative algebra and Information: e-mail: [email protected] (Australia), F. Ventriglia (Italy), G. Vidossich (Italy), T. algebraic geometry; Current Trends in Commutative fax: +38-044-513-84-07 Yanagida (Japan) Algebra, Levico, 17-21 June, (http://www.dima.unige.it/ web site: http://ln.com.ua/~tbimc/gnedenko/ Organising committee: Luigi M. Ricciardi, Chair ~rossim/Levico.html) is also of interest (http://cds.unina.it/~ricciard/), U. Amato, W. Balzano, A. Information: web site: 3-8: Abel Bicentennial Conference 2002, Oslo, Buonocore, S. Chillemi, A. Dattolo, A. Di Crescenzo, E. http://cocoa.dima.unige.it/conference/acireale/first.html Norway Di Nardo, P. Festa, V. Giorno, M. Longobardi, K. Location: University of Oslo Nakagawa, A.G. Nobile, E. Pirozzi, S. Rinaldi, L. 6-15: Fourth International Conference on Geometry, Theme: 2002 marks the bicentennial of the birth of Sacerdote Integrability and Quantization, Varna, Bulgaria Niels Henrik Abel, 1802-29. The conference will Sponsors: University of Napoli Federico II, University Information: web site: 30 EMS March 2002 CONFERENCES http://www.bio21.bas.bg/conference/ 17-21: Advanced School and Workshop on correlation inequality, martingale and decoupling [For details, see EMS Newsletter 42] Mathematical and Computational Modeling of inequalities. Biological Systems, Lisboa, Portugal Programme: plenary lectures, invited and contributed 10-14: Homology Theories, Representations and Theme: mathematical and computational modeling of half-hour lectures, and problem and discussion sessions Hopf Algebras, Luminy, France biological systems Main speakers: Luis Caffarelli (Austin, USA), Nicolai Theme: homological algebra, representation theory Aim and Format: to provide an updated overview of Krylov (St Paul/Minneapolis, USA), Rafal Latalà Topics: Green functors, tilting objects, invariance typical models and tools used in mathematical and (Warsaw, Poland), Michel Ledoux (Toulouse, France), properties of automorphism groups, Hochschild computational studies of biological tissues, organs and Gàbor Lugosi, Barcelona, Catalonia), Pascal Massart cohomology, Hopf algebras systems. The event has two components: Advanced (Orsay, France), Colin McDiarmid (Oxford, UK), Philip Programme: short courses (each of three 45-minute Course and Research Workshop Protter (Ithaca, USA), Emmanuel Rio (Versailles, lectures), also conference talks Theme: mathematics and biology, with special France), Ofer Zeitouni (Haifa, Israel) Course speakers: Serge Bouc Paris 7 (France), Dieter emphasis on modelling tissues, organs and systems of Scientific programme committee: Evarist Giné (Storrs, Happel Chemnitz (Germany), Manuel Saorin Murcia the human body USA), David Nualart (Barcelona, Catalonia), Christian (Spain) Topics: mechanics of soft tissues, mechano-electrical Houdré (Atlanta, USA) Conference speakers: N. Andruskiewitsch (Argentina), function of the heart, thermo-chemo electro-mechanics Local organising committee: David Nualart, Frederic A. Bruguieres (France), F. Coelho (Brazil), S. Dourlens of porous media, skeletal muscles and neuromuscular Utzet, Arturo Kohatsu, Maria Jolis (France), F. Dumas (France), M. Farinati (Argentina), D. control, control and mechanics of human movement Sponsors: Centre de Recerca Matemàtica, European Guin (France), M. Karoubi (France), C. Kassel (to systems, physiological fluid mechanics Commission, Ministerio de Ciencia y Teconología confirm) (France), T. Lambre (to confirm) (France), P. Main speakers: Gerhard Holzapfel (Austria), Peter (Spanish Government) and Bernoulli Society Malbos (France), E. Marcos (Brazil), S. Natale Hunter (New Zealand), J. Huyghe (Netherlands), J. van Location: Centre de Recerca Matemàtica, Universitat (Argentina), F. Patras (France), E. Reynaud (France), M. Leewen, (Netherlands), Clyde Martin (USA), Prof. Autònoma de Barcelona, Science Building 08193, Rosso (France), C. Strametz (France), M. Suarez Oliver Jensen (UK) Bellaterra, Spain Alvarez (Argentina), R. Taillefer (France), L. Unger Programme: 18 hours of Course lectures; 9 hours of Deadlines: application for financial support, 5 April; (Germany), M. Vigue-Poirrier (France), A. Workshop paper presentations and discussions registration and payment, 30 April Zimmermann (France) Call for papers: two-page abstracts containing the Information: Secretary of the conference, Consol Roca, Languages: English, French author’s name, affiliation, address, and e-mail can be Centre de Recerca Matemàtica, Apartat 50, 08193 Organising committee: Claude Cibils (France), Maria sent by e-mail (text, word, pdf, or ps format) or by fax Bellaterra, Catalonia, Spain; phone: 34-93-5811081. Julia Redondo (Argentina), Andrea Solotar (Argentina) Organising committee: J.A.C. Martins, IST, Portugal, e-mail: [email protected], web site: Sponsors: CIRM (France), Université de Montpellier 2, E.B. Pires, IST, Portugal http://www.crm.es(activities) Université de Paris 7, TMR network K-Theory, Linear Main sponsor: this event is part of the Thematic Term Algebraic Groups and Related Subjects, Ambassade de on Mathematics and Biology, sponsored by CIM (Centro 17-21: XVth Householder Symposium on Numerical France in UK Internacional de Matemática), a member of ERCOM - Linear Algebra, Peebles, Scotland Location: CIRM, Luminy, Marseille (http://cirm.univ- European Research Centres on Mathematics Information: web site: mrs.fr) Other sponsors: Instituto de Engenharia de Estruturas, http://www.maths.strath.ac.uk/~matrix/ Fees: no registration fee; cost of lodging at CIRM is Territorio e Construção (ICIST), Fundação Calouste [For details, see EMS Newsletter 42] around 45 euros a day, including meals Gulbenkian Fundação para a Ciência e a Tecnologia Deadlines: for registration, 5 May (write to (FCT) 17-22: School on Population Dynamics, Bêdlewo, [email protected]) Proceedings: to be published Poland Information: e-mail: [email protected] Location: Congress Centre of Instituto Superior Técnico Information: web site: montp2.fr, [email protected], Building of the Departamento de Engenharia Civil e http://www.math.us.edu.pl/cmmpd/ [email protected] Arquitectura Instituto Superior Técnico, Lisboa, Portugal [For details, see EMS Newsletter 42] web site: gauss.math.univ-montp2.fr/~cibils/CIRM2002 Grants: 30 euro discount for students Notes: class notes will be provided to participants 18-22: The Barcelona Conference on Stochastic 10-16: Aarhus Topology 2002, Aarhus, Denmark Deadlines: for receipt of abstracts, 15 March Inequalities and their Applications Information: web site: http://www.imf.au.dk/AT2002/ Secretariat and Address: Helena Romão, ICIST, Dep. (EuroConference), Bellaterra, Barcelona, Spain [For details, see EMS Newsletter 41] Eng. Civil e Arquitectura, Instituto, Superior Técnico, Information: web site: http://www.crm.es/stochineq Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal, phone: 11-13: Third International Symposium on Remote (+351) 21 841 8401, fax: (+351) 21 849 7650 18-23: Advanced School and Workshop on Bone Sensing of Urban Areas, Istanbul, Turkey Information: e-mail: [email protected] Mechanics: Mathematical and Mechanical Models Information: web site: web site: http://www.civil.ist.utl.pt/bio.systems for Analysis and Synthesis, Lisbon, Portugal http://www.ins.itu.edu.tr/deryamaktav Main speakers: Martin P. Bendsoe (Denmark), Andrej [For details, see EMS Newsletter 42] 17-21: Seventh international conference on p-adic Cherkaev (USA), Stephen C. Cowin (USA), Manuel functional analysis, Nijmegen, The Netherlands Doblaré (Spain), Rik Huiskes (Netherlands), Harrie 12-16: 2002 WSEAS International Conferences on [analysis in and over valued fields other than R or C] Weinans (Netherlands), José M. Guedes (Portugal), Signal Processing, Robotics And Automation (ISPRA Scientific committee: W. Schikhof (Netherlands), A. Helder Rodrigues (Portugal) ‘02); Microwaves, Antennas & Radar Systems Escassut (France), C. Perez-Garcia (Spain) Organising committee: H. Rodrigues (Portugal), J. (IMARS ‘02); Electronics & Hardware Systems Programme: each participant is asked to contribute a Guedes (Portugal) (IEHS ‘02), Cadiz, Spain half-hour lecture on recent research, in English Proceedings: to be published Information: web site: Abstracts: to Ms. W. van de Sluis (local manager), e- Location: Instituto Superior Tecnico, Av. Rovisco Pais, http://www.wseas.org/conferences/2002/spain mail: [email protected] Lisboa, Portugal Proceedings: we intend that these will be published. Information: e-mail: [email protected] 16-23: Second Russian-German Geometry Meeting, Participants are asked to deliver a manuscript at the start web site: http://www.dem.ist.utl.pt/~bonemec St Petersburg, Russia of the conference: more details will be available later [dedicated to the 90th anniversary of A.D. Alexandrov Sponsors: Mathematical Research Institute (MRI) 19-21: EUROMECH Colloquium 437: Identification (1912-99)] (Netherlands), NWO (Netherlands Organization for and Updating Methods of Mechanical Structures, Topics: differential geometry, non-linear differential Scientific Research) (Netherlands), Subfaculty of Prague, Czech Republic equations in geometry, geometric analysis, singular Mathematics, University of Nijmegen (Netherlands) Location: Institute of Thermomechanics, Czech spaces, foundations of geometry, applications of Deadlines: for abstracts, 1 May Academy of Sciences geometry to mathematical physics and algebra Information: e-mail: [email protected] Theme: mathematical modelling of mechanical Organisers: W. Ballmann (Bonn), Yu. Burago (St web site: http://www.sci.kun.nl/math/p-adic2002 structures Petersburg), Yu.G. Reshetnyak (Novosibirsk) Topics: parametric identification in frequency and time Co-organisers: S.V. Buyalo (St Petersburg), D. Schueth 17-21: Stochastic Inequalities and their Applications, domain, curve fitting of transfer functions, identification (Bonn), I.A. Taimanov (Novosibirsk) Barcelona, Catalonia of vibrating systems with small non-linearity, spectral Location: Euler International Mathematical Institute, Aim: the topics to be covered belong to different areas and modal sensitivity, updating methods of finite Pesochnaya nab. 10, St Petersburg 197022 of probability, statistics and analysis, and therefore the element models, tuning and vibro-diagnostics of Deadline: for registration, 15 April conference will provide a unique opportunity for mechanical structures, robustness of model-based Information: e-mail: [email protected], exchange of ideas occurring in different fields and for decisions with respect to uncertainties [email protected], [email protected] interdisciplinary contact and collaboration Main speakers: G. Lallement (France), J. Piranda web site: http://www.pdmi.ras.ru/EIMI/2002/geo2/ Topics: to include concentration and deviation (France), M. Balda (Czech Republic), E. Hahn inequalities for various types of processes using (Australia) 17-19: 24th World Conference on Boundary Element isoperimetry, differential inequalities and information Call for papers: participants are invited to contribute Methods incorporating Meshless Solutions Seminar inequalities, other exponential and moment inequalities papers on the above topics. Oral presentation should be Sintra, Portugal for sums of independent or weakly dependent random in English (25 minutes including discussion). Information: web site: http://www vectors and related variables, inequalities in Malliavin Contributors should submit, as an attached file via e- [For details, see EMS Newsletter 42] Calculus, geometric inequalities for log-concave mail to the e-mail conference address: [email protected] probability measures, particularly the Gaussian or [email protected], a one-page extended

