The Impact on Mathematics of Political Changes in Eastern Europe

Home , Future of mathematics, Klaus Roth, Oleg Viro, Vladimir Arnold

CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY

EDITOR-IN-CHIEF ROBIN J 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 Building 303 NEWSLETTER No. 31 DK2800 Lyngby, Denmark e-mail: [email protected] March 1999 KRZYSZTOF CIESIELSKI Mathematics Institute Jagiellonian University Reymonta 4 30-059 Krakow, Poland e-mail: [email protected] A message from the new Editor-in-Chief ...... 2 KATHLEEN QUINN Open University [address as above] Editorial by the new EMS President, Rolf Jeltsch ...... 3 e-mail: [email protected] EMS News ...... 4 SPECIALIST EDITORS INTERVIEWS 3rd European Congress of Mathematics: first announcement ...... 7 Steen Markvorsen [address as above] SOCIETIES Caring for the mathematical past: a recent British experience ...... 10 Krzysztof Ciesielski [address as above] Interview with Robert M. Mattheij, President of ECMI ...... 13 EDUCATION Vinicio Villani World Mathematical Year 2000: Poster Competition ...... 15 Dipartimento di Matematica The impact on mathematics of political changes in Eastern Europe ...... 16 Via Bounarotti, 2 56127 Pisa, Italy 1999 anniversaries: Maria Agnesi and Hilbert’s ‘Geometrie’ ...... 18 e-mail: [email protected] MATHEMATICAL PROBLEMS Societies: The Union of Bulgarian Mathematicians ...... 20 Paul Jainta London Mathematical Society: De Morgan House ...... 21 Werkvolkstr. 10 D-91126 Schwabach, Germany Obituary of André Weil: Beyond the frontier of numbers ...... 22 e-mail: [email protected] Oberwolfach Programme 2000 ...... 23 ANNIVERSARIES June Barrow-Green and Jeremy Gray Call for proposals for the Banach Center, Warsaw ...... 24 Open University [address as above] e-mail: [email protected] Forthcoming conferences ...... 25 and [email protected] Recent books ...... 31 CONFERENCES Kathleen Quinn [address as above] RECENT BOOKS Ivan Netuka and Vladimir Soucek Mathematical Institute Charles University Sokolovská 83 Designed and printed by Armstrong Press Limited 18600 Prague, Czech Republic Unit 3 Crosshouse Road, Southampton SO14 5GZ, UK e-mail: [email protected] phone: (+44)-1703-333132; fax: (+44)-1703-333134 and [email protected] Published by European Mathematical Society ADVERTISING OFFICER ISSN 1027 - 488X Martin Speller Department of Mathematics Glasgow Caledonian University Glasgow G4 0BA, Scotland NOTICE FOR MATHEMATICAL SOCIETIES e-mail: [email protected] OPEN UNIVERSITY PRODUCTION Labels for the next issue will be prepared during the second half of May. TEAM Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Daniel Dubin, Kathleen Quinn, Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; Liz Scarna e-mail: [email protected]

EMS March 1999 1 EDITORIAL

A message from the new Editor-in-Chief

As the new Editor-in-Chief of the EMS Newsletter, it is my first pleasant duty to express my thanks to my predecessors at Glasgow Caledonian University—Roy Bradley, Iain Clark, Jagan Gomatam, Vikram Jha, Gerry Kennedy, Martin Speller and Julie Wilson. During their two-and- a-half years at the helm, the format and contents of the Newsletter has developed considerably, with a new attractive style of cover and many interesting articles. I am very grateful to them for the help that they have given me during the recent handover period. At the end of December 1998 several members of the Executive Committee reached the end of their terms of office, and their contributions to the Society will be sorely missed—in particular, Jean-Pierre Bourguignon (President), David Wallace (Vice-President), Peter Michor (Secretary), Aatos Lahtinen (Treasurer), and ordinary member Alberto Conte; we also lose our publicity officer, Mireille Chaleyat-Maurel. The recent committee meeting in Denmark included members of both the old and new committees, and I should like to thank them all for their encouragement and help as we discussed ways of making the Newsletter even more attractive and interesting in the future. You will meet several members of the new committee on page 5. The basic structure of the Newsletter will remain much as before, with many features unchanged—in particular, you will continue to see regular updates of EMS news, interviews, information about conferences, the problems corner and book reviews. However, there are a number of changes on which I would welcome your views: • I have tried to make the layout more attractive—in this context I should like to thank Armstrong Press of Southampton for their help with the design • I hope to make the tone of the Newsletter a little more informal with the introduction, from the next issue onwards, of a ‘Letters page’; I am keen that you as readers will come to regard the Newsletter as ‘yours’, that you will contribute short articles or other items for inclusion, and that you will send me your suggestions as to what you would like to see in future issues • I also hope to make the Newsletter a little less ‘cosy’ by including some items of a controver- sial nature, such as the articles on the sale of the Turner collection and the impact on mathematics of political changes in Eastern Europe; please send in your views on such articles, and make suggestions for other ones • EMS news has been collected together into a special section near the beginning of each issue • I have introduced a new ‘Anniversaries’ section, compiled by June Barrow-Green and Jeremy Gray; this issue contains anniversaries related to Agnesi and Hilbert, and the June issue will commemorate Klein, Lie and Krull; please contact June or Jeremy if you would like to contribute to this section • in the past the ‘Euronews’ section has consisted mainly of announcements of future conferences; these have now been collected into an expanded ‘Forthcoming conferences’ section in which some attempt has been made to standardize the style of the contributions. I hope to reintroduce the Euronews section and include more items of a personal nature (prizes, pro- motions, brief obituaries, etc.); for this purpose it would be most helpful to have a representative in each country who would send me news on a regular basis—if you would like to play this role, please contact your national mathematical society and let me know In this issue, in order to get the show on the road, I have commissioned several articles from British colleagues and friends. I hope that the content of future issues will be more international, and I rely on you to send me appropriate material for inclusion.

Robin J Wilson [e-mail: [email protected]]

2 EMS March 1999 EDITORIAL Editorial by the new EMS President Rolf Jeltsch When you pick up this issue, two Reference levels in mathematical and I urge you, if you have not already things will immediately catch your eye: education This project has been set up done so, to join EMS and to encourage the EMS has a new president for the at the request of the European your colleagues to do the same. The next four years, and this issue is the Commissioner for Science and aims at joining-up procedure is described on first one produced by our new Editor- establishing ‘Reference levels for the EMIS, and for some reviewers of in-chief, Robin Wilson. I am sure that teaching of mathematics’ for 16-year- Zentralblatt, especially those from east- you will not only notice but appreciate old students. In later phases, similar ern Europe, membership fees can be his style. studies will be carried out for 18-year- paid from their reviewers’ accounts at Let me briefly share my thoughts old students and for students after two Zentralblatt. with you on the European years of university education. Obviously, the EMS also organises Mathematical Society. First of all—and World Mathematical Year 2000 In scientific activities of its own: the most importantly—the main objectives 1992 the International Mathematical Diderot Mathematical Forums, the of the EMS remain unchanged: Union declared the year 2000 as EMS summer schools, the EMS lec- • strengthening the feeling of a World Mathematical Year. The EMS tures and the European Mathematical European identity among mathe- will naturally play an active part in the Congress. They are all set up to pro- maticians planning of this event. One project is mote the European dimension of our • functioning as the European partner to create a series of posters about society. You will find all the dates of in mathematics for the European mathematics that will be displayed in future events in the Agenda on page 4. Union and for outside Europe public transport systems in major The first issue of our newly-founded • nurturing relations between the cities to increase the public’s aware- Journal of the European Mathematical mathematical community and soci- ness of mathematics. The EMS is run- Society, JEMS, appeared a few weeks ety as a whole. ning a competition for the creation of ago and aims to become a leading Clearly, we don’t want to reproduce on these posters (details below). journal covering all of mathematics. As a European level what our corporate No fewer than three of the above a member of the EMS, you are entitled member societies already do excellent- projects are concerned with making to a reduced subscription price. To ly. However, certain tasks lie ahead mathematical data electronically avail- help the mathematical community in which can only be dealt with on a able to researchers; indeed, the EMS central and Eastern Europe, special European level. Let me give you some recognised the necessity for this a long reduced rates are available for these examples of on-going projects: time ago and has duly created the regions. For more information, see the MPRESS preprints index This pro- European Mathematical Information advertisement at the beginning of this ject was launched to create a harvest- System, EMIS, at http://www.emis.de/, issue. ing system to collect comprehensive which is freely available. It already At the turn of the year, several information on preprints and to pro- contains an extensive electronic members of our various committees vide easy facilities to search preprints library and we are working hard to finished their terms in office. I would on the Web. It will give access to pub- include even more publications. You like to thank them for all they have lications in their earliest available can also find more information on the done for the EMS and the mathemati- form. If you want to participate in the above projects at this website, as well cal community. Without their willing- system, visit MPRESS on our website. as our Conference Calendar. Since ness to put in extra hours after their EULER This project was started last events can be ordered according to regular work, the EMS could not func- year with the goal of producing strict- subject, you will not be overwhelmed tion. It goes without saying that we are ly user-oriented, integrated network- by an avalanche of information that in need of more colleagues who are based access to mathematical publica- you don’t need. It is easy to submit prepared to devote some of their time tions. The EULER service intends to your own conference information to our common cause. offer a ‘one-stop shopping site’ for directly on to the Web, too. The more Let me end on a somewhat philo- users interested in mathematics. It is a organisers enter their events, the more sophical note: I think the multicultur- truly European venture, since univer- powerful this tool will be. The same al society we have in Europe provides sities, libraries and documentation applies to the Euro-Math-Job link on a great opportunity to create new ideas institutions from five European coun- EMIS which leads to open positions through interaction. Despite this, we tries are involved in its development. for mathematicians. are sometimes forced to acknowledge Zentralblatt MATH The EMS wants to With 52 member societies, the EMS that communication is not always easy. get this major bibliographical database represents practically the entire As mathematicians we all have the recognised as a ‘large infrastructure’ European mathematical community. same objective, which surely makes it within the 5th framework program of However, as an applied mathemati- easier for us to overcome cultural, lin- the EU, which started this year. If cur- cian, I hope to increase the represen- gual, financial and political barriers. I rent plans are realised, institutions in tation of societies where applied math- am convinced that we can set a fine at least four European countries will ematics plays an important role. I example of prejudice-free co-opera- work together to make Zentralblatt would also like to see an increase in tion. And now—enjoy this issue of the MATH even more attractive. the number of individual members Newsletter!