EMS March 2002 31 CONFERENCES abstract of their proposed paper including its title, Polynomials: Orthogonal Polynomials and (Australia), N.Z. Shor (Ukraine), I.V. Skrypnyk author’s name, affiliation, full mail address and e-mail Approximation Theory (IWOP’02), Leganes, (Ukraine), M. Thera (France), V.M. Tikhomirov address. The extended abstracts will be reviewed by the Madrid, Spain (Russia), V.Ye. Tretyakov (Russia), V.O. Zhukovskii Scientific Committee; authors will be notified about Topics: approximation theory, quadrature formulas, (Russia) acceptance by the end of April 2002. All accepted orthogonal polynomials Organising committee: A.A. Chikrii (Chair, Ukraine) papers will be published in the Book of Abstracts of the Main speakers: J.S. Geronimo (Atlanta, USA), P. Organisers: Glushkov Institute of Cybernetics of the EUROMECH Colloquium 437. The proceedings will Gonzalez Vera (La Laguna, Spain), L. Jodar (Valencia, National Academy of Sciences, Institute for Applied be available for delegates attending the Colloquium. Spain), A.B.J. Kuijlaars (Leuven, Belgium), A. System Analysis of the National Academy of Sciences Selected papers from the Colloquium will be Martinez-Filkenshtein (Almeria, Spain), H. Stahl and the Ministry of Education and Science of Ukraine, recommended for the publication in international (Berlin, Germany) National Technical University ‘Kyiv Polytechnical journals for theoretical and applied mechanics Abstracts: if you wish to present an oral Institute’ Preliminary scientific committee: Miroslav Balda communication, submit your abstract (plain ASCII or Book of abstracts: to be published (Czech Academy of Sciences), Vasyl Chekurin LaTeX, up to two pages) via the web site Location: in Kyiv, on the campus of the National Pidstryhach (National Academy of Sciences, Ukraine), Scientific committee: Jesus Dehesa (Granada), Antonio Technical University ‘KPI’ Ivan Dobias (Czech Academy of Sciences), Jaromir Duran (Sevilla), Guillermo Lopez Lagomasino (Madrid), Deadline: for submission of abstracts, 15 April Horacek (Czech Academy of Sciences), Jean Piranda Paco Marcellan (Madrid), Walter Van Assche (Leuven) Information: web site: (University Franche Comte), Ladislav Pust (Czech Organising committee: Renato Alvarez-Nodarse www.icyb.kiev.ua/conferences/conferences.html Academy of Sciences), Alexandru Valentin Radulescu (Sevilla: [email protected]), Jorge Arvesu (Madrid: (University Politehnica, Bucharest), Gu Zhengqi (Hunan [email protected]) and Paco Marcellan (Madrid: 25-28: 8th International Conference on Applications University, P.R. China) [email protected]) of Computer Algebra, Volos, Greece Chairs: Gerard Lallement AML RC, University Franche Proceedings: a special volume of the proceedings is Themes: computer algebra, symbolic computation Comte, Besancon, France, Jan Kozanek, Institute of planned Topics: computational quantifier elimination, computer Thermomechanics, Czech Academy of Sciences Location: Escuela Politecnica Superior, Universidad algebra and cagd, numerical-symbolic methods in Location: Institute of Thermomechanics, Czech Carlos III de Madrid, Leganes, Spain physical modelling, Gröbner bases and applications, Academy of Sciences, Dolejskova 5, 182 00 Prague 8, Deadline: for abstracts, 30 April robotics, mathematical physics and control theory, non- Czech Republic Information: contact members of the organising standard applications, industrial and engineering Grants: some reduction of fees for young participants committee applications of computer algebra, symbolic and exact Deadlines: for submission of extended abstracts, 29 web site: http://merlin.us.es/~renato/iwop02/ linear algebra, automatic theorem proving, celestial March (acceptance by 30 April); for payment, 10 May mechanics, combinatorial and computational methods in Information: e-mail: [email protected] 24-28: Conference on Mathematical Modelling of algebraic geometry and singularities, mathematical [email protected] Population Dynamics, Bêdlewo, Poland implementations, algebraic tools for differential fax: +420-2-86584695, Information: web site: equations, computer algebra in education, dynamical web: http://www.it.cas.cz/ec-437/ http://www.math.us.edu.pl/cmmpd/ systems and mechanics, new developments in [For details, see EMS Newsletter 42] mathematica, approximate algebraic computation and 21-26: Symmetries and Integrability of Difference stabilisation, symbolic-numerical methods in Equations: EuroConference on Discrete Painlevé 25-28: International Conference dedicated to the computational science, computational commutative and Equations and the Solvability of Difference 65th Anniversary of B.N. Pshenichnyi (1937-2000), differential algebra Equations, Giens (near Toulon), France Kyiv, Ukraine General chairs: Alkiviadis G. Akritas, Ilias S. Kotsireas Topics: to include analytic and algebraic aspects of Scope: optimisation, mathematical theory of control, Administrative assistance: Theodora Terlexi difference equations, difference Galois theory, the dynamic games Programme chairs: Victor Edneral, Eugenio Roanes- Painlevé property and singularity analysis, growth and Topics: necessary conditions for extremum, Lozano branching phenomena in rational mappings, difference mathematical programming, computational methods of Organising committee: Stanley Steinberg, Michael analogues of the Painlevé equations, isomonodromic optimisation, convex analysis and theory of set-valued Wester deformation theory, asymptotics of orthogonal mappings, dynamic games, search for moving objects, Local arrangements committee: Thomas Kylindris, polynomials, symmetries of difference equations, mathematical theory of control, identification and Yiannis Parassidis, Korina D. Tsilika, Loukas Zachilas applications to numerical analysis minimax estimation of parameters, models of economic Scientific committee: ACA Working Group, A.G. Main speakers: Mark J. Ablowitz (Boulder, USA); dynamics, decision making under uncertainty, Akritas, (Greece), J. Calmet (Germany), V. Edneral Alexander Its (Indianapolis, USA); Reinout Quispel optimisation problems of the charged particle beam (Russia), V. Ganzha (Germany), V. Gerdt (Russia), H. (Bundoora, Australia); Claude Brezinski (Lille, France); dynamics, controlled processes simulation, applications Hong (USA), E. Kaltofen (USA), I.S. Kotsireas Nalini Joshi (Adelaide, Australia); Alfred Ramani (Paris, in all areas (Canada), B. Kutzler (Austria), R. Liska (Czech France); Peter Clarkson (Canterbury, UK); Martin Main speakers: A. Azimov (Turkey), A.B. Kurzhanski Republic), B. Pletsch (USA), E. Roanes-Lozano (Spain), Kruskal (Rutgers, USA); Konstantin Rerikh (Dubna, (Russia), Y.S. Ledyaev (Russia), A.G. Chentsov S. Steinberg (USA), Q. Tran (USA), N. Vassiliev Rumania); Robert Conte (Saclay, France); Ilpo Laine (Russia), A.A. Chikrii (Ukraine), V.S. Melnik (Ukraine), (Russia), M. Wester (USA) (Joensuu, Finland); Jacques Sauloy (Toulouse, France); V.F. Demyanov (Russia), B. Mordukhovich (USA), A. Sponsors: Greek Ministry of Culture, Waterloo Rod Halburd (Loughborough, UK); Decio Levi (Rome, Ioffe (Israel), A. Rubinov (Australia), F.M. Kirilova MAPLE, Greek Telecommunications Organisation, Italy); Junkichi Satsuma (Tokyo, Japan); Peter E. Hydon (Belarus), V.M. Tikhomirov (Russia) Wilfrid Laurier University, University of Thessaly, (Surrey, UK); Jean-Marie Maillard (Paris, France); Call for papers: authors are invited to submit an Greek Railways, Ontario Research Centre For Computer Walter van Assche (Louvain, Belgium); Gertruida electronic version of their extended abstract (one full Algebra, Alpha Bank, Texas Instruments, Wiley, Immink (Groningen, Netherlands); Frank Nijhoff single-spaced A4 page in English, LaTeX format): the IMACS, Cotopaxi, City of Volos (Leeds, UK); Alexander Veselov (Loughborough, UK); name, affiliation and e-mail of the author are to be Proceedings: a volume with the abstracts of the papers Arieh Iserles (Cambridge, UK); Vassilis Papageorgiou shown under the title of the paper. Address for presented at ACA 2002 will be available at the (Patras, Greece); Pawel Winternitz (Montreal, Canada) submission of abstracts: [email protected]. conference. Participants should submit their abstracts in Programme: available on-line The files should also be sent to the conference chair: text or LaTeX form to the session organisers. Selected Chairs: Claude Viallet (CNRS Paris, France), Jarmo [email protected] full papers from those presented at the conference, as Hietarinta (University of Turku, Finland) Programme: lectures and contributed papers well as at ACA 2001, will be published in a special issue Sponsors: European Commission, Research DG, Programme committee: Chair: I.V. Serhienko of the Journal of Symbolic Computation, entitled Human Potential Programme, High-Level Scientific (Ukraine); Co-Chairs: M.Z. Zhurovskii and V.M. ‘Special Issue on Applications of Computer Algebra’ Conferences (Contract No: HPCF-CT-2001-00013), Kuntsevich (Ukraine); Members: A. Azimov (Turkey), Deadlines: for submissions of abstracts, 20 April; for INTAS V.D. Batukhtin (Russia), L. Berkovitz (USA), A.G. submissions of full papers, 30 December Location: VVF Presqu’île de Giens La Badine Chentsov (Russia), F.L. Chernousko (Russia), A.A. Location: University of Thessaly, Department of Grants: available in particular for nationals under 35 Chikrii (Ukraine), F. Clarke (Canada), J.-P. Dedieu Computer Engineering, Telecommunications and from EU or associated states (Bulgaria, Cyprus, Czech (France), V.F. Demyanov (Russia), G. Feichtinger Networks Republic, Estonia, Hungary, Iceland, Israel, Latvia, (Austria), R.F. Gabasov (Belarus), E. Galperin (Canada), Information: phone: + 30-421-074886, e-mail: Liechtenstein, Lithuania, Norway, Poland, Romania, F. Giannessi (Italy), O. Hajek (USA), J.-B. Hiriart- [email protected] Slovakia and Slovenia). Some support will also be Urruty (France), Y.C. Ho (USA), F. Imado (Japan), A. web site: http://www.orcca.on.ca/~ilias/aca2002.html available for scientists of 35 years old or under from the Ioffe (Israel), J. Kaluski (Poland), F.M. Kirilova New Independent States of the former Soviet Union (Belarus), I.N. Kovalenko (Ukraine), N.N. Krasovskii 27- 3 July: Fifth International Conference on Curves (NIS) (Russia), J. Krawczyk (New Zealand), A.V. and Surfaces, Saint-Malo, France Deadline: for grants, 28 March Kryazhymskii (Russia), A.B. Kurzhanski (Russia), Y.S. Information: Information: contact Rachid Adghoughi Ledyaev (Russia), V.N. Malozyomov (Russia), V. web site: http://www-lmc.imag.fr/saint-malo/ ([email protected]), Conference Organiser, European Marchenko (Belarus), A.A. Melikyan (Russia), V.S. [For details, see EMS Newsletter 42] Science Foundation, Euresco Office, 1 quai Lezay- Melnik (Ukraine), A. Meystel (USA), Ye.F. Mishchenko Marnésia, 67080 Strasbourg (Russia), B. Mordukhovich (USA), M.S. Nikolskii 27-2 July: 19th International Conference on web site: http://www.esf.org/euresco/02/pc02185 (Russia), Yu.S. Osipov (Russia), M. Papageorgiou Operator Theory, Timisoara, Romania (Greece), P. Pardalos (USA), Z. Parsa (USA), J.-P. Topics: operator theory, operator algebras and their 24-27: International Workshop on Orthogonal Penot (France), V.N. Redko (Ukraine), A. Rubinov applications: differential operators, complex functions,

32 EMS March 2002 CONFERENCES mathematical physics, matrix analysis, systems theory, Theoretical Physics (Kyoto, Japan) community in theoretical biology and medicine in etc. Location: CAMTP: Center for Applied Mathematics Europe and beyond Main speakers (tentative): A. Atzmon (Israel), J. and Theoretical Physics, University of Maribor Krekova Topics: biotechnology and bioengineering, Bellissard (France), L.G. Brown (USA), I. Gohberg 2, Maribor, Slovenia bioinformatics and computational biology, biomedical (Israel), Ch.R. Johnson (USA), L. Kerchy (Hungary), R. Grants: limited financial support for participants from imaging, cardiovascular system, cell signalling, cellular Nest (Denmark), J.R. Partington (England), R. Rochberg Eastern European and developing countries. Apply by e- organisation, ecology, environmental sciences, (USA), M. Rordam (Denmark), Z.J. Ruan (USA), G. mail to [email protected] evolution, immunology, infectious diseases, individual Weiss (USA) Deadlines: for application with abstract (poster or based models, computational neuroscience, visualisation, Programme committee: W.B. Arveson (USA), N.K. report) or without presentation, 15 May; for late regulatory gene networks Nikolskii (France), N. Salinas (USA), S. Stratila application, 27 June; for application for financial Main speakers: Marina Alexandersson (Sweden), (Romania), F.H. Vasilescu (France) support, 18 April; for hotel reservation , 27 June Giuseppe Baselli (Italy), Tom Britton (Sweden), Klaus Proceedings: expected to be published Information: e-mail: [email protected] Dietz (Germany), Wulfram Gerstner (Switzerland), Location: West University of Timisoara http://www.camtp.uni-mb.si/chaos/2002/ Hans-Christian Hege (Germany), Claudia Neuhauser Sponsors: Institute of Mathematics of the Romanian (USA), A. Neumann (Israel), Alfio Quarteroni (Italy), Academy and West University of Timisoara Jonathan Sherratt (UK), Karl Sigmund (Austria), Denis Grants: some financial support for PhD students and July 2002 Thieffry (France), Daniel Tranchina (USA), Tamiki young researchers will be available: contact also the Umeda (Japan), Hans Westerhoff (Netherlands), Simon EURROMMAT programme 1-5: Congrès de mathématiques appliquées à la Wood (UK) (http://pompeiu.imar.ro/~eurrommat/positions.html) mémoire de Jacques-Louis Lions, Paris, France Programme: organised in sections, each comprising an Deadlines: for registration, 30 March Speakers: L. Ambrosio, F. Baccelli, J. Ball, F. Brezzi, invited speaker and 2-hour mini-symposia; posters can Information: e-mail: [email protected] L. Caffarelli, M.-P. Cani, A. Chorin, J.-M. Coron, L. be presented in special sessions web site: http://www.imar.ro/~ot Evans, O. Faugeras, M. Fink, M. Ghil, T. Hou, A. ESMTB Board: V. Capasso (President), Z. Agur, O. Majda, L. Nirenberg, G. Papanicolaou, A. Patera, B. Arino, M. Chaplain, M. Gyllenberg, J.A.P. Heesterbeek, 30-14 July: ‘Let’s Face Chaos through Nonlinear Perthame, R. Rannacher, P. Souganidis, E. Tadmor, S. M. Kaufman, V. Krivan, A. Stevens, P. Tracqui Dynamics’, 5th International Summer School and Varadhan, C. Villani, M. Vishik, J.-C. Yoccoz, E. Programme committee: P. Cinquin, A. De Roos, P. Conference, Maribor, Slovenia Zuazua Deuflhard, A. Goldbeter, P. Jaegers, W. Jager, P. [dedicated to the 75th birthday of Prof. Hermann Haken] Honour committee: H. Curien, H. Fujita, P. Lax, E. Lansky, P. Maini, H. Metz, R. Nisbet, C. Peskin, S. Themes: non-linear dynamics, chaos theory, Magenes (Chair), G. Marchuk Rinaldi, L. Segel. Liaisons: A. Hastings (SMB), M. synergetics, complex systems Patronages: International Mathematical Union and Mimura (JSMB) Scope: lecture courses (delivered by invited speakers) Académie des Sciences de Paris Supported and Organising committee: V. Capasso, E. Beretta, P. starting at introductory level adapted to senior sponsored by: Ministère de la Recherche, CNRS, CNES, Cerrai, P. Colli-Franzone, S. Cerutti, A. De Gaetano, A. undergraduate and graduate students, and concluding INRIA, Collège de France, Ecole Polytechnique, Fasano, P. Fergola, A. Gandolfi, E. Galli, M. Gatto, F. with the most recent research results comprehensible for Université Pierre et Marie Curie (Paris VI), SMAI and Grandoni, A. Mari, C. Matessi, A. Morabito, D. Morale, most of the audience and subject to discussion among SMF G. Naldi, S. Paveri-Fontana, L. Preziosi, A. Pugliese, L. the attending invited speakers, experts and specialists Location: Collège de France Sacerdote Aim: scientific exchange among seemingly distant Registration: free of charge: please register directly on Sponsors: European Union, Centro Nazionale delle disciplines, allowing students and junior scientists to the web site Ricerche Universita’ degli Studi di Milano, Politecnico understand better the role of interdisciplinary research, to Information: postal address: Laboratoire d’analyse di Milano, Milan Research Centre for Industrial and bring them in touch with science in making, and to offer numérique Université Pierre et Marie Curie Boî te Applied Mathematics (MIRIAM), Universita’ degli the opportunity to present their own research work (in courrier 187 75252 Paris cedex 05 France, Studi di Pavia, MURST-COFIN Processi Stocastici a short reports and posters) fax : + 33 1 44 27 72 00, Struttura Spaziale, Domus Galilaeiana, Topics: atomic physics, biophysics, chaos, classical e-mail: [email protected] STMicroelectronics mechanics, computational physics, condensed matter, web-site: http://acm.emath.fr/congres-jllions/ Grants: more than 100 fellowships for eligible (less electromagnetism, fluid dynamics, general physics, than 35 years and members of the Union or an mathematical physics, mathematics, medical physics, 1-6: Advanced Course on Mathematical Finance: Associated State) young researchers have been mesoscopic physics, molecular physics, non-linear Models, Bellaterra, Barcelona, Spain supported by the European Union. Probably some dynamics, plasma physics, quantum chaos, quantum Coordinator: Joan del Castillo support will be available without the EU criteria mechanics, solid state physics, statistical physics, Information: web site: http://www.crm.es/matfin Deadlines: for applications for financial support, passed; theoretical physics for early registration, 1 April; for papers, 31 December Invited lecturers: Y. Aizawa (Japan), V. Anishchenko 1-6: 2nd International Conference on the Teaching Information: e-mail: [email protected] (Russia), O. Bohigas (France), T. Bountis (Greece), G. of Mathematics at Undergraduate Level, web site: http://ecmtb.mat.unimi.it Casati (Italy), P. Cvitanovic (USA), T. Frank Chersonissos, Crete, Greece (Netherlands), H. Fujisaka (Japan), G. Gallavotti (Italy), Information: web site: http://www.math.uoc.gr/~ictm2 7-14: 6th WSEAS CSCC Multiconference on P. Gaspard (Belgium), I. Grabec (Slovenia), S. [For details, see EMS Newsletter 42] Circuits; Systems; Communications; Computers; Grossmann (Germany), I. Guarneri (Italy), F. Haake Applied Informatics; Signal Processing and (Germany), H. Haken (Germany), H. Hasegawa (Japan), 1-6, 2002 Workshop on Wavelets and Applications, Computational Geometry and Vision; Scientific Y. Kuramoto (Japan), J. Laskar (France), M. Matsushita Barcelona, Spain Computations and Soft Computing, Rethymna (Japan), P. McClintock (UK), E. Mosekilde (Denmark), Topics: EDPs, numerical analysis, probability theory, Beach, Crete K. Nakamura (Japan), D. Pagon (Slovenia), J. Pichard signal processing Information: e-mail: [email protected] (France), P. Prelovsek (Slovenia), T. Prosen (Slovenia), Main speakers: C. Canuto (Politecnico di Torino), R. web site: http://www.wseas.org/conferences/2002/crete M. Robnik (Slovenia), V. Romanovski (Slovenia), M. Gundy (Rutgers U.), T. Nguyen (U. California, San Rosenblum (Germany), A. Ruffing (Germany), J. Diego), A. Tabacco (Politecnico di Torino), G. Weiss 8-26: School and Conference on Algebraic K-theory Schumacher (Germany), T. Seligman (Mexico), A. (Washington U.) and its Applications, Trieste, Italy Shudo (Japan), M. Sonis (Israel), A. Stefanovska Intended audience: graduate students and young Theme: K-theory and related topics (Slovenia), H. Stoeckmann (Germany), G. Tanner (UK), researchers Aim: to update information on recent developments in P. Tass (Germany), J. Weele (Netherlands), M. Organising committee: M.J. Carro, J. Cerda, J. Martin, the field and re-emphasise the multidisciplinary nature of Wilkinson (UK) J. Soria K-theory and its usefulness in solving problems arising Programme: 77 invited 60-minute lectures, at school Sponsors: Institute of Mathematics of the University of in several areas of mathematics and conference level; opportunities to present research Barcelona (IMUB) Topics: K-theory and algebraic topology; K-theory and work as a short report (20 minutes) or poster; a rich Location: University of Barcelona, Gran Via 585, non-commutative geometry; a survey of the cultural and social programme 08007 Barcelona developments of K-theory in the last 45 years; K-theory Call for papers: apply with abstract (posters or short Deadlines: for registration, 31 May and arithmetics; K-theory and representation theory; K- report); see http://www.camtp.uni- Information: http://www.imub.ub.es/wavelets theory and algebraic geometry mb.si/chaos/2002/apply.html Main speakers: L. Barbieri-Viale (Italy), J. Berrick Organising committee: director: M. Robnik (CAMTP, 2-6: 2002 Barcelona Conference on Algebraic (Singapore), S. Bloch (USA), J. Cuntz (Germany), E. Slovenia); honorary directors: G. Casati (Italy), P. Topology (a EuroConference), Barcelona, Spain Friedlander (USA), H. Gillet (USA), L. Hesselholt Cvitanovic (USA), S. Grossmann (Germany), H. Haken Information: web site: http://www.crm.es/2002bcat (USA), N. Higson (USA), R. Jardine (Canada), B. Kahn (Germany); members: Y. Aizawa (Japan), T. Bountis (France), M. Karoubi (France), M. Kolster (Canada), (Greece), H. Hasegawa (Japan), I. Mozetic (Slovenia), J. 2-6: 5th Conference of the European Society of A.O. Kuku (Italy), M. Levine (USA), S. Lichtenbaum Pichard (France), T. Prosen (Slovenia), A. Ruffing Mathematics and Theoretical Biology on (USA), J.-L. Loday (France), W. Lueck (Germany), P. (Germany), A. Stefanovska (Slovenia) Mathematical Modelling and Computing in Biology May (USA), F. Morel (France), I. Panin (Russia), E. Sponsors: Ministry of Education, Science and Sport, and Medicine, Milano, Italy Pedersen (USA), C. Pedrini (Italy), U. Rehmann Nova Kreditna Banka Maribor, Telekom Slovenia Aim: to foster interdisciplinary collaboration between (Germany), J. Rosenberg (USA), S. Saito (Japan), V.P. Proceedings: accepted papers will be published, mathematicians and bioscientists and to act as the main Snaith (UK), C. Soulé (France), V. Voevodsky (USA), together with the lectures of invited speakers, as a forum for the exchange of recent research results and C. Weibel (USA) special volume of the Supplement of Progress in new research directions to the widest possible Programme: the first two weeks (8-19 July) will EMS March 2002 33 CONFERENCES comprise invited expository lectures on several aspects theory, finite model theory, formal aspects of program Weiermann (Münster) of the field; the last week (22-26 July) will be a analysis, formal methods, hybrid systems, lambda and Invited speakers: Toshiyasu Arai (Hiroshima), Joan Conference featuring mainly research lectures by invited combinatory calculi, linear logic, logical aspects of Bagaria (Barcelona), André Nies (Chicago), Martin Otto specialists, with possible contributions by some selected computational complexity, logics in artificial (Swansea), Charles Parsons (Cambridge, USA), Anand participants intelligence, logics of programs, logic programming, Pillay (Urbana-Champaign), Michael Rathjen (Leeds), Organising committee: M. Karoubi (France), A.O. modal and temporal logics, model checking, Johan van Benthem (Amsterdam- Stanford) Kuku (Italy), C. Pedrini (Italy) programming language semantics, reasoning about Sponsors: Deutsche Vereinigung für Mathematische Sponsor: Abdus Salam International Centre for security, rewriting, specifications, type systems and type Logik und für Grundlagen der Exakten Wissenschaften Theoretical Physics theory, and verification (DVMLG) Deutsche Forschungsgemeinschaft Proceedings: will be published Main speakers: Stephen Cook (University of Toronto), Information: web site: Location: Abdus Salam International Centre for Georg Gottlob (TU Wien), John Reynolds (Carnegie http://wwwmath.uni-muenster.de/LC2002/CL2002.html Theoretical Physics (Strada Costiera 11, Trieste) Mellon), Natarajan Shankar (SRI), Maurizio Lenzerini Grants: some financial grants are available for (Universita di Roma ‘La Sapienza’) 10-11: Colloquium Logicum 2002, Münster, applicants from, and working in, developing countries Programme committee: Franz Baader (Aachen), Germany only, to be selected by the organisers; there may also be Marco Cadoli (Rome), Vincent Danos (Paris), Anuj [satellite conference of Logic Colloquium 2002] other support for participants from European countries Dawar (Cambridge), Rocco De Nicola (Firenze), Harald Information: Deadline: already passed Ganzinger (Saarbrücken), Orna Grumberg (Haifa), web site: http://wwwmath.uni-muenster.de/LC2002/ Information: e-mail: [email protected] Robert Harper (Carnegie Mellon), Furio Honsell [For details, see EMS Newsletter 41] web site: http://www.ictp.trieste.it/www_users/math/ (Udine), Phokion Kolaitis (Santa Cruz), Johann maths2002.html Makowsky (Haifa), Oded Maler (Grenoble), Yoram 25-30: Wireless and Optical Communications Moses (Haifa), Robert Nieuwenhuis (Barcelona), Peter (WOC’02), Miedzyzdroje, Poland 10-13 VISIT-ME-2002 (Vienna International O’Hearn (London), Doron Peled (Austin), Benjamin Information: web site: Symposium on Integrating Technology into Pierce (Philadelphia), Andrew Pitts (Cambridge), http://www.worldses.org/wses/calendar.htm Mathematics Education), Vienna, Austria Gordon Plotkin (Chair, Edinburgh), Andreas Podelski Aim: to bring together experts and non-experts with an (Saarbrücken), Andre Scedrov (Philadelphia), Peter 25-30: Nanoelectronics, Nanotechnologies (NN’02), interest in this topic Thiemann (Freiburg), Andrei Voronkov (Manchester) Miedzyzdroje, Poland Topics: include CAS-based curricula and teaching Information: e-mail: [email protected] Information: web site: methods, dynamic geometry systems as teaching tools, web site: http://www.worldses.org/wses/calendar.htm assessing with technology, internet as a teaching aid, http://www.dcs.ed.ac.uk/home/grohe/lics/lics02/ dispensable and indispensable mathematical skills and 27-2 September: Third International School- abilities, CAS as pedagogical tools for visualisation, 22-26: Universal Algebra and Lattice Theory, symposium: Symmetry and Cosymmetry experimentation, concentration, new classroom Szeged, Hungary Applications in the Theory of Bifurcations and Phase examples using CAS, the next generation: PeCAS = [dedicated to the 70th birthday of B. Csakany] Transitions, Big Sochi, Russia Pedagogical CAS, applications in mathematics, the Main speakers: J. Berman (Chicago), P. Dehornoy Theme: mathematical physics natural sciences, research and development, economy, (Caen), M. Goldstern (Vienna), E.W. Kiss (Budapest), Topics: symmetry and cosymmetry, theory of social sciences, industry, interfaces to other M. Maroti (Nashville), P.P. Palfy (Budapest), I.G. bifurcations, phase transitions programs/tools, producing and using utility files, Rosenberg (Montreal) Programme: symmetry in classical mechanics, programming in Derive, TI-89/92, and other CAS, Call for papers: we are using the facilities of Atlas integrability of conservative systems, connection with problems and limitations, web resources going on-line, Mathematical Conference; if you wish to present a talk, symmetry and cosymmetry, conservative chaos, teaching and learning with Derive and other CAS, please submit your abstract at http://at.yorku.ca/cgi- convection of homogeneous and multicomponent fluids connecting computer algebra and computational logic bin/amca/submit/caiv-01 – phase transitions, bifurcation, asymptotic models, Main speakers: Bruno Buchberger (Austria), Miguel de Programme committee: J. Jezek (Prague), K. Kearnes influence of electromagnetic field, convection of fluid in Guzman (Spain), Albert Rich (USA), Hans-Georg (Boulder), R. Poeschel (Dresden), A. Romanowska a porous medium, chaotic motions, phase transitions in Weigand (Germany) (Warsaw), A. Szendrei (Szeged), R. Willard (Waterloo) ferro- and antiferro-magnets and in liquid crystals, Languages: English and German Organising committee: A. Szendrei (Szeged), L. Szabo symmetry and cosymmetry influence, symmetry and Programme committee: Josef Boehm (Austria), Vlasta (Szeged), M. Dorman (Szeged) cosymmetry in classical hydrodynamics, theory of Kokol-Voljc (Slovenia), Bernhard Kutzler (Austria), Grants: reduction of the registration fee or contribution stationary motions and their stability, applications to Carl Leinbach (USA), Brian Denton (UK), Wilfried to accommodation costs may be provided upon request hydrodynamics and others fields of mathematical Herget (Germany), Jean-Baptiste Lagrange (France), for some participants, especially for students and young physics, magnetodynamics problems Edith Schneider (Austria), James Schultz (USA), people who are not supported by their universities Sessions: Section 1: Phase transitions in continuous Marlene Torres-Skoumal (Austria), Bernard Deadlines: for registration, 15 April; for abstracts: 1 media and scenarios of chaos origin; Chairs Victor Winkelmann (Germany), Michel Beaudin (Canada), July Yudovich (Russia), George Zaslavsky (USA). Section Josef Lechner (Austria), Francisco Puerta (Spain), Information: e-mail: [email protected] 2: Phase transitions in solid states and fluids; Chairs Eugenio Roanes (Spain), Theresa Shelby (USA), David web site: Jakow Granovskii (Poland), Yurii Gufan (Russia) Sjoestrand (Sweden), Hubert Weller (Germany), Johann http://www.math.u-szeged.hu/confer/algebra/2002/ Programme committee and main speakers: V. Wiesenbauer (Austria) Yudovich (Russia), V. Pukhnachev (Russia), Yu. Gufan Organising committee: Josef Boehm (Austria), Helmut August 2002 (Russia), E. Vinberg (Russia), G. Zaslavsky (USA), G. Heugl (Austria), Bernhard Kutzler (Austria) Iooss (France), G-F. Sartory (Italy), J. Granovskii Sponsors: Austrian Ministry of Education, Soft (Poland), B. Karasözen (Turkey), Jai Sam Kim (South Warehouse Europe, Texas Instruments 3-9: Logic Colloquium 2002 (ASL European Korea), A. Sadkov (Russia) Proceedings: to be published with an ISBN on CD- Summer Meeting), Muenster, Germany Organising committee: V. Yudovich (Russia), Yu. ROM [change of date] Gufan (Russia), J. Erusalimsky (Russia), A. Sadkov Location: University of Vienna, Strudlhofgasse, Vienna, Sponsors: Association of Symbolic Logic, Westfälische (Russia) Austria Wilhelms-Universität Münster Rheinische Friedrich- Languages: English and Russian e-mail: [email protected] Wilhelms-Universität Bonn Deutsche Call for papers: 2-page extended abstracts must be web site: http://www.acdca.ac.at/visit-me-2002 Forschungsgemeinschaft submitted by e-mail to [email protected] or Deadlines: for travel grants, 1 April; for submission of [email protected] 15-18: Modular Curves and Abelian Varieties abstracts, 1 May Sponsors (provisional): RFBR and INTAS (EuroConference), Bellaterra, Barcelona, Spain Note: satellite meeting: Colloquium Logicum 2002 Proceedings: to be published Coordinator: J. Quer Information: web site: http://www.math.uni- Location: camping ‘Slava’ on the Big Sochi coast of the Information: web site: http://www.crm.es/mcav02 muenster.de/LC2002/ Black Sea [For details, see EMS Newsletter 41] Grants: we may be able partially to reimburse 16-22: 7th International Spring School: Nonlinear subsistence expenses for young scientists, students and Analysis, Function Spaces and Applications (NAFSA 5-9: International Conference on Ill-Posed and lecturers 7), Prague, Czech Republic Inverse Problems, Novosibirsk, Russia Deadlines: for registration, 1 June; for abstracts, 1 July Information: web site: http://www.math.cas.cz/~nafsa7 Information: web site: Information: e-mail: [email protected] or [For details, see EMS Newsletter 40] www.math.nsc.ru/conference/mml [email protected] [For details, see EMS Newsletter 42] web site: 22-25: IEEE Symposium on Logic in Computer http://www.math.rsu.ru/mexmat/kvm/school2002 Science (LICS’02), Copenhagen, Denmark 9-11: Colloquium Logicum 2002, 2nd Biannual [part of the 2002 Federated Logic Conferences – Meeting of the DVMLG, Münster, Germany FloC’02] [satellite meeting of Logic Colloquium 2002] September 2002 Topics: automata theory, automated deduction, Organising and scientific committee: Justus Diller categorical models and logics, concurrency and (Münster), Peter Koepke (Bonn), Benedikt Löwe 1-9: 8th AHA 2002, International Congress on distributed computation, constraint programming, (Bonn), Wolfram Pohlers (Münster, Chair), Christian Algebraic Hyperstructures and Applications, constructive mathematics, database theory, domain Thiel (Erlangen), Wolfgang Thomas (Aachen), Andreas Samothraki Island, Greece