EMS March 1999 3 EMS NEWS EMS News: Committee and Agenda EMS COMMITTEE EMS Agenda PRESIDENT (1999-2002) Prof. ROLF JELTSCH Seminar for Applied Mathematics 1999 ETH 17 – 18 April CH-8092 Zürich, Switzerland Executive Committee Meeting, hosted by the Institut d’Estudis Catalans, e-mail: [email protected] Barcelona VICE-PRESIDENT (1999–2002) 1 May Prof. LUC LEMAIRE Deadline for submission of proposals for the WMY 2000 Mathematical posters Department of Mathematics Université Libre de Bruxelles competition (see page 5) C.P. 218 - Campus Plaine contact: Vagn Lundsgaard Hansen, e-mail: [email protected] Bld du Triomphe 15 May B-1050 Bruxelles, Belgium 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 31 May Department of Pure Mathematics Deadline for submission of proposals for the 2000 EMS Summer schools The Open University contact: Rolf Jeltsch, e-mail: [email protected] Milton Keynes MK7 6AA, UK e-mail: [email protected] May - June TREASURER (1999–2002) Third EMS lectures: Real and complex dynamics by Prof. M. Lyubich (SUNY Prof. OLLI MARTIO Stony Brook, USA) Department of Mathematics contact: e-mail: EMS Secretariat, [email protected] P.O. Box 4 17 - 22 May: Russian Academy of Sciences, St Petersburg (Russia) FIN-00014 University of Helsinki contact: Anatoly Vershik, e-mail: [email protected] Finland 31 May - 4 June: Universitat de Barcelona, Barcelona (Spain) e-mail: [email protected] ORDINARY MEMBERS contact: Nuria Fagella, e-mail: [email protected] Prof. BODIL BRANNER (1997–2000) 14 - 18 June: Technical University of Denmark, Lyngby (Denmark) Mathematical Institute contact: Bodil Branner, e-mail: [email protected] Technical University of Denmark 28 June – 6 July Building 303 CIME-EMS Summer School at Martina Franca (Italy) in Pure Mathematics: DK-2800 Lyngby, Denmark e-mail: [email protected] Iwahori-Hecke algebras and representation theory Prof. DOINA CIORANESCU (1999-2002) contact: V. Baldoni (Rome), e-mail: [email protected] Labo. d’Anal. Numer. 15 August Univ. Pierre et Marie Curie Deadline for submission of material for the September issue of the EMS 4 Place Jussieu Newsletter F-75252 Paris Cedex 05, France e-mail: [email protected] contact: Robin Wilson, e-mail: [email protected] Prof. ANDRZEJ PELZCAR (1997–2000) 6 – 21 September Institute of Mathematics EMS Summer School at Heidelberg, Freiburg, Karlsruhe, Stuttgart, Tübingen Jagellonian University (Germany) and Zürich (Switzerland) in Applied Mathematics: Raymonta 4 Numerical simulation of flows PL-30-059 Krakow, Poland e-mail: [email protected] organizer: University of Heidelberg Prof. RENZO PICCININI (1999–2002) contact: Gabriel Wittum, e-mail: [email protected] Dipto di Matem. F. Enriques 9 – 10 October Universit di Milano Executive Committee Meeting hosted by the ETH, Zürich Via C. Saldini 50 I-20133 Milano, Italy 15 November e-mail: [email protected] Deadline for submission of material for the December issue of the EMS Prof. MARTA SANZ-SOLE (1997–2000) Newsletter Facultat de Matematiques contact: Robin Wilson, e-mail: [email protected] Universitat de Barcelona Gran Via 585 3 – 4 December E-08007 Barcelona, Spain Diderot Mathematical Forum Mathematics and music, in Lisbon (Portugal), Paris e-mail: [email protected] (France) and Vienna (Austria) Prof. ANATOLY VERSHIK (1997–2000) contact: Mireille Chaleyat-Maurel, e-mail: [email protected] P.O.M.I. Fontanka 27 191011 St Petersburg, Russia e-mail: [email protected] 2000 3 – 7 July EMS SECRETARIAT ALHAMBRA 2000: a joint mathematical European-Arabic conference in Ms. T. Mäkeläinen Granada (Spain), promoted by the European Mathematical Society and the Department of Mathematics Spanish Royal Mathematical Society P.O. Box 4 contact: Ceferino Ruiz, e-mail: [email protected] FIN-00014 University of Helsinki website: www.ugr.es/~ruiz/ Finland tel: (+358)-9-1912-2883 10 – 14 July fax: (+358)-9-1912-3213 Third European Congress of Mathematics (3ECM)} in Barcelona (Spain) telex: 124690 contact: S. Xambo-Descamps, e-mail: [email protected] e-mail: [email protected] website: www.iec.es/3ecm/ website: http://www.emis.de 4 EMS March 1999 EMS NEWS Introducing the Committee : part 1

Rolf Jeltsch (President) is Professor at the Eidgenössische Technische Hochschule (ETH) in Zürich. He received his doctorate there in 1972 and subsequently held visiting appointments in Halifax (Nova Scotia), Los Angeles, Stanford, Kentucky, Bochum and Helsinki. In 1979 he became Professor in Mathematics and Director of the Institute for Geometry and Practical Mathematics of the University of Technology RWTH Aachen, before returning to ETH as Professor in 1989. His research interests include numerical analysis (from theoretical investigations to engineering applications), parallel computing and computational sciences. At ETH he has introduced a new curriculum on Computational Sciences and Engineering. He was elected an EMS Council Member in 1994 and has been a member of the electronic publishing committee. He became a member of the Executive Committee in 1997, and President in January 1999.

Luc Lemaire (Vice-President) received a Doctorat from the Université Libre de Bruxelles in 1975 and a Ph.D. from the University of Warwick in 1977. From 1971 to 1982 he held a research position at the Belgian F.N.R.S., and has been a professor at the Université Libre de Bruxelles since then. His research interests lie in differential geometry and the calculus of variations, with a particular interest in the theory of harmonic maps. A former chairman of the Belgian Mathematical Society, he has been associated with the European Mathematical Society since its creation in 1990, being a member of the Council from 1990 to 1997, a member of the group on relations with European Institutions since 1990, and Liaison Officer with the European Union since 1993.

David Brannan (Secretary) has been a professor of mathematics at the Open University, UK, since 1979, and is currently Dean and Director of Studies in the Mathematics and Computing Faculty. He has worked for many years in aspects of geometric function theory, and has an abiding interest in functions of bounded boundary rotation. He has also worked in potential theory in the plane, looking at asymptotic paths and growth problems. For three years he was joint organiser of major complex analysis research meetings in Durham. From 1971 to 1981 he was Council and General Secretary of the London Mathematical Society, and has held other LMS posts, including Publications Secretary from 1986 to 1996. He helped to found the journal Nonlinearity, and to develop the overall publishing programme of the LMS. He has also served on the council of the Association of Learned and Professional Society Publishers and on the management committee of the Isaac Newton Research Institute in Cambridge.

Bodil Branner is an associate professor at the Technical University of Denmark, Lyngby (Copenhagen). She graduated from the University of Aarhus in 1967 in algebraic topology, but for the last 20 years has concentrated on problems within dynamical systems, in particular in holomorphic dynamics. She has been a visiting professor at Cornell University and the Université de Paris-Sud, and a visitor at the Max-Planck- Institut für Mathematik in Bonn and the Mathematical Sciences Research Institute (MSRI) in Berkeley. She has also been involved in establishing the network of European Women in Mathematics from its beginning in 1986. Since 1992 she has been a delegate of the Council of EMS, representing individual members, and has been a member of the Executive Committee since 1997. She is currently the President of the Danish Mathematical Society and a member of the Danish Natural Science Research Council.

Marta Sanz-Solé studied at the University of Barcelona, receiving her Ph.D. in 1978. After working at the Universitat Politèchnica de Catalunya, she became associate professor at the Universitat Autònoma de Barcelona, later becoming professor at the Universitat de Barcelona in 1986 and Dean of the Faculty of Mathematics from 1993 to 1996. Her research interests include stochastic differential equations, stochastic partial differential equations, analysis on the Wiener space and Malliavin calculus. She has been active in the creation of a research group in stochastic analysis in Barcelona. She was elected to the EMS Executive Committee in 1996.

EMS March 1999 5 EMS NEWS infrastructure. The President also remarked that it would be important to EMS Executive Committee Meeting have good representation of mathematics in Lyngby, Copenhagen, 28 – 29 November 1998 in the Commission’s INTAS programme. — The President met the new Secretary A weekend meeting was held at the General of the ESF. Under discussion had Technical University of Denmark, been the possible support of the ESF to the Lyngby, on 28-29 November 1998, attend- Zentralblatt-MATH database and the ed by members of the ‘old committee’ [Jean- Diderot Mathematical Forums, with special Pierre Bourgignon (President), David attention paid to the planned DMF on Wallace (Vice-President), Peter Michor telecommunications. • UNESCO: The President submitted a (Secretary), Aatos Lahtinen (Treasurer), plan for support of EMS actions to the and Ordinary members Bodil Branner, UNESCO-ROSTE (Venice) office which Alberto Conte, Rolf Jeltsch, Andrzej supports scientific activities in Eastern and Pelczar, Marta Sanz-Solé and Anatoly Central European countries and in coun- Vershik], members of the ‘new commit- tries around the Mediterranean Sea; tee’ [Luc Lemaire, David Brannan, Olli Professor Dalafi, director of the office, Martio, Doina Cioranescu and Renzo hopes that a grant of about US $50,000 will Piccinini] and invited guests [Mireille be assigned to the EMS for various pro- Chaleyat-Maurel, Tuulikki Mäkeläinen, jects, including the Alhambra conference Carles Casacuberta, Vagn Lundsgaard in 2000. • The 100th Anniversary of the Union of Hansen and Robin Wilson]. Bulgarian Mathematicians: The President Among the items discussed were the fol- (Vice-President) has offered to write the history of the Society from its inception in and the President-elect (Rolf Jeltsch) par- lowing: Madralin; the format of the publication ticipated in this celebration in Sofia, which • New Individual Members: 289 new will be decided later. offered an excellent opportunity to meet members have joined since the October • EMIS: EMIS now has 32 mirrors and mathematicians from Balkan countries 1997 meeting; the total of individual mem- includes over 30 journals; the material per- (Serbia, Macedonia, Greece, Turkey) rep- bers was 1782 on 1 November 1998. taining to EMS is to be managed by EMS. resenting their national societies. • EMS Summer Schools: • European Congress of Mathematics, • Authorisation for the Financing of — The organiser for the 1997 Portuguese ECM 2000: There was extensive discussion Special Projects: The value of the contract Summer School is currently completing of ECM 2000; full details can be found in between the EMS and the OECD was FRF the Proceedings. the First Announcement on page 7. 75 000 ( = 11 305,20 ecu); the EC earlier — The 1998 EMS Summer Schools were • The Zentralblatt-MATH database: authorised the expenses (about 3000 ecu) successful. The report on the Orsay sum- — In November the President (Jean-Pierre connected with the opening of the mer school was accepted by EU/EC. The Bourguignon) and Secretary (Peter Strasburg mirror to be taken out of this financing for the Cluj school was possible Michor) attended the Coordination income. In addition, it was decided at the without an EMS grant, thanks to the sup- Committee meeting for the Zentralblatt- Helsinki meeting to use part of this con- port given by the UNESCO Venice office MATH database held in Berlin, and the tract income for publicity at the Berlin and the money given by the French speak- President attended the meeting of the ICM98; the costs for the booth and recep- ers on the stipends they got from the Innovations Committee for Zentralblatt- tion in Berlin were about 1200 ecu. French Embassy. However, in spite of MATH. • The Offer of International Press: great efforts, gathering money for cheaper — The extension of the database to International Press has offered to give a meetings in Eastern Europe is difficult. Eastern European countries is proceeding discount of its publications to EMS individ- — The call for applications for the 1999 well: centres in Eastern European coun- ual members. summer schools was not very successful: tries are working for Zentralblatt-MATH • World Mathematical Year 2000: V. L. there is one application for a school in an producing notices. For the first time in 15 Hansen, Chairman of WMY2000, reviewed applied field but none in pure mathemat- years, Zentralblatt-MATH is close to finan- the activities of the WMY 2000 committee. ics. cial viability; 60-70 new subscriptions are One project discussed was the subway pro- • EMS Newsletter: There was a discussion needed to break even. ject: the plan to have posters in subways has on the editorial policy and contents of the — Discussions on the application to be won wide support and concerted action is Newsletter. A division of responsibilities was made to the European Union in the Large called for, as a definite scheme of action planned so that Steen Markvorsen would Infrastructure component of the 5th with cost estimates has to be prepared for take care of interviews and education, Framework Programme have been initiat- the European Commission. A competition Krzysztof Ciesielski of member societies, ed. The aim is to ask for support for for designs for the subway posters has been and Anatoly Vershik and Peter Michor of actions that would improve the proposed (see page 15). Other ideas have the column on Eastern Europe. A page of Zentralblatt-MATH database once and for included mathematical themes in shop- ‘Letters to the editor’ should be intro- all, such as the keyboarding of back issues, ping bags with leaflets in libraries explain- duced. As Editor-in-Chief, Robin Wilson and the setting up of an author database ing the content, posters in petrol stations, would like to establish a net of representa- and a journal database. The cooperation of etc. In several countries mathematical tives of member societies. There was a dis- several countries would enhance the stamps will be issued in 2000. cussion on the cover, the design of which chances for success for this application. • MPRESS (European Mathematical was decided to be kept for the time being. Germany and France are already cooperat- PREprint Server System): There is an on- The possibility of selling the Newsletter to ing, but two more countries would be going project to develop a European com- mathematics departments and libraries needed. ponent for a system to facilitate the search was considered. — The President and Vice-President-elect for and the world-wide access to electronic • EMS Publicity Officer: M. Chaleyat- (Luc Lemaire) met several persons on the preprints in mathematics. Germany, Maurel was due to end her term as EMS staff of Edith Cresson, Commissioner in France, Austria, and the Topology Atlas Publicity Officer on 1 January 1999. The charge of Science, following up a direct are already involved in it. EC expressed its deep gratitude for the meeting of the President with her in Paris • Next meetings: Marta Sanz-Solé and time and energy she devoted to the in September; the main points under dis- Rolf Jeltsch invited the Executive Society, which resulted in numerous suc- cussion were the Fifth Framework Committee to meetings in Barcelona on cessful new projects and products. Programme and the possibility of having 17-18 April and Zurich on 9-10 October • The History of the EMS: David Wallace Zentralblatt-MATH recognised as a large 1999. 6 EMS March 1999 3ecm 3rd European Congress of Mathematics Shaping the 21st Century Barcelona, 10–14 July 2000 First Announcement The Organizing Committee is pleased to 3. Algebraic and Analytic Geometry several fields may be chosen from the announce that the Third European 4. Differential Geometry above list). Congress of Mathematics will take place in 5. Topology Registration Barcelona from Monday 10 July to Friday 6. Discrete Mathematics and The period for registration for the 14 July, 2000. It is organised by the Computer Science 3ecm will begin in the Autumn of Societat Catalana de Matemàtiques, under 7. Modelization and Simulation 1999. Detailed information about the the auspices of the European Mathematical 8. Ordinary Differential Equations registration process will be given in Society. and Dynamical Systems the Second Announcement and posted 9. Partial Differential Equations on the web site. The registration fee is Plenary speakers 10. Functional Analysis 29,000 pta (174 euros) before 1 April ! Robbert Dijkgraaf, Universiteit van 11. Complex Analysis 2000, or 41,000 pta (246 euros) after Amsterdam, NL 12. Probability and Statistics this date. There is a reduced registra- ! Hans Föllmer, Humboldt- 13. Real Analysis tion fee for individual members of the Universität zu Berlin, DE 14. Mathematical Physics European Mathematical Society and ! Hendrik W. Lenstra, Jr., Univ. of the Societat Catalana de California at Berkeley, USA/ Committees Matemàtiques: 23,000 pta (138 euros) Universiteit Leiden, NL ! The Scientific Committee is before 1 April 2000, or 33,000 pta ! Yuri I. Manin, Max-Planck-Institut chaired by Sir Michael Atiyah (198 euros) afterwards. The registra- für Mathematik, Bonn, DE (University of Edinburgh, UK) tion fee for those accompanying fully ! Yves Meyer, Ecole Normale ! The Prize Committee is chaired by registered participants is 12,000 pta Supérieure de Cachan, FR Jacques-Louis Lions (Collège de (72 euros) before 1 April 2000, or ! Carles Simó, Universitat de France, FR) 18,000 pta (108 euros) after this date. Barcelona, ES ! The Round Table Committee is This fee will entitle participants to ! Marie-France Vignéras, Université chaired by Miguel de Guzmán attend social events organized during de Paris 7, FR (Universidad Complutense de the 3ecm, and will entail other bene- ! Oleg Viro, Uppsala Universitet, Madrid, ES) fits. SE/POMI St Petersburg, RU ! The Organizing Committee is Continuing the tradition set by the ! Andrew J. Wiles, Princeton chaired by Sebastià Xambó previous European Congresses, the University, USA Descamps (Universitat Politècnica Organizing Committee will secure de Catalunya, ES) funds for conference grants covering Scientific programme The Scientific Committee, Prize registration and/or accommodation The programme of the Congress Committee and Round Table expenses. Deadlines for applications includes nine plenary lectures, thirty Committee were appointed by the will be specified in the Second invited lectures in parallel sessions, European Mathematical Society. The Announcement. lectures given by the EMS prizewin- Scientific Committee held its first ners, mini-symposia, round-table dis- meeting in October 1997 in Barcelona Call for posters cussions, and poster sessions. As in and will meet again in April 1999. The All registered participants will have previous European Congresses, a Organizing Committee was appointed the opportunity to present their math- number of prizes will be awarded to by the Societat Catalana de ematical work in the form of a poster. mathematicians under the age of 32. Matemàtiques. Decisions on acceptance will be made Mini-symposia are a new feature of the by the Organizing Committee on the 3ecm; several current interdisciplinary Pre-registration basis of an abstract which should reach topics will be selected by the Scientific If you wish to receive the Second the organizers before 1 April 2000. Committee. The full programme of Announcement and e-mail informa- Abstracts submitted after this date will lectures, mini-symposia and round- tion about the 3ecm, please pre-regis- not be considered. Acceptance will be table sessions will appear in the ter via the web site http://www.iec.es/ confirmed before 20 April 2000. Second Announcement. Short com- 3ecm (if you have not done so A poster is a display in a vertical munications by participants will be already). Pre-registration is free and space of approximately 100 cm by 80 possible in the form of posters; implies no obligation whatsoever. In cm, where the main points of a mathe- instructions for submission of poster order to become a participant in the matical work are presented in a syn- abstracts are given below. 3ecm, subsequent full registration and thetic form that can be grasped quick- Demonstrations of mathematical soft- payment of the registration fee are ly by other mathematicians. Accepted ware, video and multimedia are also necessary. Pre-registration is also pos- posters will be grouped according to planned. sible by e-mail to [email protected], or by subject, and will be displayed for a lim- For organizational purposes, the fol- ordinary mail to the Societat Catalana ited time between 11–13 July 2000. lowing list of scientific fields has been de Matemàtiques (see address below). Authors will be required to be pre- established: Please indicate your name, institution, sent and available for questions and 1. Logic and Foundations full mailing address, e-mail address, discussions during a specified period 2. Algebra and Number Theory and scientific fields of interest (one or (yet to be determined). Abstracts of