34 EMS March 2002 CONFERENCES Topics: hypergroups, semi-hypergroups, notification of acceptance or rejection by 3 July, full fluid dynamics hypergroupoids, hyperrings, hyperfields, hypervectorial paper submission by 4 November Speakers: include D. Brydges (Canada), L. Chierchia spaces, Hv-structures (Hv-groups, semigroups, rings), Information: e-mail: {Franz.Winkler, (Italy), E.G.D. Cohen (USA), G. Dell’Antonio (Italy), S. non-associative and feebly associative hypergroupoids, Manasi.Athale}@risc.uni-linz.ac.at Doplicher (Italy), H. Epstein (France), J. Froelich join spaces, hyperstructures associated with geometric web site: (Swiss), L. Galgani (Italy), G. Gentile (Italy), S. Graffi spaces, ordered hyperstructures, fuzzy hyperstructures, http://www.risc.uni-linz.ac.at/conferences/adg2002 (Italy), F. Guerra (Italy), G. Jona Lasinio (Italy), J. hypergraphs, generalisations and applications Lebowitz (USA), E. Lieb (USA), C. Liverani (Italy), R. Main speakers: P. Corsini (Italy), Y. Sureau (France), I. 4-6: 3rd International Conference on Mathematical Livi (Italy), C. Marchioro (Italy), S. Miracle-Sole Rosenberg (Canada), S. Comer (USA), J. Jantosciak and Computational Applications, Konya, Turkey (France), E. Olivieri (Italy), V. Rivasseau (France), D. (USA), J. Mittas (Greece), R. Migliorato (Italy), V. Theme: engineering, natural sciences or social sciences Ruelle (France), Ya. Sinai (USA) Loereanu (Romania), M.M. Zahedi (Iran), M. where mathematical and/or computational techniques are Organising committee: G. Benettin (Italy), G. Benfatto Konstantinidou-Serafimidou (Greece) necessary for solving specific problems (Italy), F. Bonetto (USA), M. Cassandro (Italy), A. Call for papers: to present an oral communication, Aim: to provide a medium by which a wide range of Celletti (Italy), R. Esposito (Italy), C. Falcolini (Italy), submit an abstract (type and centre the title, in capitals, experiences can be exchanged among researchers from A. Giorgilli (Italy), V. Mastropietro (Italy) author’s name and affiliation in this order; restrict your diverse fields such as engineering (electrical, Location: Department of Physics, University of Roma text to 200 words) via [email protected] mechanical, civil, industrial, aeronautical, nuclear etc.), ‘La Sapienza’ Programme committee: P. Corsini (Italy), S. Comer natural sciences (physics, mathematics, chemistry, Notes: there is no registration fee: only invited (USA), J. Jantosciak (USA), M. Konstantinidou- biology etc.) or social sciences (administrative sciences, communications will be presented Serafimidou (Greece), R. Migliorato (Italy), I. economics, political sciences etc.) Deadline: for registration, 15 May Rosenberg (Canada), S. Spartalis (Greece), Y. Sureau Scope: papers may be theoretical where mathematics is Information: (France), T. Vougiouklis (Greece) used in a non-trivial way or computational, or a web site: http://www.mat.uniroma2.it/pmp2002 Organising committee: T. Vougiouklis (Greece), S. combination of both; papers containing only Spartalis (Greece), H. Sakonidis (Greece) experimental techniques and abstract mathematics 8-13: ALGORITMY 2002, Conference on Scientific Sponsors: Democritus University of Thrace, Hellenic without any sign of application are discouraged Computing, High Tatra Mountains, Podbanske, Ministry of Education Topics: papers will be submitted in two categories: (1) Slovakia Proceedings: to be published journal papers (only papers of the highest quality that Information: web site: http://www.math.sk/alg2002 Location: Hotel Aeolos, Samothraki Island, Greece contain original ideas and research will be published in [For details, see EMS Newsletter 42] Deadlines: for registration, 31 March; for abstracts, 30 the journal Mathematical and Computational April; for hotel deposit 30 June Applications); (2) conference papers 9-12 : Conference on Harmonic Analysis, Information: e-mail: [email protected], Call for papers: we are using the facilities of Internet Luxembourg-Metz (Luxembourg-France) [email protected], [email protected] and International Journal of Applied Mechanics and Topics: non-commutative harmonic analysis, Engineering (V. 6, No. 4, 2001) representation theory, real and complex analysis related 3-7: 8th International Conference on Stability, Programme committee: H. Adeli (USA), M. Akbaba to groups Control and Rigid Bodies Dynamics, Donetsk, (Bahrain), R. Aliev (Azerbaijan), N. Allahverdi Organisers: Bachir Bekka, Jean Ludwig, Carine Ukraine (Turkey), S. Ay (Turkey), O. Balci (USA), A. Molitor-Braun, Norbert Poncin; organised jointly by the Information: web site: Baykasoglu (Turkey), M. Bikdash (USA), N. Bildik Centre Universitaire of Luxembourg and the University http://www.iamm.ac.donetsk.ua/conf2002.html (Turkey), F. Botsali (Turkey), D. Bozkurt (Turkey), B. of Metz [For details, see EMS Newsletter 42] Can (Turkey), M. Can (Turkey), Z. Celep (Turkey), A. Location: Centre Universitaire of Luxembourg (9-10 Caliskan (Turkey), K. Carman (Turkey), T. Dereli September) and University of Metz (11-12 September) 4-6: Fourth International Workshop on Automated (Turkey), A.H. Elkholy (Kuwait), K. Erciyes (USA), A. Main speakers (preliminary list): C. Anantharaman- Deduction in Geometry, RISC-Linz, Erisen (Turkey), E. Murat Esin (Turkey), Z. Fazekas Delaroche, J.P. Anker, Y. Benoist, E. Damek, H. Hagenberg/Linz, Austria (UK), I. Guler (Turkey), K. Gulez (Japan), F. Gurgen Fujiwara, H. Oh, E. Kaniuth, A. Lubotzky, D. Müller, Theme: automated deduction in geometry (Turkey), E. Hasanov (Turkey), H. Huseynov (Turkey), K.H. Neeb, D. Poguntke, G. Robertson, W. Schmid, T. Topics: polynomial algebra, invariant and coordinate- C. Isci (Turkey), S. Kahramanli (Turkey), H. Kaplan Steger, A. Valette, A.M. Vershik free methods, probabilistic, synthetic, and logic (Turkey), H. Karagulle (Turkey), R. Karakuzu (Turkey), Programme: in addition to the regular conference approaches, techniques for automated geometric B. Karlik (Bahrain), M. Keskin (Turkey), S. Kocak programme, communication sessions for participants to reasoning from discrete mathematics, combinatorics, and (Turkey), A. Kuliev (Turkey), A. Kucukbursa (Turkey), present their research in a 20-minute talk are planned numerics, symbolic and numeric methods for geometric A.C.J. Luo (USA), F.M. Mahomed (South Africa), D.L. Proceedings: speakers may publish their contribution in computation, geometric constraint solving, automated Mitov (Bulgaria), P.M. Oliveira (Portugal), M. a special issue of the journal Travaux mathématiques, generation/reasoning and manipulation with diagrams, Pakdemirli (Turkey), J. Saleh (Jordan), E. Savas Publications du Centre Universitaire design and implementation of geometry software, (Turkey), O. Sayman (Turkey), S. Selvi (Turkey), Z. Sen Grants: a limited number of grants will be available for special-purpose tools, automated theorem provers, (Turkey), A. Sinan (Turkey), K. Soltanov (Azerbaijan), young researchers experimental studies, applications of ADG to mechanics, M. Tekelioglu (Turkey), O. Tokhi (UK), M. Turhan Sponsors: Fonds National de la Recherche geometric modelling, CAGD/CAD, computer vision, (Turkey), I. Uluer (Turkey), U. Uzman (Turkey), F. (Luxembourg), Centre Universitaire de Luxembourg, robotics and education Unsacar (Turkey), G. Unal (Turkey), V. Vagin (Russia), Université de Metz, Laboratoire de Mathématiques Main speakers: two invited talks: names of speakers to A. Vidybida (Ukraine), E. Walicki (Poland), A. Yavas (MMAS) de l’Université de Metz be announced shortly (USA), A.S. Yigit (Kuwait), Information: e-mail: [email protected] Call for papers: see the web site Organising committee: N. Allahverdi (Turkey), K. web site: http://www.cu.lu/harmonic_analysis Programme committee: Shang-Ching Chou (Wichita, Carman (Turkey), T. Sisman (Turkey), A. Gunes USA), Andreas Dress (Bielefeld, Germany), Desmond (Turkey), M.N. Ornek (Turkey), I. Saritas (Turkey), L. 10-20: Advanced Course on Geometric 3-Manifolds, Fearnley-Sander (Hobart, Australia), Xiao-Shan Gao Civcik (Turkey) Bellaterra, Barcelona, Spain (Beijing, China), Hoon Hong (Raleigh, USA), Deepak Location: Suleyman Demirel Culturel Centre, Campus, Coordinator: Joan Porti Kapur (Albuquerque, USA), Josef Schicho (Linz, Konya Information: web site: http://www.crm.es/geom-mani Austria), Bernd Sturmfels (Berkeley, USA), Gert Vegter Grants: probably support for participants from countries (Groningen, Netherlands), Dongming Wang (Paris, in a difficult economic situation and young 20-25: International Conference on Computational France), Volker Weispfenning (Passau, Germany), Neil mathematicians Methods in Science and Eng. (CMMSE-2002), White (Gainesville, USA), Franz Winkler (Linz, Organisers: Technical Education Faculty of Selcuk Alicante, Spain Austria), Chair Lu Yang (Chengdu, China) University, Association for Scientific Research Information: web site: www.ua.es/cmmse2002/ Organising committee: F. Winkler (Chair, Austria), M. Deadlines: for full papers, passed; for registration, 30 [For details, see EMS Newsletter 42] Athale (Austria) June Proceedings: authors of extended abstracts and full Information: e-mail: [email protected] 23-27: Ramification in Arithmetic and Geometry, papers accepted for presentation will be invited to web site: http://www.selcuk.edu.tr/icmca2002 Paris, France submit full and/or revised papers for publication in the Organisers: A. Abbes (Paris), B. Erez (Bordeaux), T. proceedings of ADG 2002 after the workshop; the 4-7: International Conference on Dynamical Methods Saito (Tokyo) submitted papers will be formally reviewed by PC for Differential Equations, Valladolid, Spain Location: Institut Galilee, Universite Paris 13 members and external referees. It is expected that the Information: web site: Information: accepted papers will be published as a volume in the http://wmatem.eis.uva.es/~dmde02/ http://www-math.math.univ-paris13.fr/~ramifica/ LNAI series by Springer-Verlag. (The proceedings of [For details, see EMS Newsletter 41] ADG ’96, ADG ’98 and ADG ’00 appeared as LNAI 25-28: 2nd WSEAS International Conferences on: 1360, LNAI 1669 and LNAI 2061) 4-7: Perspectives in Mathematical Physics, Rome, Simulation, Modelling and Optimization; Signal, Location: Schloss Hagenberg (15km north of Linz), the Italy Speech and Image Processing; Multimedia, Internet home of Johannes Kepler University’s Research Institute [in honour of the 60th birthday of Prof. Giovanni and Video; Robotics, Distance Learning and for Symbolic Computation (RISC-Linz): see the RISC Gallavotti] Intelligent Communication Systems, Skiathos, Greece homepage (http://www.risc.uni-linz.ac.at) for more Topics: mathematical physics, such as classical and Information: e-mail: [email protected] information quantum statistical mechanics, dynamical systems, web site: Deadlines: extended abstract submission by 3 June, hamiltonian perturbation theory, macroscopic limits, http://www.wseas.org/conferences/2002/skiathos/ EMS March 2002 35 RECENT BOOKS Yu.I. Manin, G. Margulis, D. McDuff, S. Mori, D. Mumford, R. Penrose, K.F. Roth, D. Ruelle, P. Sarnak, S. Smale, R.P. Stanley, C. Vafa, A. Wiles, E. Witten, S.-T. Yau, V.I. Arnold, P.D. Lax RecentRecent booksbooks and B. Mazur. This book should be in the library of every edited by Ivan Netuka and Vladimír Sou³ek working mathematician. (vs)