EMS March 1999 7 3ecm accepted posters will be available plementary material: Mathsoft 3ecm from all areas of mathematics. through the web site of the Congress. (Prof. Santiago Zarzuela), Facultat de The size of each contribution must Abstracts should conform with the Matemàtiques, Universitat de Barcelona, be of the equivalent of approximately following instructions. It is strongly Gran Via 585, E-08007 Barcelona, 5 minutes of video at most. Larger recommended that abstracts be sub- Spain. special contributions may also be con- mitted electronically by using the form Submissions should be written in sidered. Contributions should be of provided in the web site http://www. English, indicating the name and affil- interest to a broad audience, and meet iec.es/3ecm/posters.htm. Abstracts iation of the contributors. They should the highest standards with respect to may also be sent by e-mail to posters. include clearly explained information mathematical content, visualization [email protected], with the Subject field about the foundations with regards to techniques, artistic design and avail- containing exclusively the relevant the systems, the fields of application, ability. The Organizing Committee section number (see the list of sections the targeted user community, the soft- will evaluate and select a number of above). If electronic submission is not ware design and techniques, and the contributions according to criteria of possible, the following mail address availability of the software. A URL will quality, interest, originality and the- should be used: Posters 3ecm (Prof. Josep also be very useful. matic balance. Non-commercial con- M. Font), Facultat de Matemàtiques, Contributors will be notified of the tributions will be given preference. Universitat de Barcelona, Gran Via 585, Submissions must be received by the E-08007 Barcelona, Spain. organizers before 1 February 2000. Abstracts should preferably be writ- They should be sent by ordinary mail ten in English, and prepared in to: Video 3ecm (Prof. Santiago Zarzuela), LaTeX using only standard commands Facultat de Matemàtiques, Universitat de and AMS macros, symbols and fonts. Barcelona, Gran Via 585, E-08007 They should have the following struc- Barcelona, Spain. Each entry should ture: include a complete signed submission ! section number form written in English. Submission ! name and affiliation of author(s), forms are available at http://www.iec. indicating a return address (e-mail es/3ecm/video.htm, where additional if possible) detailed information about how to ! title of the poster submit may be found. ! text of the abstract, not exceeding Contributors will be notified of the 300 words, including references acceptance or rejection of their sub- ! 1991 mathematics subject classifica- mission by the Organizing Committee tion acceptance or rejection of their sub- by 1 April 2000. Those selected will be ! key words mission by the Organizing Committee asked to send a final version of their by 1 April 2000. A timetable will sub- work if necessary and any other useful Call for presentations of mathemati- sequently be organized depending on information to prepare the final DVD. cal software the selected presentations. Contrib- It is the contributor’s responsibility A session on mathematical software utors will be asked to send an abstract to secure any necessary permission will take place during the Congress. In which will be available through the and licences for visual and audio mate- this session, mathematical software web pages of the Congress. At this rial contained in their work. systems relating to all fields of mathe- stage, demands for special equipment The address [email protected] matics, and applicable to a variety of needed for presentations can be dis- may be used to contact the organizers purposes, will be presented. cussed. of this complementary activity or to The scheduled length of a presenta- It is the contributor’s responsibility ask any related questions. tion including discussion will be 30 to secure any necessary permission minutes. The systems presented and licences for any material con- Satellite activities should meet the highest standards tained in the presentation or hand- The following is a list of satellite activ- with respect to mathematical content outs. ities which have been acknowledged by and technical quality in design and Additional information will be avail- the 3ecm Executive Committee by implementation. Public domain soft- able and further indications will be January 1999. Proposals for further ware will be given preference over given on the Congress web site. The satellite congresses or other mathe- commercial software. The Organizing address [email protected] may matical events will be welcome. They Committee will evaluate and select a be used in order to contact the orga- should be communicated to the number of contributions according to nizers of this session or to ask any President of the Organizing criteria of mathematical originality, related questions. Committee before 1 February 2000, novelty and range of applications, either by e-mail to [email protected] or by bearing in mind the thematic balance Call for video and multimedia mail to the Societat Catalana de of the session. Several complementary activities and Matemàtiques (see address below). Submissions must be received by the cultural events are planned during the The Executive Committee of the organizers before 1 February 2000. 3ecm. One of these is the preparation 3ecm offers the following advantages They may be made electronically by and production of a DVD containing to organizers of satellite activities. A using the form provided in the web both short videos and multimedia with summary of information about each page http://www.iec.es/3ecm/math mathematical content. This DVD will satellite activity will be freely distrib- soft.htm, or by e-mail to mathsoft. be exhibited in several general public uted through the printed and elec- [email protected] with a Subject field con- sessions. It will also be available to tronic systems of the 3ecm. The taining exclusively the word mathsoft. individuals at various places through- reduced registration fee offered to The following mail address can also be out the 3ecm site. Submission of con- participants of the 3ecm registered used for submission or to send com- tributions for this DVD may be made before April 2000 will be extended

8 EMS March 1999 3ecm until the beginning of the 3ecm for Abrantes, G. de Abreu, T. Nunes, C. ism, and striking contemporary participants of satellite activities. Alsina, J. M. Fortuny, M. A. Canals, achievements. In the sphere of art, Addresses of satellite activity partici- L. Rico, L. Balbuena, V. Rivière, N. Barcelona offers also a wide range of pants may be included in the mailing Gorgorió. Programme Committee: X. possibilities: classical music, opera, list of the 3ecm for distribution of Vilella, Ll. Girondo, C. Aguadé, A. and ballet; one of the best collections information. Violant, M. Berini, R. Codina, C. of Romanesque painting in the world; ! Summer School on Interactions Lladó, I. del Blanco, N. Gorgorió. the Picasso museum, the foundations between Algebraic Topology and Contact: Xavier Vilella (FEEMCAT), of Joan Miró, Antoni Tàpies, and Invariant Theory: Ioannina, e-mail: [email protected] Thyssen-Bornemisza, or the new Greece, 26 June - 1 July 2000. ! Distributions with given Marginals museum of contemporary art by Speakers: F. Cohen, L. Smith, N. and Statistical Modelling. Richard Meier. Night life goes on until Marmaridis, N. Kechagias. Contact: Barcelona, 17–19 July 2000. the small hours with an excellent Nondas Kechagias (University of Organizing Committee: C. M. choice of restaurants, shows, and ultra- Ioannina), e-mail: [email protected] Cuadras, J. Fortiana, F. Oliva, J. A. modern bars. ! Functional Analysis Valencia Rodríguez-Lallena. Scientific Tours Catalonia offers excellent possi- 2000, an International Functional Committee: C. Alsina, J. A. Cuesta, C. bilities for excursions: the Costa Brava Analysis Meeting on the Occasion Genest, R. Nelsen, I. Olkin, J. with the Dalí Museum, the cava winer- of the 70th Birthday of Professor Quesada-Molina, C. Sempi, B. ies, the monasteries of Montserrat, Manuel Valdivia: Valencia, 3–7 Schweizer. Contact: Carles M. Poblet, Santes Creus, and Vallbona, July 2000. Invited Speakers: G. Cuadras (Universitat de Barcelona), the picturesque village of Sitges, or the Dales, T. W. Gamelin, G. Godefroy, e-mail: [email protected] historical cities of Girona and J. Lindenstrauss, N. Kalton, R. Tarragona. Meise, A. Pelczynski, G. Pisier, D. Barcelona, Catalonia Accommodation A list of hotels of var- Vogt, P. Wojtaszczyk. Scientific The country of Catalonia, with six mil- ious categories will be offered in the Organizing and Programme Committee: lion people, lies in the north-east of Second Announcement, together with R. M. Aron, K. D. Bierstedt, J. Spain. Catalan and Spanish are its offi- instructions for reservation. A large Bonet, J. Cerdà, H. Jarchow, M. cial languages. Catalonia offers a great number of rooms at low prices will be Maestre, J. Schmets. Contact: José variety of landscapes, ranging from available in student residences. Bonet (Universidad de Valencia), e- sunny beaches to the high peaks of the mail: [email protected], or Klaus Pyrenees. Visitors can find a wide Sponsors D. Bierstedt (Universität Pader- choice of sights and events, such as The following list of sponsors has been born), e-mail: vlc2000@uni pader- Romanesque churches and paintings, updated as of February 1999: born.de, website: http://www. Gothic cathedrals, many museums, Generalitat de Catalunya, Comissionat per upv.es/VLC2000/ classical or modern music perfor- a Universitats i Recerca ! 6th International Conference on mances, and exhibitions of all kinds. Generalitat de Catalunya, Departament Harmonic Analysis: El Escorial, Barcelona, the second largest city of d’Ensenyament Madrid, 3–7 July 2000. Invited Spain and the capital of Catalonia, is Ministerio de Educación y Cultura, S.E.U.I.D. Speakers: A. Carbery, M. Christ, C. located on the shores of the Fundació Catalana per a la Recerca Kenig, P. Mattila, F. Ricci, P. Mediterranean Sea and enjoys a mild Ajuntament de Barcelona Sjögren, E. Stein, S. Wainger, G. climate throughout the year. Founded Institut d’Estudis Catalans Weiss. Organizing Committee: P. by the Romans more than 2000 years Universitat de Barcelona Cifuentes, J. García-Cuerva, E. ago, it maintains a rich historical her- Universitat Autònoma de Barcelona Hernández, F. Soria, J. L. Torrea, itage and deeply rooted cultural tradi- Universitat Politècnica de Catalunya A. Vargas. Contact: Eugenio tions. With the Olympic Games in Institut d’Estadística de Catalunya Hernández (Universidad Autónoma 1992, Barcelona underwent a renova- International Mathematical Union de Madrid), e-mail: eugenio.hernan tion of its public and private infra- Real Sociedad Matemática Española [email protected] structure, reinforcing its role as one of Sociedad Española de Matemática Aplicada ! Alhambra 2000, a joint Mathemat- the most modern cities in Europe, and Fundación Retevisión ical European-Arabic Conference. an attractive destination for business, Fundació ‘la Caixa’, Museu de la Ciència Granada, 3–7 July 2000. Promoted tourism, and culture. Barcelona has Borsa de Barcelona by the European Mathematical acquired a solid reputation as a site for Port de Barcelona Society within the activities of the successful conferences and sport Fundació Caixa Catalunya WMY2000. Contact: Ceferino Ruiz events of the highest level. Fundació Banc Sabadell (Universidad de Granada), e-mail: Travel Barcelona is within three hours Fundació Caixa de Sabadell alhambra2000 @ugr.es flight of all the main cities in Europe, Logic Control ! First Euro-Mediterranean Topo- Northern Africa, and the Middle East. Springer-Verlag logy Meeting. Bellaterra, 4–7 July The modern, recently renovated air- 2000. Organizing Committee: C. port has flights to many other destina- Contact addresses Broto, R. Piccinini, L. Schwartz. tions throughout the world. An air Congress e-mail: [email protected] Contact: Carlos Broto (Universitat shuttle with Madrid facilitates connec- Congress web site: Autònoma de Barcelona), e-mail: tions with intercontinental flights. http://www.iec.es/3ecm/ or [email protected] Leisure and Culture Everyone identi- http://www.si.upc.es/3ecm/ ! cem 2000, Congrés d’Educació fies Barcelona as the city of Gaudí; his Mailing address: Societat Catalana de Matemàtica, I Jornades best-known works are the Pedrera, the Matemàtiques, Institut d’Estudis d’Educació Matemàtica a Sagrada Família, and the Park Güell. Catalans, Carrer del Carme 47, E- Catalunya. Mataró, 3–5 or 5–7 July Many other architectural treasures can 08001 Barcelona; tel: (+34)-93-270- 2000. Advisory Committee: K. be admired in Barcelona, from Gothic 16-20; fax: (+34)-93-270-11-80 Clements, A. J. Bishop, P. Boero, P. to splendid modernism, to rational-

EMS March 1999 9 FEATURE Caring for the mathematical past: a recent British experience John Fauvel

The most prominent mathematics claims which seemed less and less tune to acquire such a special collec- story to make the front page of the defensible, and showed a remarkable tion, and the young University of national Press in the UK in recent lack of awareness of the repercussions Keele fitted this criterion exactly. months, if not years, hit The books which Charles Turner the news stands just gave to Keele were indeed a choice before Christmas, until it collection of the masterworks of four was squeezed off the centuries. There were sixteen items front page by the misde- published before 1500, including meanours of yet another Ratdolt’s 1485 edition of Sacrobosco’s Cabinet Minister. Alas, Sphaera mundi, the first printed book the story the newspaper to utilize more than two colours, and had to tell was not of a his magnificent 1482 edition of new mathematical result, Euclid’s Elements. Besides this, the first nor of further recogni- printed edition of Euclid, Turner col- tion and success for lected a further twenty-four Euclids British mathematicians in printed before 1600, and thirty-five international meetings, more from 1600 onwards. The collec- nor indeed of debates tion of British mathematical works was about the quality of our very good, with authors ranging from mathematics teaching. It the great mediaeval mathematician was a much sadder story, Thomas Bradwardine (who died in of the secret destruction 1349) up to leading nineteenth-centu- of a public asset by those ry mathematicians such as Cayley and supposed to guard it and Clerk Maxwell, and a particularly fine care for it, which raises sub-collection of eighteenth century melancholy reflections fluxional works (the calculus used in about the governance of England, under Newton’s influence, our universities today. It while the rest of Europe was using points to a lack of respect Leibnizian calculus). As well as a large for mathematics and for number of books by Isaac Newton, scholarship which raises including all three editions of questions about the Principia, at least eight of Turner’s increasing divergence Newton’s ‘Method of Fluxions’, one of the books sold by Keele books were from Newton’s library, between age-old academ- University to a book dealer. some with annotations in his own ic values and the brave hand. Works by Viète, Kepler, Galileo new world of those who manage uni- of their selfish actions for researchers, and Descartes were all there too. . . versities with the values of accoun- teachers and curators throughout the some 1400 books in all. Of course any tants. mathematical and scholarly communi- one of them, bar those significant ‘Fury at £1m sale of Keele mathe- ties. through their ownership or annota- matics collection’ ran the headline on Keele is a small university, just off tions, is likely to be found in some 22nd December 1998 all across the the motorway between Manchester other library too — that’s why books front page of The Daily Telegraph, a and Birmingham, founded after the were invented — but the Collection as newspaper which sells a million or war with high ideals: the closest of a collection was unique, and its being more copies each day to readers rep- English universities to the concept of a located in a friendly study room in a resenting the traditional values of the liberal arts college. At first and for small university far from the great English middle and upper classes. The many years it provided, unusually for metropolitan centres also made it story was almost unbelievable: that the England, a four-year degree course, unique. managers of an English university had the first year of which engaged stu- Charles Turner gave his life’s collec- secretly sold to a book-dealer a collec- dents in a cross-disciplinary curricu- tion to Keele. It would never have tion of mathematical texts, including lum involving both arts and sciences. crossed his mind, nor that of the some of the great mathematical books When the elderly civil servant Charles Librarian and Vice-Chancellor who of four centuries, which had been Turner (1886–1973) looked around accepted the gift, that their successors given to the University only thirty for a permanent home for the collec- would prove such unworthy custodians years before for the benefit of students tion of mathematics books he had built of their heritage. Had he known what and scholars. The secret conversion of up over a lifetime, his eye fell upon kind of people would be leading Keele a public good into a private possession Keele through his friendship with a in the 1990s, he would doubtless have by the secret decision of a University member of the academic staff there, built into his gift a clause that the Council deeply offends everyone’s the physicist David Ingram. It was Collection should not be sold secretly sense of what a university is for. As the Turner’s wish that the collection into private ownership in order to story unravelled, the University man- should go to a university which had finance the Department of agers’ defensiveness led them into not had the opportunity or good for- Management’s MBA programme. But 10 EMS March 1999 FEATURE as he didn’t, he didn’t. sadly ironic that the Keele manage- such as the London Mathematical What was the Turner Collection ment should apply cynical accountan- Society are now offering to help find. used for, and who used it? Many gen- cy values—knowing, in Whistler’s Many people would have been only erations of Keele students had come to words, the price of everything and the too glad to help raise the money, in see the Collection, to handle and read value of nothing—to their custodian- the process raising the profile of the the original works of the great mathe- ship of a great mathematics collection Collection and of the history of math- maticians of the past. They sometimes at precisely the moment when the rest ematics. All of this was pre-empted by did projects, sometimes just absorbed of the world was beginning to recog- the foolish, short-sighted, hasty, inspiration from the very existence nise the interest and importance of its shameful, duplicitous decision of the and appearance of the books. history for both teaching and research senior management which has Members of staff used the brought Keele University into disre- Collection in connection with pute. teaching programmes at both What lessons for the mathematics undergraduate and graduate community can be learned from this level, in mathematics and in sad episode? One very obvious one is educational studies in particu- the value of community. Even while lar, though by no means con- one laments that this is an occasion of fined to that. Outside bodies bringing the community together, it is also valued and used the heartening to discover that those who Collection. The Open are concerned and offended at the loss University, founded shortly of the Turner Collection include most after Keele had accepted members of the mathematical commu- Turner’s gift, has made a nity as well as historians, teachers and great deal of use of the scholars of all kinds. In a striking testi- Collection over the years, mony to the renewed appreciation of including filming several tele- the importance of history of mathe- vision programmes for its matics for the culture and practice of innovative history of mathe- mathematics, the London Mathemat- matics course. The British ical Society has played a leading role Society for the History of in its strong encouragement of moves Mathematics, founded in to trace the Collection and restore it to 1971, held a meeting at the a public institution. Collection in 1992 with sever- But another sobering reflection is al talks about different aspects surely that university administrators — of the Collection. Two articles in Britain, at least, battered by twenty were written about the years of government funding attrition Collection, the Leverhulme — are no longer our natural allies, Foundation gave money for it sharing the core values of pursuing to be catalogued, the British Newton’s ‘Principia Mathematica’ and supporting teaching and scholar- Library gave money for ship in a way which looks to the wider rebinding some of the books . . . In in mathematics. good of society. This was foreshad- short, everything was proceeding well Everyone will sympathize with hard- owed, perhaps, in a phrase made pop- and the Turner Collection was playing pressed university administrators try- ular in the 1920s, the ‘treason of the a key and valued role in the reinvigo- ing hard to square circular budgets clerks’. There can come times when ration of interest in the history of and lacking the resources to achieve those with a moral imperative to the mathematics which has taken place in their ambitions for students and facul- world of the mind fail in their duty to the UK, and indeed in Europe as a ty. But the decision to sell the collec- the past, and indeed the future. For it whole, over the past thirty years, tion in the secretive way chosen was is the future undergraduates of Keele, among mathematicians, teachers and entirely self-defeating and has done deprived for ever of the riches and others. immeasurable harm to the reputation benefits of a great collection of their Until, that is, the managers of the of the University, as well as to the mathematical heritage, who are the University of Keele discovered that old development of history of mathemat- losers through their managers’ selfish mathematics books are valuable and ics in Britain. For the forces currently and short-sighted secret deals. can be sold for cash to support such arrayed against Keele would have been John Fauvel [e-mail: [email protected]. causes as the MBA programme of the lined up with it in sympathy and sup- uk] is a senior lecturer in mathematics at Department of Management. None of port to raise the money, save the the Open University, UK, and is a former those who used and valued the Collection and help the Keele stu- president of the British Society for the Collection, inside or outside the dents, if only the Vice-Chancellor and History of Mathematics. University, was consulted by the her colleagues had chosen, instead of University managers before they pro- hatching secretive deals, to talk about REPLY TO JOHN moted a vote in Council to effect its the problem with the wider world. secret disposal. This was a mistake, There is no shame in needing to raise FAUVEL’S ARTICLE because now that the outside world has money, and these days a million The above article was sent to Keele belatedly learned of its loss, the dis- pounds is not a large sum to raise. University for comment; here is the may and anger of those deprived of Many wealthy organisations and many reply sent by Allan Foster (e-mail: any influence over the decision has individuals have funds to contribute [email protected]), Director of grown in volume until it is audible towards such a cause. A publicly acces- Information Services & University even behind the walls of Keele. It is sible home could have been found, Librarian, University of Keele