Books submitted for review should be sent to the fol- Stokes’ theorem. In view of their applications, A. V. Balakrishnan (ed.), Semigroups of lowing address: manifolds with a small singular part are allowed. Operators: Theory and Applications, Progress in Ivan Netuka, MÚUK, Sokolovská 83, 186 75 Praha The second part contains 100 problems for solu- Nonlinear Differential Equations and Their 8, Czech Republic. tion. Applications 142, Birkhäuser, Basel, 2000, 367 pp., The material included in this book exceeds DM 178, ISBN 3-7643-6310-X J. Adams and D. Vogan (eds.), Representation the volume usually covered in analysis courses, This volume is the proceedings of the confer- Theory of Lie Groups, IAS/Park City Mathematical and may be used for seminars or for supple- ence on C0-semigroups and their applications, Series 8, American Mathematical Society, Providence, mentary reading. The book is recommended to held at Newport Beach in December 1998. 2000, 340 pp., US$49, ISBN 0-8218-1941-0 students and to teachers of mathematical analy- These proceedings consist of 35 contributions. Each summer, there are a research programme sis. (in) Most of them are short (less than 10 pages), but and a graduate summer school organised by the a reader can nevertheless get a good insight into IAS/ParkCity Mathematics Institute. In 1998, Yu. Aminov, The Geometry of Vector Fields, the current research interests, both in theory the topic chosen was Representation theory of Gordon and Breach Publishers, Amsterdam, 2000, and applications. Most frequently, the attention reductive Lie groups. This book is a collection of 172 pp., £45, ISBN 90-5699-201-5 is paid to various aspects of stability and to ana- the written versions of lectures presented there. If we have a regular family of surfaces filling a lytic semigroups (including generation theo- The lectures concentrate on the problem of domain in 3-dimensional Euclidean space in a rems on Lie groups and fractional powers of understanding irreducible representations of nice way (without mutual intersections), we can generators). Several papers are devoted to the reductive Lie groups. The lecture series by A. introduce on this domain the field of unit nor- interaction between stochastic analysis and semi- Knapp (delivered by P. Trapa) describes the mals to the surfaces under consideration. A group theory (Feller semigroups). Applications Langlands parametrisation of irreducible great deal of geometry of a regular family of sur- are given to problems in physics (fluid dynam- (admissible) representations of such groups. faces can be described in terms of this normal ics, aero-elasticity, Dirac equation and flutter of The lectures by R. Zireau and L. Barchini field. Quite naturally, by the end of the nine- wings) and control theory (thermo-elastic describe cohomologically induced families of teenth century, the idea emerged of investigat- plates). (jmil) unitary representations, which appear in har- ing in a similar way a unit vector field that does monic analysis and the theory of authomorphic not arise from a family of surfaces. In such a sit- S. Batterson, Stephen Smale: The forms. The lectures by D. Vogan describe geo- uation one usually speaks about a non-holo- Mathematician Who Broke the Dimension metrical constructions of unitary representa- nomic vector field. Barrier, American Mathematical Society, tions, using ideas of Kirillov and Kostant (the This monograph can be considered as an Providence, 2000, 306 pp., US$35, ISBN 0-8218- method of coadjoint orbits). The lectures by introduction to the subject. We find here many 2045-1 K.Vilonen use geometrical tools (constructible classical results that are proved in a new and This is a biography of Stephen Smale, written by sheaves, semialgebraic sets and derived cate- modern way. It also contains plenty of recent a mathematician who declares himself as his aca- gories) to recover the global character of repre- results, and consequently represents an intro- demic grandson. To write this biography sentations constructed by infinitesimal methods. duction to contemporary research in the field. It involved tremendous work, but the result is bril- The last lecture in the book, by J.-S. Li, is divided into two chapters. The first chapter liant. It is designed to be accessible for non- describes restrictions of a certain class of mini- deals with domains in 3-dimensional Euclidean mathematicians. mal representations to the so-called reductive space and the vector fields on them, while the Smale is presented here first of all as a great dual pairs, introduced and studied by A. Weil second passes to domains in higher-dimension- mathematician, and together with his personali- and R. Howe. al Euclidean spaces, or even in Riemannian ty we gradually become familiar also with math- Altogether, the volume brings a coherent manifolds. The authors also present interesting ematical life in the United States. The author description of an important and beautiful part applications, mostly in the dynamics of mechan- does not avoid describing Smale’s mathematical of representation theory, which certainly will be ical systems with non-holonomic constraints, results, but having in mind the aim of the book, of substantial use for postgraduate students and and in the geometry of velocity fields of fluid he introduces them in a way that can be under- mathematicians interested in the area. (vs) flow. Quite recently, there have been applica- stood by most readers. For readers closer to tions in the description of liquid crystals and fer- mathematics, but still non-mathematicians, four H. Amann and J. Escher, Analysis III, romagnets. appendices are included, explaining his results Grundstudium Mathematik, Birkhäuser, Basel, The prerequisites required for reading are in more detail. On the other hand, the author’s 2001, 480 pp., ISBN 3-7643-6613-3 and 3-7643- modest. Basic courses of analysis and classical skilful presentation of Smale’s mathematical dis- 6614-1 differential geometry should suffice. (jiva) coveries will surely attract the interest of profes- This volume is devoted to integration and to sional mathematicians. Every mathematician global analysis. Integration theory is developed V. I. Arnold, M. F. Atiyah, P. Lax and B. Mazur knows Smale’s famous results (such as the high- along standard lines (measure spaces, measures, (eds.), Mathematics: Frontiers and Perspectives, er-dimensional Poincaré conjecture), but not outer measure, integrability, Lebesgue measure, International Mathematical Union, American many of them know that he is also a respected integrable functions, convergence theorem, Mathematical Union, Providence, 2000, 459 pp., mineral collector (and in this field he is as good Lebesgue spaces, Fubini’s theorem, change of US$49, ISBN 0-8218-2070-2 as in mathematics), and a prominent photogra- variables) with one notable exception: the inte- The change of a millennium was an occasion to pher. The author also describes Smale’s political gration of Banach space-valued functions (the reflect on the state of mathematics and to try to anti-war activities, and informs us also about his Bochner-Lebesgue integral) is introduced sys- see future perspectives. This book collects thirty adventurous trips, such as sailing to the tematically. Much space is devoted to less tradi- articles by leading mathematicians (half of them Marquesas. tional subjects: convolutions, the Fourier trans- recipients of the Fields Medal) on the occasion This is the first biography written by S. form on Schwartz spaces, distributions, linear of the World Mathematical Year 2000. Batterson, but in many respects it is a master- differential operators, weak derivatives, Sobolev Different articles are written with different piece. (jiva) spaces, the Heisenberg uncertainty relation. aims. Some of them bring a list of problems in a The part on integration covers a half of the text, chosen specific area, some are reviews of possi- M. B. Bekka and M. Mayer, Ergodic Theory approximately 250 pages, and is accompanied ble future developments, others bring more per- and Topological Dynamics of Group Actions by 194 problems associated with the individual sonal viewpoints. There are many articles show- on Homogeneous Spaces, London Mathematical sections. ing how important has been the recent interac- Society Lecture Note Series 269, Cambridge In the second part of the volume, about 160 tion between mathematics and theoretical University Press, Cambridge, 2000, 200 pp., pages are devoted to manifolds in Euclidean physics for future development in mathematics. £24.95, ISBN 0-521-66030-0 spaces, multi-linear algebra, the theory of differ- There are also articles on the connections The book is intended as an introduction to ential forms, vector fields, the Riemann metric between pure mathematics and certain areas of ergodic theory, with emphasis on two types of and vector analysis. The last part of the book applied mathematics. The authors are M.F. dynamical system. The geodesic flows on the deals with integration on manifolds: integration Atiyah (preface), A. Baker, G. Wustholz, J. unit tangent bundle of a locally symmetric space of differential forms and Stokes’ theorem, Bourgain, S.-S. Chern, A. Connes, S.K. and unipotent actions on homogeneous spaces. including such special cases as the Gauss-Green Donaldson, W.T. Gowers, V.F.R. Jones, D. The book is well organised and gradually theorem, Green’s formulae and the classical Kazhdan, F. Kirwain, P.-L. Lions, A.J. Majda, develops the theory in six chapters. In Chapter

36 EMS Maarch 2002 RECENT BOOKS I, we find an introduction and some classical ed non-complete metric space, it is possible to serves well as a first encounter with cryptogra- examples and results from ergodic theory, introduce on it a suitable quasi-hyperbolic dis- phy. (ad) including von Neumann’s ergodic theorem on tance. Roughly speaking, if we pass from the ini- strong mixing. Geodesic flows form the main tial metric to the quasi-hyperbolic distance, uni- E. Cohen, R. F. Riesenfeld and G. Elber, topic of Chapter II: the chapter begins with a form spaces become Gromov hyperbolic; con- Geometric Modeling with Splines. An short section on hyperbolic geometry and geo- versely, special conformal deformations of the Introduction, A. K. Peters, Natick, 2001, 616 pp., desic flows on Riemannian structures are then metric of a Gromov hyperbolic space leads to a US$59, ISBN 1-56881-137-3 studied. The vanishing theorem of Howe and uniform metric. If we compose these two modi- The authors present a broad base of fundamen- Moore is presented in Chapter III, together with fications, the initial and final spaces belong to tally important techniques for curve and surface Moore’s ergodicity theorem and mixing of all the same quasi-similarity class. Numerous fur- representations in computer-aided modelling, orders arising as a strengthening of strong mix- ther results on Gromov hyperbolic spaces are with a focus on their applications in design. ing. Horocycle flows in Chapter IV are studied established in the book. The Gehring-Hayman Balancing mathematical rigour and broad for finite-area surfaces covered by the hyperbol- theorem is generalised to this framework. applicability, the authors show how theoretical ic plane: Hedlund’s minimality theorem is a Loewner spaces are investigated, their definition properties can be used to derive practical algo- main result of this chapter. Chapter V intro- being based on the concept of the modulus of a rithms. The book offers a thorough study of duces Siegel sets and their applications to lat- family of curves. Planar Gromov hyperbolic applications of splines in general, and B-splines tices in n-dimensional Euclidean spaces. In the spaces are characterised, and a partial charac- in particular, to the domain of geometric mod- last chapter, treating Oppenheim’s conjecture, terisation is also given in higher dimensions. elling. there is an application to number theory. Quasi-conformal homeomorphisms of Gromov The first two chapters contain background This book can be used as a guide to modern hyperbolic spaces of bounded geometry are material. The next eleven chapters (conic sec- ergodic theory and dynamics. It can be used by studied. A description of the Martin boundary of tions, differential geometry for space curves, graduate students and by researchers in differ- a Gromov hyperbolic domain establishes a link Bézier curves and Bernstein approximation, B- ent areas, since the contents of the book range with potential theory. splines curves, spline spaces, differential geom- from elementary results to modern theories. This book is an original research work with etry for surfaces and surface representations) The background needed to understand the many deep and interesting results. It provides a could form the basis for a one-semester intro- book is a familiarity with elementary results well-written contribution to the geometric theo- ductory class. A two-semester class would from functional analysis, measure theory and ry of metric spaces. It is a favourite and topical include most of the remaining chapters of the Lie theory. (dh) theme to recognise which results can be gener- book (data fitting with B-splines, fitting surfaces, alised from Euclidean spaces to spaces with a modelling with B-spline surfaces, subdivision R. A. Bertlmann, Anomalies in Quantum Field more complicated geometry, and to find meth- and refinements for splines, modelling of other Theory, International Series of Monographs on ods that could be fruitful in this framework. This polynomial bases for interpolation, other Physics 91, Oxford University Press, Oxford, 2000, research has many applications to concrete derivations of B-splines, set operations to effect 566 pp., £29.95, ISBN 0-19-850762-3 problems on manifolds and more general modelling, model data structures, subdivision An ‘anomaly’ in field theory means a violation of spaces. (jama) surfaces and higher-dimension tensor products classical symmetry at the quantum level. of B-splines). The chapters conclude with exer- Anomalies play a key role in modern quantum J. A. Buchmann, Introduction to Cryptography, cises to be solved. field theory and they have been studied inten- Undergraduate Texts in Mathematics, Springer, New This is a nicely written book of great value for sively since the late-1960s. Although the litera- York, 2001, 281 pp., DM 69, ISBN 0-387-95034-6 stimulating active work by students. In particu- ture on this subject is enormous, a comprehen- This book describes many of the well-known lar, it can be strongly recommended as an sive monograph on anomalies has long been symmetric and public-key cryptosystems, undergraduate or graduate text, and as a com- missing – Bertlmann’s book thus represents a together with the necessary mathematics, in a prehensive source for a self-study. (knaj) highly desirable filling of the gap. way that is accessible to students with a limited The core of the monograph is a discussion of mathematical background. B. Conrad and K. Rubin (eds.), Arithmetic the deeper mathematical aspects of chiral and The first quarter of the book is devoted to Algebraic Geometry, IAS/Park City Mathematics gravitational anomalies that will appeal mostly definitions of basic mathematical structures that Series 9, American Mathematical Society, Providence, to the mathematically oriented theoretical are needed in modular arithmetics, the associat- 2001, 569 pp., US$75, ISBN 0-8218-2173-3 physicists specialising in quantum field theory ed basic algorithms (extended Euclidean algo- This book consists of lecture notes from the and elementary particle physics. It is shown, in rithm, fast exponentiation), and the analysis of 1999 Graduate Summer School (and from the particular, that the techniques of modern differ- these algorithms and of basic modular opera- corresponding Mentoring Program for Women ential geometry (which are necessary in this con- tions with respect to their computational cost. in Mathematics, MPWM) of the IAS/Park City text) are useful, not only as an elegant language Other mathematical concepts appear in the Mathematics Institute. The lecture courses were for the formulation of the theory but also as a book later, always in connection with a cryp- centred around topics related to A. Wiles’s work practical computational tool. In studying these tosystem. Block ciphers are associated with per- on modular elliptic curves – the arithmetic of advanced parts, the reader is greatly helped by mutations, affine ciphers with matrices and lin- elliptic curves, modular forms and Galois repre- the introductory chapters that include some ear maps, and the Vernam one-time pad with a sentations. basic material on differential geometry and discussion of probability notions, including The lectures by J.P. Buhler provide an intro- topology and make the book fairly self-con- Shannon’s theorem on perfect secrecy. The part duction to these topics, essentially without tained. The detailed discussion of the mathe- about symmetric cryptosystems concludes with a proofs. Those by A. Silverberg focus on open matical aspects tends to restrict the exposition of thorough exposition of the DES algorithm. questions in the arithmetic of elliptic curves and the physical applications of anomalies; on the The second half of the book is concerned abelian varieties (rational torsion points, ranks other hand, the whole subject is so vast that a with public key encryption, including the con- of groups of rational points, the conjecture of one-volume monograph can hardly be fully cepts of digital signature, cryptographic hash- Birch and Swinnerton-Dyer, the ABC-conjecture exhaustive. functions, identification, and certification and its variants). The lectures by K.A. Ribet Bertlmann’s book can be warmly recom- authorities. RSA cryptosystems, Rabin encryp- (written jointly with W.A. Stein) are devoted to mended to Ph.D. students, lecturers and tion, Diffie-Hellman key exchange and ElGamal Serre’s conjecture on the modularity of odd researchers working in the quantum field theory encryption are all described in detail, including Galois representations ρ: Gal (cl(Q) /Q) → GL2 and mathematical physics, since its contents are some discussion of the prime number genera- (cl(Fk)). The ‘weak’ Serre conjecture states that ρ unique within the existing literature and cover, tion (Carmichael numbers, Miller-Rabin test), comes from a modular form f; while the ‘strong’ in an essential way, the development of modern factoring (p–1 method, quadratic sieves) and the conjecture specifies the exact weight and level of methods in this area. (jho) discrete logarithm problem (the Shanks, Pollard f. The lectures sketch proofs of various results of and Pohlig-Hellman algorithm). the form ‘weak conjecture implies strong one’ – M. Bonk, J. Heinonen and P. Koskela, This book retains the form of a mathematical the weight optimisation (Edixhoven) and the Uniformizing Gromov Hyperbolic Spaces, text, with statements of theorems and proofs, level optimisation (Ribet et al.; this result pro- Astérisque 270, Société Mathématique de France, but its main purpose seems to be to give a gen- vides a link between modularity of elliptic curves Paris, 2001, 99 pp., FRF 150, ISBN 2-85629-098-1 eral and reasonably elaborated understanding and Fermat’s last theorem). The lectures of F.Q. The unit disc U in the complex plane can be of basic cryptographic notions. From this point, Gouvêa concentrate on deformation of Galois equipped with two natural geometries: the it makes sense that a several concepts are men- representations. The first six lectures – inspired Euclidean one, and hyperbolic geometry, which tioned without being really explained (such as by B. Mazur’s earlier accounts – develop the forms on U the structure of a complete pseudo-random numbers, class groups and general theory, while the remaining two lectures Riemannian manifold of constant negative cur- number field sieves). There is also no attempt to sketched the (still mainly conjectural) links to p- vature. This is a model case of a much more gen- formalise the concepts of algorithm complexity. adic families of modular forms. The lectures of eral situation that is studied here. However, in this and other cases, the reader is R. Greenberg treat Iwasawa theory of elliptic Given a locally compact, rectifiably connect- referred to appropriate sources. The book surves, with emphasis on its algebraic aspects:

EMS March 2002 37 RECENT BOOKS variations of Mordell-Weil groups and of analyt- Birkhäuser, Basel, 2001, 558 pp., DM 260, ISBN prerequisites from simplicial homotopy theory ic ranks in towers of number fields; Selmer 3-7643-6573-0 are needed. More precisely, this book should be groups, Λ-modules and Mazur’s Control A conference held at Groningen (Netherlands) accessible for a second-year graduate student. Theorem. Two lectures by J. Tate summarise in December 1998 was organised on the occa- After so many years of intensive develop- basic properties of Galois cohomology groups. sion of the 70th birthday of Israel Gochberg, ment, we cannot expect the monograph to cover Appendices by B. Conrad and K. Buzzard, and who is one of the initiators of the series of all subjects in the field. It is oriented mostly by M. Dickinson, T. Weston and M. Emerton, to International Workshops on Operator Theory towards algebraic topology, while other fields of the articles by Ribet and Stein, and Gouvêa, con- and its Applications (IWOTA), to which the con- applications, such as homological algebra, alge- tain several technical results alluded to in the ference belonged. This volume is a selection of braic geometry, number theory and algebraic K- main text. The articles by W.-C. W. Li and N. 35 papers in operator theory, related to lectures theory are not included. Nonetheless, another Yui are based on their lectures at MPWM. Li presented at the meeting. aim of the monograph is to provide specialists in states basic results on modular forms, while Yui Most of the papers contain rather long intro- other fields, intending to use simplicial homo- discusses the arithmetic of L-functions of Calabi- ductions that can be used by non-experts as a topy theory in their own fields, with a necessary Yau 3-folds. guide to a current state of research in the theo- working knowledge of the theory. Having this in The book is aimed at Ph.D. students in num- ry of linear operators in Hilbert spaces. The arti- mind, the authors have prepared the list of ref- ber theory. It begins at a fairly introductory cles deal with analytic operator functions, inter- erences in such a way that it gives a basic orien- level, but gives a good overview of the subject polation and extension problems, dilation and tation in the above-mentioned fields of applica- and proceeds naturally to more technical commutant lifting theorems, several problems tion. aspects of the theory. An attractive feature of the connected with control theory, Hilbert function But the main aim is to gather together old book is the presence of many exercises for stu- spaces and spaces with indefinite metrics. There and new results and serve specialists in the field dents. (jnek) are also applications to partial differential equa- of simplicial homotopy theory. It is nice that old tions (spectra of elliptic operators, scattering results are sometimes presented in a new form, J. F. Davis and P. Kirk, Lecture Notes in theory, multiplier theorems and R-bounded- with a deeper insight and surprising relations. Algebraic Topology, Graduate Studies in ness). The authors have decided not to include exer- Mathematics 35, American Mathematical Society, A short description of I. Gochberg’s mathe- cises or problems; instead, they saturate the text Providence, 2001, 367 pp., US$55, ISBN 0-8218- matical work (by M.A. Kaashoek) and a com- with many interesting and inspiring examples. 2160-1 plete list of his publications are added. (jmil) The whole monograph is carefully and nicely This book is based on a second-year course on written, and for experts it is quite indispensable. algebraic topology and the authors present H. M. Enzensberger, Drawbridge Up: For its quality and importance it should be material which, in their opinion, ‘every young Mathematics - A Cultural Anathema, A. K. Peters, included in every mathematical library. (jiva) topologist should know’. The second aim of the Natick, 1999, 47 pp., US$9.95, ISBN 1-56881- authors is to provide enough information from 156-X H. Grassmann, Extension Theory, History of algebraic topology for people interested in geo- This book contains the bilingual version Mathematics 19, American Mathematical Society, metric topology. (German and English) of an address given by London Mathematical Society, Providence, 2000, In order to make the book self-contained, the author at the 1998 International Congress of 411 pp., US$75, ISBN 0-8218-2031-1 the authors present three chapters on basic facts Mathematicians in Berlin. The first edition was This book is an English translation of from homological algebra. The first chapter in paperback form in 1999: a review of it can be Grassmann’s Ausdehnungslehre, which was pub- consists of a brief introduction to chain com- found in this Newsletter, No. 34, Dec 1999, p.37. lished in Berlin in 1862. The translation by plexes, homology and cohomology, with appli- (vs) Lloyd C. Kannenberg (who has also translated cations to CW-complexes, simplicial and singu- Peano’s Calcolo geometrico secondo lar theory. The second chapter gives an T. Friedrich, Dirac Operators in Riemannian l’Ausdehnungslehre di H. Grassmann, preceduto delle overview of homological algebra, including uni- Geometry, Graduate Studies in Mathematics 25, operazioni della logica deduttiva, Birkhäuser, versal coefficient theorems. Chapter 3 is devot- American Mathematical Society, Providence, 2000, Boston, 2000) is based on Hermann ed to products in the homology and cohomolo- 195 pp., US$34, ISBN 0-8218-2055-9 Grassmann’s Gesammelte mathematische und gy, including the Künneth formulas and the This book is a nice introduction to the theory of physikalische Werke (Teubner, Stuttgart, Leipzig, Poincaré duality theorem. spinors and Dirac operators on Riemannian 1896). The theory of fibre bundles is explained in manifolds. It consists of an algebraic part, intro- The German mathematician Hermann the fourth chapter, which is also the starting ducing Clifford algebras, spin groups and spin- Günter Grassmann (1809-77) developed a circle point of an advanced course. Both principal and ors, a topological part, discussing existence and of ideas relating multi-dimensional geometry, associated bundles are introduced here, and the a classification of spin structures on compact linear algebra and vector analysis. The first edi- Èech cohomology is mentioned as well. The Riemannian manifolds, and an analytical part, tion of his Extension Theory appeared in Leipzig homology and cohomology of spaces with local where the Dirac and the twistor operators and in 1844 under the name Die lineale coefficients are presented in Chapter 5. their properties are studied in detail. Special Ausdehnungslehre, ein neuer Zweig der Mathematik. Fibrations, cofibrations and homotopy groups attention is paid to eigenvalue estimates and to In 1861, the book was essentially rewritten and are studied in the sixth chapter: this chapter solution spaces of special spinorial field equa- extended, and the author skipped unnecessary also presents a brief introduction into homotopy tions, such as Killing spinors and twistor spinors. philosophical parts. The second edition was theory, ending with the Hurewicz and The main text is completed by two appendices printed under the name Die Ausdehnungslehre. Whitehead theorems. that are also of special interest and contain New material not included in the first edition In the next part of the book, obstruction the- material that is needed earlier in the book. covers, for example, a development of the inner ory and Eilenberg-MacLane spaces, bordism, Appendix A contains a nicely written description product, the concept of angle, Grassmann’s the- spectra and generalised homology are dis- of the Seiberg-Witten theory of invariants for 4- ory of functions and Grassmann’s contributions cussed. At the end of the book, spectral dimensional manifolds, one of the main topics to the Pfaff problem. sequences are defined and explained, and their in 4-dimensional manifold theory in recent This book contains Grassmann’s Extension applications to several problems in algebra and years. Appendix B is devoted to the theory of theory (325 pp.), the Editorial Notes (59 pp. from algebraic topology are presented; for example, principal bundles and connections, their reduc- Grassmann’s Gesammelte Werke, 1896), there are applications to computations of homo- tions and holonomy theory. Supplementary Notes (8 pp.) and Subject Index topy groups of spheres, cohomology operations This book can be strongly recommended to (13 pp.). Grassmann’s classical work can be and construction of bordism invariants. The anybody interested in the theory of Dirac and warmly recommended to mathematicians and to final chapter is devoted to a study of simple- related operators. (jbu) historians of mathematics as a source of homotopy theory and torsions, such as the Grassmann’s mathematical ideas. (jbe) Whitehead and the Reidemeister torsion and P. G. Goerss and J. F. Jardine, Simplicial their applications. There are many exercises Homotopy Theory, Progress in Mathematics 174, J. E. Graver, Counting on Frameworks. and comments in the book, which complement Birkhäuser, Basel, 1999, 510 pp., DM 118, ISBN Mathematics to Aid the Design of Rigid the material, as well as suggestions for further 3-7643-6064-X Structures, Dolciani Mathematical Expositions 25, study, presented in the form of projects. Since the last monograph on simplicial homo- Mathematical Association of America, Washington, The book is a nice advanced textbook on topy theory appeared more than twenty-five 2001, 180 pp., £23.95, ISBN 0-88385-331-0 algebraic topology and can be recommended to years ago, one of the aims of this monograph is This is a nice little introduction to combinatori- anybody interested in modern and advanced to fill this gap, at least partially. Quillen’s work al rigidity theory by an experienced author. A algebraic topology. (jbu) on closed model structures, which now belongs very careful and accessible exposition (some- to the foundations of simplicial homotopy theo- times even a little slow for someone used to A. Dijksma, M. A. Kaashoek and A. C. M. Ran ry, is one of the main subjects of this mono- reading mathematics) starts from simple exam- (eds.), Recent Advances in Operator Theory, graph. However, the monograph starts from the ples and ideas and proceeds to a theory of the Operator Theory Advance and Applications 124, very beginning, from the simplicial sets, and no rigidity of frameworks made of rods in dimen-