EMS March 1999 11 FEATURE John Fauvel’s account of the sale of the Supplement which, interestingly, the John Fauvel’s dismissive reference Turner Collection is flawed in several Editor did not choose to print. Full to the proceeds of the sale being used respects. That he has repeated a num- minutes of the Senate and the Council to finance the University’s MBA pro- ber of the misleading tabloid-style debates were available on the gramme is quite wrong. In fact, a sig- newspaper by-lines does him no cred- University’s internal web site early in nificant proportion is being invested it. Despite the campaign of vilification the 1998/9 academic year. The back into the Library’s many unique waged by him and others, the Council gave delegated power to the special collections including the list- University has acted legally and with two most senior lay members and the ing, conservation and digitisation of integrity in this matter. I will deal with Vice-Chancellor to determine the papers from Arnold Bennett, some of the main points he raises. means of the sale. Following further Wedgwood, Sneyd, Karl Mannheim The Collection was sold in order to investigation and consultation, the and others. Many academics at the generate an urgent need for substan- decision to sell to the private buyer was University and outside are delighted tial investment in library materials to later confirmed. Whether commenta- that we will be at long last able to pro- support current and future teaching tors approved of the final decision or vide the care and improved access to and research programmes. For many not, there is no doubt that the process these collections which will benefit years the University has been unable was conducted with probity through- scholarship so tangibly. Other funds to allocate sufficient funds for library out and following a very careful con- will be directed to increase the range resources. With the national unit of sideration of the issues involved. of printed and electronic scholarly resource diminishing year by year, Whilst there is no doubt that the resources across all disciplines to sup- there was no prospect of significant Collection is a very interesting one, port present and future teaching and additional funds to provide this essen- with some unusual and rare items, vir- research programmes. Given the open tial support. The difficulties of tually all the books are also held in nature of our access policies, these libraries maintaining and developing major centres — Trinity College resources will not only benefit staff adequate holdings of printed materi- Cambridge, University College and students at the University but also als, together with the new generation London (the Graves Collection), members of the public in the locality of electronic resources, are well Edinburgh University, and and scholars everywhere. known. We are determined to provide Manchester. These collections are Finally, Fauvel’s remarks about the this essential infrastructure at Keele. A much bigger than Turner and much philistinism of university administra- strategic review of our special collec- more accessible for scholars. This tors can not be allowed to pass without tions, together with the development explains why the use of the Turner comment. The history of Keele, like of a collections development policy, material was so poor—for instance, most universities, is based on a careful emphasised the need to concentrate two external visitors in the last two and creative partnership between our limited resources on those collec- years, nine postal enquiries in a senior administrators (usually notable tions and materials which are relevant decade. The British mathematical academic themselves, of course), the to teaching and research programmes, community, apparently now so body of the academic community in its now and in the future. This was not an opposed to the sale, showed relatively entirety, support staff and, last but not opportunistic, spur of the moment little interest in it during the 30 years least, students. Additional to these decision but one over which the it was at Keele. The eight items from groups, of course, are the local and University agonised, weighing up the Newton’s library are of great interest national communities represented by options very carefully. but they are dwarfed by the 800 items lay members of university councils, The decision to sell the Collection from his library held at Trinity College courts and boards. In as much as the was not taken in secret, far from it. Cambridge. The Graves Collection on formal process of governance reflects The proposal to sell was debated the history of mathematics at this richness, the decision to sell the extensively by the VC’s Committee University College London has ten Turner Collection was the collective (the University’s management team), times the number of Turner volumes wisdom of the University community. the Finance Committee, the Senate and replicates many of these items. Crude analysis of differences between and the University Council during the The professional advice we received academics and administrators, ‘them’ May to June period last year. So open was that no other public institution was and ‘us’, really won’t do. As the prob- was the debate that, given that it was likely to buy the Collection in its lems of developing universities in a cli- seen as a matter of conscience for entirety at the valuation that had been mate of ever tighter finances become senior colleagues, the process was han- made. Our earnest objective of doing more complex, then we need every dled as a series of set piece debates nothing that would lead to the break member of the institution, not just aca- with two members of the VC’s up of the Collection guided us demics, to pull together and make Committee leading the ‘pro’ and ‘anti’ throughout. Before we sold the their unique contribution. sale cases. There was a close vote in a Collection, the University decided to straw poll of members of the Senate retain all Newton annotations and Editor’s note: (22 against the sale; 19 in favour). The dog-ears, and other books from the Since the above articles were written, indi- Council took this into account when it Collection, in facsimile, photographic vidual books from the Turner Collection agreed to the sale in principle on 26th and copied form for the use of schol- have been advertised within the book trade, June 1998 by a vote of 14 for, 8 ars within and outside Keele. Some of indicating that the Collection is indeed against, plus 1 abstention. There were these will be distributed to these larg- being broken up. Also, Keele University has passionate speeches both for and er collections mentioned above. We agreed to set up a review of the sale of the against the sale. Academic colleagues also plan to digitise these selectively Turner Collection, to be carried out by the said that the Senate debate had been and to make them available interna- Audit Committee of Council. the best one in living memory. The tionally over the World Wide Web. Please let me have your views on John University’s students were unanimous- Thus scholars will continue to have Fauvel’s article and Allan Foster’s reply for ly behind the sale and said so in a let- access to the material in a variety of the ‘Letters page’ in the June issue. ter to the Times Higher Educational forms.

12 EMS March 1999 INTERVIEW Interview with Robert M. Mattheij (Eindhoven) [President, European Consortium for Mathematics in Industry (ECMI)] interviewer: Vincenzo Capasso (Milan)