38 EMS Maarch 2002 RECENT BOOKS sions 1, 2, and 3. Several advanced theorems book will be useful for graduate and postgradu- metric and binomial series (Amou, Katsurada and their proofs are presented, or at least ate students of theoretical physics. (vs) and Väänänen, Matala), higher power residue sketched, and further reading is suggested for symbols (Helou), representation of primes by the more advanced topics. The main theme is G. W. Johnson and M. L. Lapidus, The special quadratic forms (Jackson), binary addi- complemented by sections concerning history, Feynman Integral and Feynman’s Operational tive divisor problem (Meurman). The volume is geodesic domes, linkages and tensegrity frame- Calculus, Oxford Mathematical Monographs, carefully prepared. (šp) works (made of rods and cables). Clarendon Press, Oxford, 2000, 771 pp., £90, ISBN While some calculus and linear algebra are 0-19-853574-0 W. J. Kaczor and M. T. Nowak, Problems in assumed, the basic notions and results of graph This is a representative monograph (770 pages) Mathematical Analysis, II. Continuity and theory are carefully explained. (jmat) on all aspects of the mathematical theory of the Differentiation, Student Mathematical Library 12, Feynman integral. This ‘elusive and formidable’ American Mathematical Society, Providence, 2001, H. Hauser, J. Lipman, F. Oort and A. Quirós subject has attracted mathematicians from its 398 pp., USD$49, ISBN 0-8218-2050-8 (eds.), Resolution of Singularities, A Research very beginning, and several different approach- This book is the second volume of a series of Textbook in Tribute to Oskar Zariski, Progress in es to the ‘rigorous mathematical theory of the problem books in mathematical analysis: the Mathematics 181, Birkhäuser, Basel, 2000, 598 pp., Feynman integral’ have appeared in the course first appeared a year ago and others will follow. DM 168, ISBN 3-7643-6178-6 of the last half-century, after the heuristic con- It contains three chapters and covers subjects The basic question treated in the book is: given cept of ‘summation over all paths’ was formulat- like limits, continuity, differentiation, and limits a variety X, determine a subvariety Z of X such ed by R. Feynman in 1949. This book sum- and series of functions. Numerous problems are that blowing up X in Z resolves the singularity of marises all existing approaches and explains well chosen and solutions of all of them are pro- X. The book is a report on recent results and their mutual relations (and, often, their equiva- vided. The first chapter contains 212 problems, problems concerning this problem. It is dedicat- lence). Much of the original work on the subject including some on functional equations (con- ed to the memory of the well-known algebraic is due to the authors of the book. nected mostly with ‘elementary functions’) and geometer Oskar Zariski, who created fundamen- The book starts with an extensive and thor- continuity on metric spaces, while the second tal parts of the theory. ough introduction, as for the more specialised and third chapters contain 238 and 130 prob- The book divides into two parts. Part I con- themes in the subsequent chapters. This makes lems, respectively. sists of extended manuscripts of lectures given the book accessible, even for beginners. In addi- As with the first volume, the book is of great at a Working Week on Resolutions of tion, many quotations of sayings by famous per- help for problem seminars and also for self- Singularities, at Obergurgl in Tirol, Austria, in sonalities (related to the subjects treated in the study. Some problems are not new and the September 1997. It contains contributions by D. book) provide amusement for the reader. authors mention some sources in the preface. Abramovich and F. Oort (Alternations and reso- (However, some readers could find it unusual Almost two-thirds of the volume are devoted to lution of singularities), J. M. Aroca (Reduction that the same script is used in the book for both the presentation of solutions, usually in a rela- of singularities for differential equations, and the theorems and the remarks.) tively detailed manner; those who know the first Puiseux solutions of singular differential equa- The first part of the book (Chapters 1-13) volume will probably appreciate this continua- tions) and S. Encinas and O. Villamayor (A contains, among other things, a complete treat- tion. course on constructive desingularisation and ment of existing approaches to the concept of This book can be recommended for libraries equivariance). the Feynman path integral – namely, the and for students. (jive) Part II contains articles written especially for method of analytical continuation (in time or this volume: there are fifteen contributions alto- mass) converting the problem of Feynman inte- W. M. Kantor and A. Seress (eds.), Groups and gether. We mention just a few, by G. Bodnar and gral to the well-established theories of Wiener Computation III, Ohio State Univ. Mathematical J. Schicho (A computer program for the resolu- integrals and Brownian motion, the method of Research Institute Publications 8, Walter de Gruyter, tion of singularities), B. van Geemen and F. Trotter formulas employing many deep results Berlin, 2001, 368 pp., DM 248, ISBN 3-11- Oort (A compactification of fine moduli space of from the theory of operator semigroups, and 016721-2 Curves), G. Muller (Resolution of weighted the modified method, due to the authors of the This collection of 23 papers presents a fairly homogeneous surface singularities) and M. book, that replaces the exponentials in the accurate picture of the current trends and likely Vaquie (Valuations); in these articles, special Trotter formulas by suitable resolvent operators. future developments in computational group related questions are discussed. There are also (The concept of a ‘Fresnel integral’ is also dis- theory. While permutation groups and matrix short communications describing the life and cussed, but is postponed to the last chapter of groups remain in the focus of the researchers, work of O. Zariski by J. Lipman, and an inter- the book.) It is shown that all these approaches the emphasis shifts discernibly towards the more esting historical account by H. Hauser on the (if applicable) coincide under reasonably gener- general model of a black box group, introduced resolution of singularities, in the period 1860- al conditions. The second part of the book in 1984. The nature of this model calls for prob- 1999. (jbu) (Chapters 14-19) is devoted to a related subject: abilistic algorithms (Monte Carlo, Las Vegas) Feynman’s operational calculus for non-com- that consequently appear throughout the vol- D. J. Hurley, and M. A. Vandyck, Geometry, muting variables; again, this subject is explained ume. Spinors and Applications, Springer and Praxis thoroughly from the very beginning. The papers can be somewhat artificially Publishing, London, 2000, 369 pp., DM 179, ISBN To summarise, this book should serve as a divided into five categories (in order of frequen- 1-85233-223-9 standard reference for anybody interested in the cy): group recognition, computational solutions The main topics in this book are covariant deriv- mathematical theory of Feynman path integrals to classical group-theoretical problems, brief atives of spinor fields and their use in theoreti- and the related operational calculus. (mzahr) surveys of computational group theory, theoret- cal physics (Newtonian mechanics, electromag- ical results concerning groups and algorithms, netism, gravitation). The first two parts of the M. Jutila and T. Metsänkylä (eds.), Number and software documentation. The concrete top- book present the necessary prerequisites. Theory, Proceedings of the Turku Symposium on ics range from the recognition of finite special In the first part, standard linear algebra tools Number Theory in Memory of Kustaa Inkeri, 1999, linear groups and experimentation with coset (vector spaces and their duals, tensors, exterior Walter de Gruyter, Berlin, 2001, 328 pp., DM 268, enumeration to a solution of the Andrews-Curtis algebra, Clifford algebras) are developed in ISBN 3-11-016481-7 conjecture and a classification of unisingular detail. In the second part, basic notions of This volume contains selected contributions by groups. Many results are based on Aschbacher’s smooth manifolds, tangent spaces, vector fields, 71 participants at a conference organised by the classification of maximal subgroups of classical Lie derivatives, connections and covariant deriv- Rolf Nevalinna Institute in honour of the groups. References to machine computation atives are explained, with special parts devoted founder of the Finnish number theory tradition, (implemented in GAP, MAGMA, MEATAXE) to the Riemannian case, Lie groups and the cor- Kustaa Inkeri (1908-97). The papers cover a are omnipresent and form a vital part of many responding Lie algebras. These notions are used broad spectrum of elementary, analytic and arguments. Although the tools for parallel com- for a description of fibre bundles and vector algebraic number theory. puting have now been included in algebraic bundles, and connections and covariant deriva- The reader will find many interesting contri- packages (such as ParGAP), most of the algo- tives on them. The main part of the book is butions: the life and work of Inkeri (Metsänkylä rithms remain non-parallel – a certain target for devoted to a description of spinor fields on and van der Poorten), Diophantine problems the future. (pseudo)-Riemannian manifolds and covariant (Bugeaud and Frey, Mignotte), sieve methods Computational group theory evolves dramat- derivatives acting on them (not necessarily com- (Greaves and Huxley), arithmetic functions ically, as is eloquently documented by the patible with the metric structure). Special atten- (Haukkanen), Lucas and Pell numbers unusually high amount of cross-referencing tion is paid to the Minkowski case. (Ribenboim and McDaniel, Strazdins), among the contributions to this volume. The book is clearly written for theoretical Riemann, Dirichlet, Hecke and L-series (Iviæ, Naturally, this phenomenon is a consequence of physicists, but uses a lot of standard coordinate- Jutila, Matsumoto, Laurin, Sands), exponential the close interaction of the authors with the edi- free mathematical tools. The notation employed sums (Huxley and Kolesnik), summation of mul- tors, whose careful and precise work have made is a mixture of those used in mathematics and in tiple series (Dilcher, Haller), arithmetic aspects the papers look almost as chapters in a book physics, but should be understandable. The of functional equations (Bundschuh), hypergeo- written by one author. Their effort will be great-

EMS March 2002 39 RECENT BOOKS ly appreciated by experts and readers with some Reed-Muller codes, the Bruck-Ryser-Chowla C. J. Mozzochi, The Fermat Diary, American knowledge of the area. Beginners, however, theorem, Baranyai’s theorem). Mathematical Society, Providence, 2000, 196 pp., must look for the preliminaries elsewhere. (ad) This well written textbook can be highly US$29, ISBN 0-8218-2670-0 recommended to any student of combinatorics As the title indicates, this book is an eye-witness J. Kigami, Analysis on Fractals, Cambridge and, because of its breadth, has many new account of the events leading to the final solu- Tracts in Mathematics 143, Cambridge University things to tell researchers in the field also. (mk) tion of Fermat’s Last Theorem. The author Press, Cambridge, 2001, 226 pp., £35, ISBN 0- attended each of the lectures that are now 521-79321-1 A. Mehlmann, The Game’s Afoot! Game Theory labelled as milestones on the way leading to the This book contains some very important tools in Myth and Paradox, Student Mathematical correct solution of this problem, which became for studying the dynamical aspects of objects Library 5, American Mathematical Society, one of the most famous ones in mathematics. He modelled by fractals, and builds the theory of Providence, 2000, 159 pp., US$26, ISBN 0-8218- took notes during the lectures, read and sum- ‘analysis on fractals’. This is a developing area 2121-0 marised the reports in the newspapers and jour- of mathematics that focuses on the dynamical Looking at the title and the format of this book, nal, and took more than thousand photographs aspects of fractals, such as heat diffusion on one is inevitably reminded of the well-known during and after the lectures and the connected fractals and the vibration of a material with The Compleat Strategyst by J. Williams (Dover social events. fractal structure. Publications, N.Y., 1986). However, this first This material forms the backbone of the The book provides a self-contained intro- impression quickly disappears after the reading report contained in the book. It is written in a duction to the subject, starting from the basic of the first few pages. Mehlmann’s book is no lively style and is easy to read and as such, it can geometry of self-similar sets and going on to ‘primer in the theory of games’, but a rather be recommended to those of us who were not recent results, including the properties of advanced treatment of different aspects of the lucky enough to have an opportunity to follow eigenvalues and eigenfunctions of the theory of games and its applications. Various these events personally. With its many interest- Laplacians, and the asymptotic behaviour of concepts and problems are discussed from dif- ing facts, often unattainable to those not direct- heat kernels on self-similar sets. ferent points of view and illustrated by means of ly engaged in the story, its many personal quo- Requiring only a basic knowledge of parables from history, mythology and literature tations, and pictures of personalities involved, advanced analysis, general topology and mea- of fiction. These features make the book a fasci- the book will certainly be an important source sure theory, this book will be of value to grad- nating, entertaining and enlightening reading. for historical details surrounding the proof for uate students and researchers in analysis and In the author’s words, the book is intended contemporaries and those born later. (šp) probability theory. It will also be useful as a as ‘a light-hearted excursion into the world of supplementary text for graduate courses cov- strategic calculation’. However, to enjoy this H. Niederreiter and C. Xing, Rational Points ering fractals. Individual chapters contain excursion fully, the reader should depart on it on Curves over Finite Fields. Theory and such topics as the geometry of self-similar sets, equipped with some basic knowledge of the fun- Applications, London Mathematical Society Lecture analysis on limits of networks, the construction damentals of game theory and a fairly broad Note Series 285, Cambridge University Press, of Laplacians on P.C.F. self-similar structures, general cultural background. (jmach) Cambridge, 2001, 245 pp., £27.95, ISBN 0-521- eigenvalues and eigenfunctions of Laplacians 66543-4 and heat kernels. Some mathematical back- R. A. Minlos, Introduction to Mathematical Many important results from number theory ground (self-adjoint operators, quadratic Statistical Physics, University Lecture Series 19, and geometry have their roots in the properties forms, semigroups, Dirichlet forms, Nash American Mathematical Society, Providence, 2000, of algebraic curves. This book focuses on alge- inequality and the renewal theorem) is 103 pp., US$24, ISBN 0-8218-1337-4 braic curves over finite fields and their function described in the Appendix. (pp) This is a book on rigorous statistical physics. fields, with a special emphasis on applications. The author is one of the co-founders and lead- The first three chapters cover the necessary S. Levy (ed.), The Eightfold Way. The Beauty of ing figures of this important, and (after 40 years background on algebraic number fields, class Klein’s Quartic Curve, Cambridge University of development) still flourishing field of field theory and global function fields for the Press, Cambridge, 2001, 331 pp., £19.95, ISBN research. The subject of the book – the ‘theory following core chapters. In the first two chapters 0-521-00419-5 of interacting multicomponent systems’ lies on the reader finds how to construct global function The first edition of this book appeared in the border between mathematics and other sci- fields with many rational places, and meets 1999, and a review can be found in this ences. The greatest impact came from physics, results about the asymptotic behaviour of the Newsletter, No. 39, March 2001, p.32. This is not only through phenomena like phase transi- number of rational places of global function the second unchanged paperback edition of tions but also some important methods devel- fields. the book. (vs) oped originally by theoretical physicists. These The book mostly reflects recent results, and methods, like the method of expansions, were so the application chapters discuss methods of J. H. van Lint and R. M. Wilson, A Course in later converted (notably also by the author of algebraic geometry in coding theory (Goppa, Combinatorics, second edition, Cambridge this book) into important technical tools of pure NXl and XNL codes), applications to cryptogra- University Press, Cambridge, 2001, 602 pp., mathematics. On the other hand, another phy (almost perfect sequences, perfect hash £24.95, ISBN 0-521-00601-5 important and traditional tool of mathematical functions and low-discrepancy sequences). In this second edition, some material has been statistical mechanics is probability theory. Because of the carefully selected contents and added (list-colorings of graphs, the Lovász In the 103 pages of this book, the author lucid style, the book can be warmly recommend- sieve, associative block designs) and there are presents a concise introduction to the subject. ed to mathematicians interested in the above- many new exercises. The book is unique in the In Part I he discusses basic concepts (phase mentioned topics or in algebraic curves over variety of topics treated, in 38 chapters on space, dynamics, statistical ensembles) and finite fields with many rational points. (šp) more than 550 pages and in the large space basic examples (ideal gas, lattice gas) of the the- devoted to non-graph-theory combinatorics. ory. He then gives a concise explanation of W. F. Pfeffer, Derivation and Integration, The following list provides a brief overview, important statistical ensembles (micro-canoni- Cambridge Tracts in Mathematics 140, Cambridge by no means exhaustive, of the areas covered: cal, canonical, grand-canonical) and of their University Press, Cambridge, 2001, 266 pp., £45, graph theory (Eulerian and Hamiltonian cir- mutual relations. He then explains, in Part II, ISBN 0-521-79268-1 cuits, spanning trees, Turán’s theorem, Hall’s the method of correlation functions (expan- This book is devoted to the theory of non- theorem, Ramsey’s theorem, connectivity, pla- sions) based on the use of Kirkwood-Salsburg absolutely convergent integrals in Euclidean narity, squared squares, graphs on surfaces), equations. Finally, he discusses various thermo- spaces, and was written by one of the leading posets (Dilworth’s theorem, Sperner’s theo- dynamical potentials – entropy, pressure, free specialists in this field. It is natural to ask rem), permanents (the Minc and van der energy, etc. Part III deals with phase transi- whether there exists a generalisation of the Waerden conjectures), Latin squares (count- tions. The author explains the famous Peierls Lebesgue integral such that the Gauss-Green ing, the Evans conjecture, the Dinitz conjec- method of contours, not only for the simplest theorem in Rn holds for each differentiable vec- ture, orthogonal Latin squares), enumeration case of the Ising model, but also in detail for its tor field v and suitable sets A, if the integral over (de Bruijn sequences, the Möbius function, more sophisticated form, the Pirogov-Sinai the- A of div v is taken in the sense of this generalised generating functions, Bell and Stirling num- ory. Finally, in an epilogue, he adds a short dis- integral. If we also need ‘good properties’ of the bers, Lagrange inversion, partitions, the cussion of Wulff droplets and the roughening generalised integral (in particular, its rotation Jacobi triple product identity, Young tableaux, transition. invariance), the problem cannot be solved by a 0-1 matrices, Pólya theory), algebraic combi- There is a vast journal literature on the sub- direct generalisation of the Denjoy-Perron inte- natorics (projective and combinatorial geome- ject of this book, but relatively few standard ref- gral. However, in the last twenty years, several tries, Gaussian numbers, q-analogues, strongly erence texts. This new textbook will surely find solutions have been found; they use the idea of regular graphs, difference sets, Singer’s theo- its place among existing monographs (Ruelle, the Kurzweil-Henstock (‘Riemann type’) defini- rem, Shannon capacity, association schemes), Sinai, Georgii, Simon, etc.) that do not usually tion of the Denjoy-Perron integral. and designs and codes (Hadamard matrices, cover every important topic or are directed The solution presented in this book is based Paley matrices, Steiner systems, Golay codes, towards a more specialised reader. (mzahr) on the theory of (finitely) additive set functions,

40 EMS March 2001 RECENT BOOKS defined on the family of all bounded BV sets in book are self-contained and each special topic complex calculations with polynomials, but may Rn; such set functions, which are continuous with can be studied independently. have nearly no experience with abstract struc- respect to a suitable topology, are called The book consists of five chapters on limit tural mathematics. This can be observed in the charges. In the book, a deep theory of deriva- theorems in probability theory, written by lead- care with which the author explains notions tives and variations of charges is presented. ing researchers in the area. The classical part of related to factorisation, both in the context of Using a type of variation, the important class of limit theorems is presented by V. V. Petrov in ring ideals and submodules. AC* charges is defined. The basic definition of Chapter I. Central limit theorems, laws of large In addition to the basic material, the first the R-integral is a descriptive one, and is based numbers, the Berry-Esséen inequality, and the half of the book is concentrated around the pri- on the notion of the indefinite R-integral. law of the iterated logarithm are covered in this mary decomposition of ideals, the structure of Roughly speaking, the indefinite R-integral of f chapter. V. Bentkus et al. wrote Chapter II, con- commutative Noetherian rings and the struc- is an AC* charge for which DF(x)=f(x) for taining the problem of accuracy of Gaussian ture of modules over principal ideal domains. almost all x, where DF(x) is a suitable type of approximation for distribution on infinite- As an application, the author derives the canon- derivative. An equivalent ‘Riemann-type’ defini- dimensional Banach spaces. Chapter III, written ical forms of square matrices, and presents tion of the R-integral is also given (hence the let- by J. Sundoklas, treats the asymptotic behaviour some applications to field theory, up to tran- ter R). Using the R-integral, a very general of sums of weakly dependent random variables scendental extensions. The closing chapters Gauss-Green theorem can be proved, and the and its approximation by the normal distribu- (about 100 pages) deal with integral depen- author explains how it can be extended to the tion. In Chapter IV, homogeneous Markov dence, affine algebras over fields, dimension Stokes theorem on Lipschitz manifolds. In the chains and their central limit theorem is stud- theory, regular sequences (and grade) and final chapter, the R-integral is extended to the ied; this chapter is written by P. Gudynas. The Cohen-Macaulay rings. The latter two chapters GR-integral, which has even better properties final chapter, by L. Saulis and V. Statulevièius, is did not appear in the first edition, and consti- than the R-integral. devoted to limit theorems on large deviation. tute the main difference between the two edi- The book is well organised and is written in This book should be at hand for any special- tions (beyond the corrections of misprints, a precise and lucid style. It can be recommend- ist on asymptotic methods in probability and sta- which are now very few). The author has suc- ed to anybody interested in the theory of non- tistics, and can also serve as a basic reference for ceeded in keeping the context within the self- absolutely convergent integrals, and has a solid graduate and Ph.D. students of stochastics. (dh) imposed limits – there is no reference to the background in graduate level analysis. (lz) tensor product, categories are touched on only L. Schwartz, A Mathematician Grappling with marginally, and the exposition is careful and J.-P. Pier, Mathematical Analysis During the His Century, Birkhäuser, Basel, 2001, 490 pp., clear. A patient reader can learn a lot, without 20th Century, Oxford Univesity Press, Oxford, DM 68, ISBN 3-7643-6052-6 having to leave the firm ground of set structures 2001, 428 pp., £59.50, ISBN 0-19-850394-6 Laurent Schwartz is one of the most distin- that are manipulated only in a way that makes This book is devoted to the history of some parts guished mathematicians of the 20th century. His it easy to keep in mind the role of individual of mathematical analysis, including probability autobiography can be considered, apart from elements. (ad) and algebraic geometry in the 20th century. other things, as a history of mathematics from While the period 1900-50 is treated in certain the 20th century, and partly also of the centuries P. N. de Souza and J.-N. Silva, Berkeley depth, the evolution from 1950 to 2000 is char- before. He describes the development of mathe- Problems in Mathematics, second edition, Problem acterised by representative achievements. The matical thinking towards its current level of Books in Mathematics, Springer, New York, 2001, book contains many original quotations (with exactness. He was for a certain time a member 535 pp., DM 73,83, ISBN 0-387-95207-1 English translations) and brief expositions of of the Bourbaki group, which contributed sub- This is the second and enlarged edition of a results chosen to illustrate the main ideas and stantially to this development. Thanks to his problem book for first-year Ph.D. students in trends. cooperation with many mathematicians all over mathematics. A review of the first edition can be The chapters contain texts on general, alge- the world, he has been able to give interesting found in this Newsletter, No. 30, Dec 1998, p.41. braic and differential topology, integration and comments on circumstances connected with sub- The new edition contains about 150 additional measure, functional and harmonic analysis, Lie stantial mathematical discoveries. In particular, problems and 250 new solutions. (vs) groups, the theory of functions and ODEs and he speaks about his most important discovery, PDEs. The text occupies approximately 350 distribution theory, which has many applica- G. Tenenbaum and M. M. France, The Prime pages, numerous references take another 60 tions in both pure and applied mathematics. Numbers and their Distribution, Student pages, and two Indexes and a List of Symbols Schwartz has been, however, not only a math- Mathematical Library 6, American Mathematical take about 20 pages. It will be a valuable source ematician. Besides his scientific work and apart Society, Providence, 2000, 115 pp., US$17, ISBN book for analysts interested in the history of the from his teaching activities, he was also very 0-8218-1647-0 main ideas of analysis, as well as for others want- active in the social and political arena. He was a This is an English translation of the French edi- ing to know about developments in other fields. convinced Trotskyist. Thus, the reader will find tion, first published in 1997 as a volume in a A certain familiarity with the material included comments on significant events of the 20th cen- paperback encyclopaedia containing about will be of great help. The book can be recom- tury, mainly on both the world wars, on political 3500 titles, each of them limited to 128 pages; mended to mathematical libraries, researchers development in the USSR, and so forth. this limitation immediately implies bounds for and students. (jive) Everything is based, if not on his personal mem- such an extensive field as the theory of prime ories, on direct evidence from his numerous numbers. Nevertheless, the authors have suc- V. P. Pikulin and S. I. Pohozaev, Equations in friends from all over the world. He has always ceeded in writing an interesting volume that Mathematical Physics. A Practical Course, fought for peace and has opposed localised can be recommended to students. The reader Birkhäuser, Basel, 2001, 206 pp., DM 196, ISBN wars, especially in Algeria and Vietnam, where will find basic introductory elementary results 3-7643-6501-3 he also lived for some time. Writing a book such as the Chebyshev or Mertens theorem and This book demonstrates the basic methods for describing so many particular events precisely is Brun’s sieve applied to the twin prime conjec- solving classical linear problems in the mathe- witness to the author’s prodigious memory. He ture. The book also contains a complete and matical physics of elliptic, parabolic and hyper- remarks that he made notes to refresh his mem- self-contained elementary proof of the prime bolic types. In particular, methods of conformal ory only in his advanced age. The book is attrac- number theorem in Daboussi’s version of 1984. mappings, Fourier analysis and Green’s func- tive and can be highly recommended to any The middle chapter, on the stochastic distribu- tions are considered, as well as the perturbation reader intersted in the subject. (jjel) tion of prime numbers reflects the authors’ and integral transformation methods, among decision to describe various aspects of prime others. Each chapter contains concrete exam- R. Y. Sharp, Steps in Commutative Algebra, sec- number theory from the point of view of ran- ples with a detailed analysis of their solution, ond edition, London Mathematical Society Student domness, giving to the book a specific charm. It and ends with problems for independent study Texts 51, Cambridge University Press, Cambridge, also contains an introduction to Dirichlet and and answers to them. This handbook is 2000, 355 pp., £17.95, ISBN 0-521-64623-5 Siegel-Walfish theorems on primes in arith- addressed to students of technology institutes This book is meant as a tool for an undergrad- metical progressions, Siegel zeros and a discus- where a course on mathematical physics of rela- uate student with some knowledge of polynomi- sion of consequences of Cramer’s probabilistic tively reduced volume is offered, as well as to als and linear algebra to grasp the basic notions model of the distribution of primes generated engineers and scientists. (kn) of structural commutative algebra. The self- by the measure induced by the reciprocal of the professed goal of the book (see the preface to logarithmic function. Finally the reader can Yu. V. Prokhorov and V. Statulevièius (eds.), the first edition) is to close the gap between find the basics of uniform distribution. Limit Theorems of Probability Theory, Springer, books on basic algebra (which include topics This book can be read by anyone with a min- Berlin, 2000, 273 pp., DM 169, ISBN 3-540- like unique factorisation in Euclidean domains) imal knowledge of number theory and some 57045-4 and existing books on commutative algebra that calculus skills. (šp) This reference book is a collection of research- require much deeper experience and sophisti- level surveys covering different results on cer- cation. This book seems to assume that the G. Tian, Canonical Metrics in Kähler Geometry, tain topics of probability theory. All parts of the reader has no problems in doing even quite Lectures in Mathematics ETH Zürich, Birkhäuser,

EMS December 2001 41 RECENT BOOKS Basel, 2000, 1000 pp., DM 38, ISBN 3-7643- folds. The book explains what algebraic topolo- cussed here, both classical and modern. The 6194-8 gy is, without assuming a deep knowledge of probabilistic parts contain, for example, the laws In recent years, uniformisation theory of canon- general topology. Because of this, many proofs of large numbers, central limit theorems, the ical Kähler metrics in higher dimensions has are omitted or sketched. This is also due to a strong Markov principle, generating functions, been developed in complex differential geome- wish to include a lot of material in 140 small martingales, etc. Among the statistical topics we try. One of its applications is the use of Calabi- pages. Thus, the book will be very convenient find confidence intervals, Bayesian statistics, lin- Yau spaces in superstring theory. The presented for those who want to be acquainted with the ear models and ANOVA. The author charac- monograph is a systematic and self-contained topic in a short time, without going into many terises statistics as follows (see p. 381): ‘I do apol- introduction into the theory of canonical Kähler details (it works even better, if the book is com- ogize that I often tell you that something is a good idea metrics on complex manifolds. plementary to lectures, as it was with the only to have to say later that it does not work in many The following topics are described in the first author’s lectures). Included in the text are a suf- important cases. That is the way that Statistics is: full part of the book: Kähler metrics and their cur- ficient number of results, exercises and prob- of surprises and never dull …’. The last chapter is vature tensor, the space of Kähler metrics on a lems. (mih) devoted to quantum probability theory and given manifold, the Calabi functional, and quantum computing, which will probably be new extremal metrics and uniformisation of Kähler- D. Williams, Weighing the Odds. A Course in to most readers. Einstein manifolds. In the second part a holo- Probability and Statistics, Cambridge University The book is a rich and enjoyable source of morphic invariant for Kähler manifolds (called Press, Cambridge, 2001, 547 pp., £24.95, ISBN 0- ideas, motivations and examples, which can be the Calabi-Futaki invariant) is introduced and 521-00618-X, ISBN 0-521-80356-X used by teachers of probability and statistics. (ja) its properties are described. Special attention is In the Preface the author warns that the book paid to the scalar curvature of Kähler metrics in has many unusual features: this is why the book R. J. Wilson, Stamping Through Mathematics, the corresponding symplectic geometry, and the is so interesting. In the parts devoted to proba- Springer, 2001, 126 pp., £17.00,11, ISBN 0-387- Calabi-Yau theorem on the existence of the met- bility theory the results are precisely stated, but 98949-8 ric with given Ricci form is proved. Kähler- most of the proofs are omitted. The sections on This book is really exceptional: there are only a Einstein metrics with positive scalar curvature statistics are nearly free from statements of tech- few books of this sort. Despite the fact that it on a compact manifold with positive first Chern nical conditions under which the theorems hold. contains a minimum of mathematics, it will be class are also discussed, and necessary and suffi- The book describes mainly the motivation of appreciated by many mathematicians, in partic- cient conditions for the existence of such a met- probabilistic and statistical thinking. One of the ular by those interested in stamp collecting. The ric are presented. Examples of Kähler-Einstein sections is called ‘Sharpening our intuition’: it book shows nice pictures of 400 stamps without metrics, especially on Fermat hypersurfaces are seems that this would be a better candidate for descriptions which are appreciated only by real given, and there is an example of a manifold the title of the whole book. The author‘s views collectors. The book contains chapters of vari- without Kähler-Einstein metric. The mono- are declared very sharply and very clearly and, ous kind. Here are some examples: the Middle graph is well written and can be recommended maybe, some readers will not agree with them Ages (Pope Sylvester II, Albertus Magnus and to anybody interested in the topic. (jbu) completely; for example, the sentence on p. 223 Nicolas of Cusa), Globes, Nicolaus Copernicus ‘A celebrated result, the Neyman-Pearson lemma (not (stamps of Poland, GDR and Venezuela), Isaac V. A. Vassiliev, Introduction to Topology, discussed in this book), does prove that the LR Test is Newton (stamps of GB, North Korea, Monaco Student Mathematical Library 14, American unquestionally best (‘most powerful’) in a certain sim- and Nicaragua), France and the Enlightment Mathematical Society, Providence, 2001, 149 pp., ple situation of little practical importance’ will be (d’Alembert, Condorcet, Lagrange and US$25, ISBN 0-8218-2162-8 considered by many teachers as heretical – but Laplace), Russia (Kovalevskaya, Lyapunov, The word ‘Topology’ in the title of this book practical statisticians may hold the same opinion Ostrogradsky and Tchebychev), and much else means, roughly speaking, ‘Algebraic Topology’: as the author. besides. The book would be a nice present for homotopy, homology, cohomology, Morse theo- Although the author asserts that the book anybody with interests in mathematics and ry, Poincaré duality, degree of maps, and mani- covers a very limited area, many topics are dis- stamp collecting as well. (jive)

Max-Planck-Institut für Mathematik in den Naturwissenschaften Max Planck Institute for Mathematics in the Sciences

At the Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany), we have an open position for a postdoc in the field of

Mathematical Modelling of Cognitive Systems.

Applicants should be able to build upon a solid education in mathe- matics or physics in order to develop and analyze formal models, for example neural networks, that lead to new insights about information processing and cognitive structures. The work will take place in an open interdisciplinary group at a research institute with a strong back- ground in mathematics and with many and diverse international con- tacts. Collaborations with researchers at the University of Leipzig or other institutions are possible.

The position is offered for two years, with the possibility of an exten- sion in case of mutual interest. The beginning date is flexible.

Handicapped applicants will be given preference in case of equal qual- ification. The Max Planck Society as the employer aims at increasing the number of female scientists in fields where underrepresented. Therefore, women are particularly encouraged to apply.

Please send your application to

Jürgen Jost Max-Planck-Institut für Mathematik in den Naturwissenschaften Inselstrasse 22, D-04103 Leipzig [email protected]

42 EMS December 2001