Q. I think it would be of interest to go European scale: cooperation on has met annually since 1995 and the back to the roots of ECMI, Bob. research into polymers, glass, textiles, most recent meeting, ‘Glass days in A. In 1985 a meeting in Amsterdam etc. by mathematicians. Thus the third Kaiserslautern’, attracted fifty partici- organised by Hazewinkel, van objective has induced many coopera- pants (twenty from industry) from six Groesen, and myself was named ESMI, tive efforts, quite often not even within different countries. European Symposium on Mathematics ECMI’s framework directly, but • European Study Groups with Industry in Industry. Besides being successful undoubtedly inspired or fostered by it. European study groups have been scientifically, the groundwork was laid Q. Which roles have been played by the held for many years: in 1998 alone to establish a European organisation stimulation programmes launched by they were held in Southampton, devoted to mathematics in industry. the European Union for the existence of Lyngby and Leiden. These are gen- Later, in 1986, under the steering ECMI? uine brain-storming sessions on real leadership of Helmut Neunzert, ECMI A. The very existence of ECMI as a problems, the only formal sessions was founded in Mussbach. foundation and consortium was being at the beginning and the end of Q. What are the aims of ECMI? intended to open up new financial the week. The spin-off is substantial in A. It has a three-fold philosophy: to possibilities through Brussels, encour- terms of contacts with industry and promote the use of mathematics in aging educational and research pro- genuine mathematical problems. industry, to educate young ‘industrial grammes alike. It should be noted, Q. How do you encourage young mathematicians’, and to operate on a however, that the European formula mathematicians to do applied research European scale. of ECMI is much less unique than in for industry? Q. Has ECMI matched these aims? the early days, as there are a few other A. ECMI offers opportunities for A. The first objective is quite vivid consortia who also work on some sort young researchers to work on mathe- and has only gained momentum— of cooperation between industry and matical problems in industry at doc- even worldwide—as many initiatives mathematically oriented institutes toral and postdoctoral level. EU grants for bringing mathematics to industry (albeit in narrower areas). have supported a network of postdoc- have become fruitful undertakings, toral researchers at key institutions Q. What do you consider the major who work on specific industrial prob- through meetings, mathematics-in- achievements of ECMI with respect to industry study groups, special pro- lems and take part in a joint training its original aims? programme. grammes and even special institutes, A. In summary, ECMI’s basic ideas ECMI postdoctoral fellowships are where funding from industry is essen- have been implemented in the follow- tial. important for maintaining and ing activities: strengthening its research base and The second objective has probably Conferences • : collaborative links between centres. had the most success, as far as ECMI’s — a research conference is held every joint postgraduate educational system They provide a unique possibility for two years on ‘Mathematics for indus- young researchers to learn from the is concerned. At the moment fifteen try’, attended by academic applied institutions, spread out over ten (to some extent) complementary mathematicians and industrial scien- expertise at the various centres. Up to European countries, are working tists, the latter comprising about 25% together on a programme that takes now, most have been funded under of the total attendance; the most the HCM and TMR schemes of the away a bit of their local freedom in recent one, ECMI98, was held in order to allow for a really trans- EU. Appointments are currently being Gotheborg from June 22–27, 1998 made for the TMR network national common curriculum. This is — industry days are held at various quite impressive compared to what ‘Differential equations in industry and ECMI centres each year to strengthen commerce’ which will run till 2001. many other European cooperative links between ECMI and local indus- programmes have realised thus far. tries Q. What is the scope of these postdoc- From the onset those who shaped — meetings on mathematics for spe- toral fellowships? ECMI’s ideals had in mind a clear cial areas of industrial activity are held A. To train industrial mathematicians relationship between education and several times a year at various ECMI for a career in industry; to better research. centres exploit the benefits of complementary Q. The ECMI educational programme • ECMI Educational Programme expertise at the various centres is clearly a success; ECMI has substan- — ECMI offers a European through frequent visits by ECMI fel- tial recognition in various articles that Postgraduate Programme ‘Mathemat- lows to other centres; and to increase appeared in the press. But was there ics in industry’, where some seventy the links with European industries the same success for cooperative students participate at fourteen cen- through research on relevant prob- research in the ECMI network? tres yearly lems A. The latter is visible through a vari- — training sessions and annual mod- Q. How do you envisage the role ety of meetings, from the biannual elling weeks are held for graduates played by these postdocs in the future large ECMI meeting to so-called • Special Interest Groups development of industrial mathematics ‘industrial days’. Moreover, ECMI has ECMI’s Special Interest Groups (SIGs) in Europe? special interest groups which are stimulate long-term collaboration in A. Although the ECMI network pro- application-oriented. What would not specific areas. These SIGs are applica- vides many other ways of exchange be possible for mathematicians in a tion oriented, like glass, multibody and communication, it has been clear, single country can be attractive on a dynamics, etc. The first SIG, on glass, almost from the beginning, that one of EMS March 1999 13 INTERVIEW the best ways to strengthen this net- aries, where a single European country Sometimes quite refined chemical work to the benefit of both industry may be too small. They have turned processes are needed to purify the and the participating centres alike, out to be a successful means for letting material (such as the sol-gel technique should be the employment of young industrialists discuss relevant actual for producing optical fibres). researchers who can transfer exper- problems with mathematicians, thus We mention a few questions showing tise. Naturally, these young increasing knowledge for the first and the extreme importance of mathemat- researchers themselves are the first to expertise for the second. ical modelling: benefit from this exchange pro- Q. How can one start a SIG? — residual stresses: the cooling must be gramme. A. The first SIGs arose from the done so that the stresses in the mater- Q. Do you plan to maintain, and pos- experience at meetings and other ial do not cause breakage, etc. sibly extend, this programme? ECMI activities that, despite the — morphology due to the ever-growing A. We hope to obtain both EU and generality of mathematics, both demands of customers’ optimal shape industrial money to support further researchers and industry would be bet- design for pressing and blowing students and postdoctoral researchers ter served if research were grouped requires a lot of modelling within the ECMI network around themes. ECMI is quite unique — designing production tools; production — extension to more ECMI insitutions as this is done in terms of application- of (e.g.) float glass requires appropri- should be made possible oriented, not mathematics-oriented, ate modelling of the flow/heat prob- — in addition, we are planning an areas. lems and thus (e. g.) the placement of extension of the programme to rollers. Q. What are the existing SIGs? — heat exchange: since the viscosity is include doctoral fellows A. At the moment there exist five highly dependent on the temperature, SIGs. Since the concept is working Q. How does ECMI disseminate its it is extremely important to model this well, the number is rapidly growing. results and achievements? correctly. Moreover, today there hard- A. ECMI has various publication We list them here, with the addresses ly exist measurement tools for this; in links, such as a biannual ECMI of the coordinating institution. particular, radiation is very important, Newsletter and an ECMI book series SIG on Glass but extremely difficult. One should (Teubner-Wiley). Moreover, publica- Coordinator: Prof. Dr R. M. M. realise that the energy consumption is tions of academic papers is encour- Mattheij, Department of Mathematics, the most important production cost. aged and facilitated via journals on Technische Universiteit Eindhoven, industrial and applied mathematics P.O. Box 513, Eindhoven, The Q. How does ECMI attract attention which are based at ECMI centres: Netherlands towards a SIG ? European Journal for Applied SIG on Polymers A. ECMI has organised a number of Mathematics (Oxford), Journal of Coordinator: Prof. V. Capasso, special meetings on glass: 1994, 1996, Engineering Mathematics (Eindhoven), Universitaà di Milano, Dipartimento 1997, 1998. This frequency is increas- Surveys on Mathematics in Industry di Matematica, Via C. Saldini 50, ing. The meetings are ‘Glass days’, (Linz), and IMA Journal on Industrial 20133 Milano, Italy minisymposia at conferences (ECMI Mathematics and Finance (Strathclyde). SIG on Composite materials conferences, ICIAM conferences, SIAM conferences) and ‘Modelling of Q. Have you considered the spread of Coordinator: Prof. S. McKee, University of Strathclyde, Department Glass Forming Processes’, Euromech ECMI ideas beyond the EU? 388 (Valenciennes). A. ECMI is often asked to help set up of Mathematics, 26 Richmond Street, mathematics in industry activities else- Glasgow G1 1XH, Scotland Q. Would you say more about the where. Thus it has collaborated world- SIG on Multibody dynamics ECMI conferences? wide on setting up educational pro- Coordinator: Prof. Dr. P. Rentrop, A. Conferences are an important and grammes and study groups. As an Technische Universitaet Darmstadt, integrating part of ECMI’s activities. example, teams from ECMI have led Fachbereich Mathematik, Schloss- They ensure timely distribution of industrial workshops in countries like gartenstr. 7, 64289 Darmstadt, ideas and thoughts and provide a Latvia (1996), Mexico (1995, 1997), Germany forum where ‘supply and demand’ can and Brazil (1997). SIG on Scientific computing in the elec- meet. In view of its special role ECMI tronic industry focusses on applications rather than Q. Which kinds of membership are Coordinator: Prof Dr M. Gunther, on mathematical subjects. At the same there for ECMI? Fachbereich 17, Universität time special meetings are organised A. ECMI has three levels of member- Gesamthochschule Kassel, Postfach 10 where the problem themes are central, ship: academic members, industrial 13 80, 34109 Kassel, Germany not the solution methodology as such. members and individual members. In SIGs on acoustics and paper are the past the main emphasis was on Q. What do you expect as the ‘revenue’ presently being formed. having industrial and academic mem- from an ECMI Conference? bers; they are still the most important Q. As an example, could you say some- A. The goals of an ECMI Conference categories. However, the very nature thing more about the SIG that you coor- are in synthesis: of (e.g.) SIG makes individual mem- dinate? — to provide a forum for those who bership quite meaningful. It is hoped A. Despite the fact that glass is an old are actively involved and those more that this category will further increase material there are still many interest- generally interested in mathematics in by the activities of these SIGs. ing and important problems which industry Q. Can you say more about the need to be solved. Glass is produced in — to serve as a venue for ECMI mem- research activity in collaboration with an oven from raw material through bers at large industry? heating. The products are obtained — to explore new and relevant indus- A. Special interest groups play a key from pressing and blowing. This way trial areas where mathematics plays a role in the research branch of ECMI. (e.g.) bottles and jars, but also TV role They are typically application-orient- screens, are formed. Another way is Q. What about the present structure? ed, and provide a forum across bound- the production of pane (float glass). A. Originally there was an annual 14 EMS March 1999 INTERVIEW conference. Since 1994, ECMI has between researchers in industry and industrialists. organised only one bigger meeting academic applied mathematicians Q. Do you intend to disseminate this every two years; attendance is about — to provide a large number of idea further in the future? 400 persons, with 25% from industry. experts with varied expertise to con- A. At least three study groups will be Q. How do you stimulate interaction centrate on industries’ problems held in Europe each year, in different with industry for individual members — to act as an ‘introduction meeting’, universities in order to attract a wide of ECMI? so that industrialists are able to identi- range of industrial participants. Also, A. In addition to the biannual gener- fy the most useful group for further ECMI hopes to start a journal for the al conferences, ECMI organizes more collaboration publication of case studies of general frequent meetings and workshops — to stimulate academics by working interest, and reports from the Study specifically designed for interaction on problems that are both new and Groups will provide some suitable with industry. Let me mention the relevant and often present exciting problems for such a journal. mathematical challenges most regular activities: Q. What future do you envisage for — industrial days: since 1991 many of — to introduce students to industrial research in action ECMI? these industrial days have been organ- A. At the moment ECMI is experi- ised: typically, ECMI members — to provide recruitment possibilities for students. encing a new challenge. Although the address the industries of the country success rate in obtaining funding from where the meeting is organised. Q. How and where did they start? Brussels has been quite high, given the Typical attendance is about 50 people, A. The Study Groups were pioneered amount and character of the request with 50% from industry in Oxford and have since been copied for support, the actual impact has — special topic symposia: typically, appli- all over the world. In quite a few cases been much less than originally antici- cation areas like multi-body dynamics ECMI experts have helped to set up pated. or glass are surveyed. On the one hand such initiatives elsewhere. An annual Thus, concerted action, mainly industry can display timely problems, meeting has been held in the UK since steered by the newly appointed direc- and on the other experts can talk 1968, and since 1991 the meetings tor Dr Henk Kuiken, has been under- about their results. Attendance is have been designated European Study taken. As a result, ECMI is now in the about 50-80, with a large number from Groups with Industry. These meetings process of submitting a joint proposal industry are now held under the ECMI umbrel- with ECCOMAS for a ‘Network of — study groups with industry: week-long la and in 1998 besides the UK meeting excellence’ on mathematical model- meetings where a limited number of there was one in Denmark and one in ling and simulation. problems from industrial companies Holland. Also, membership of the EMS of current interest are modelled and Q. How do you evaluate the outcome (European Mathematical Society) has analysed. of this experience? been acquired in order to help com- Q. Do you train young graduates in A. The results of a Study Group bining the forces in Europe to achieve interaction with industry? meeting are very varied, but in every more visibility for mathematics. Quite A. As part of the ECMI educational case some benefit was gained by both recently, a request has come from yet programme ‘Mathematics in Industry’, the industrial sponsor and the acade- another European institution, ECMI organizes ‘modelling weeks’: mic participants. The involvement of ERCOFTAC, to set up some joint week-long meetings for training post- students in these meetings is also very activity; this illustrates how ECMI has graduates in modelling problems aris- valuable in giving them some insight grown up and will continue to do its ing in industry. This has largely a into industrial research, as well as pro- share in the coming years for mathe- didactical purpose; attendance is viding a recruitment opportunity for matics in industry. about 70 students and 10 university teachers. World Mathematical Year 2000 : Poster competition Q. Before ECMI, what experience existed on systematic interaction Vagn Lundsgaard Hansen between academia and industry in Europe? As one of the events during the World A. One of the first successful exam- Mathematical Year 2000, the European Posters in subways, ples in this respect are the so-called Mathematical Society, together with local math displays, ‘Study Groups with Industry’. This is a committees in several countries, wishes to Says, tried-and-tested method for initiating encourage the idea of posters with a mathe- the EMS committee of WMY: collaboration between industry and matical theme to be displayed in subways let a competition fly, academic mathematicians. Industrial and other public places. These posters don’t be shy, participants bring a specific problem should catch the eye, and be representative have a try, of current interest to a week-long of mathematics and its uses. The EMS is con- why? meeting hosted by a group of applied vinced that suitable posters will contribute to For the future of Mathematics! mathematicians. Intensive discussions raising the public awareness of mathematics. are held on each problem over several The EMS committee of WMY 2000 invites mathematicians to submit pro- days, followed by a verbal report at the posals for posters, in the form of a sketch of the graphics and a suggestion end of the week. A more detailed writ- for a short text. There will be prizes of 200, 150 and 100 ECU for the three ten report is completed within a few best proposals, and the name of the proposer will appear on all those posters weeks. which are eventually used. Proposals should be sent before 1 May 1999 to the Chairman of the EMS Q. What are the aims of such an ini- committee for WMY 2000: Prof. Vagn Lundsgaard Hansen, Department of tiative? Mathematics, Technical University of Denmark, Building 303, DK-2800 A. They are: Lyngby, Denmark; e-mail: hansen@ mat.dtu.dk — to create a mutually beneficial link EMS March 1999 15 POLITICAL CHANGE The impact on mathematics of political changes in Eastern Europe moderated by Peter Michor

This is the beginning of a discussion forum on work in a bank where his salary (for his For a long time many young talented per- the changes in Mathematics caused by the polit- knowledge in computer software) cannot sons were not accepted for the universi- ical landslide in Eastern Europe in the last ten be even compared with what he gets as a ties, could not obtain positions or years. To start this column a questionnaire was student or what he can hope to get in the degrees, could not go abroad, etc., sent out which is reproduced below. The nearby future as a teacher or researcher, because of the Soviet disgraces. Today we answers are the opinions of the authors alone; he is usually more lost for science in have other problems which also seem seri- only moderate corrections of English have been Russia than if he gets a position in the ous but which are of a completely differ- done. Further contributions to this column may university at the opposite point of the ent kind. But again we have the problem be sent to [email protected], who is will- globe. (In the latter case he at least some- of how to keep young persons in mathe- ing to collect them for the Newsletter. times visits us and tells us the latest news.) matics, who cannot survive on the almost 3/4. The main thing seems to be financial zero stipendia, salary, etc. Call for articles on the impact of the support. There are some grants like 4. My impression is that these organisa- political changes in Eastern Europe on INTAS grants which are given to relative- tions must become much more involved mathematics ly small groups and provide some support in the organization of contacts between This is an invitation to write an article for members of such groups. (ISF grants Russian and foreign mathematicians, about your personal experiences during were the most well organized and gener- especially young ones: up to now, we have and after the political changes in Europe ous in this respect, but they do not exist had extraordinary possibilities for con- since 1989 and about their impact on your any more.) They provide some help to tacts, which was difficult to imagine up to life as a mathematician. The Newsletter individuals, but not so much help and not the 90s, but we use them worse than dur- plans to give room for articles of this kind for so many individuals. And I doubt ing the stagnation. It is important to orga- and to initiate a discussion on the impact whether EMS can do the same. But possi- nize international seminars, miniconfer- of the political changes on mathematics. bly you can help us, say, to get journals for ences (not only in Moscow and St Here are some questions that you may our libraries. I don’t know if you can sup- Petersburg), and workshops. Also, we answer in this article: port scientific conferences in Russia have no special programmes for short (which can include covering travel exchanges between young mathemati- 1. How did you feel the influence of the expenses inside NIS, if you have enough cians from the West and Russia—such changes of the political background in money, or only covering the organizer’s programs are very important and useful your country during the last ten years on expenses otherwise). for both sides. science and mathematics? Answer by Anatoly Vershik Answer by Vladimir Arnold 2. How do you judge the role of the [e-mail: [email protected]] [e-mail: [email protected]] ‘brain drain’ for mathematics: as natural, as regrettable, or as positive for indi- 1. Besides the evident consequences of 1. The situation of scientists and of math- viduals? political changes in Russia and Eastern ematicians in Russia and in other former Europe (openness of contacts between Soviet Union countries has changed dras- 3. What are the most important prob- Russian and foreign scientists, end of the tically. The salary of a mathematician lems in any attempt to keep the power of the KGB and communist used to be sufficient, even attractive. Now Mathematical traditions of your country bureaucracy, etc.) which were very impor- the price of food at Moscow being close to alive? tant and positive changes for most active that in Paris, the salaries of mathemati- 4. What could be the role of EMS or mathematicians, I feel a very serious dan- cians in Russia are about a hundred times other transnational mathematical orga- ger for the future of Russian mathematics. smaller than those of their American col- nizations in the process? This is because many of its leaders moved leagues. (This was written in June 1998; in to the West, perhaps because they see no September the ratio reached three hun- perspective for further development of dred). Answer by Dmitri V. Anosov our science in Russia; consequently, The fact that we still have active math- [e-mail: [email protected]] young mathematicians took up this doubt ematicians is partially due to the tradi- 1. Unfortunately in Russia, as well as in in the future as a sign for moving from tional idealism of the Russian intelligen- all New Independent States (NIS), politi- Russia. The same process in other Eastern cia (which most Westerners consider as cal changes were accompanied by eco- countries seems not so dramatic. simple foolishness), and partially to the nomical changes and in changes of atti- 2. In a sense it is a natural process: a extremely important help of the occiden- tude towards science and education which brain drain in the whole world has existed tal mathematical community (and espe- are far from being favourable for them. for many years, and as usual Russia with a cially of SMF, AMS, ISF, IMU). For me and my group the negative conse- very big delay joins this process. But the It is interesting to note that the inde- quences of one factor are more or less in case of Russia is very special: even clear- pendent evaluations of about 6000 former balance with the positive consequences of sighted observers in the West emphasize Soviet Union mathematicians by the another—more freedom, less administra- how undesirable for World mathematics it AMS/ISF and by the Russian Basic tive control (although increases in is if that process exhausts all mathemati- Research Fund more or less coincided in bureaucracy), better exchange with the cal schools in this country and if we lose 80% of the cases, while in other sciences West. But take into account that in 1991 I our strongest traditions. Those schools the correlation was minimal. achieved the highest possible position in and traditions were created a long time We may be proud to see that the math- our scientific community (full member of ago, in spite of the Soviet regime which ematical scientific community is more the Russian Academy of Sciences) which prevented the natural development of sci- objective than the others and that the cri- makes the situation better for me than it ence and thanks to many talented scien- teria used by the Russian authorities are at would be otherwise. tists who were oppressed by the bureau- present (temporarily?) scientific and non- 2. I don’t think it is the brain drain itself cracy. discriminative. that causes a problem. If a student goes to 3. The main problem of course is youth. 2. The brain drain in the present situa-

16 EMS March 1999 POLITICAL CHANGE tion is an evil that one can’t avoid: it is people. Discussing the ethnic origin of a provide a copy of the passport of the only freined by the obstacles created by candidate as the reason for voting for or British citizen inviting me, as well as the the West. If the present situation does not against him has always been (and, I hope, description of the religious ceremony change, the future of the Russian mathe- will remain) impossible at the Russian accompanying my marriage. It seems matical school seems to be similar to that Academy of Sciences, even during its however that they are using these only of the great German mathematical school worse years: our antisemites were obliged against the blacks, the yellows, and the of Klein and Hilbert or of the Italian to invent ‘scientific’ arguments. French representatives of the bad religions: they school of algebraic geometry. Academy of Sciences members have gave me the visa in spite of the absence of Chebychev, who had spent much time objected to the election of candidates who the copy of the passport of the Director of abroad, had friendly personal relations are French ‘only by passport’. the Cambridge Newton Institute, who had with foreign mathematicians, but never Having participated in many interna- already agreed to provide the copy. discussed mathematics with them, being tional committees, selecting speakers or Of course, the Western scientific com- afraid that it might be harmful to the tenured professors, etc., I have become munity is completely unaware of all these originality of his own work. accustomed to hear my Western col- facts, isn’t it? I might provide dozens of The importance of the Russian mathe- leagues proposing to use non-scientific these, and in the Moscow newspapers matical school for the world mathematical arguments to eliminate the Russian candi- there were published accounts on worse community has always been related to its dates, who otherwise would fill too many stories of people staying for hours in originality and independence of occiden- places. There were four Russian plenary (sometimes thousands-long) waiting lines tal fashions. The feeling that what one is speakers at the Kyoto International at the Western consulates at Moscow. doing now will become fashionable in Congress in 1990, three at Zürich in 1994, twenty years is extremley helpful. and none at Berlin in 1998 (I am disre- Comment by Jean-Michel Lemaire, Unfortunately, this 20-year period has garding the present place of employment Directeur adjoint, Département Sciences started to diminish now, and the brain in these calculations, considering people Physiques et Mathématiques, Centre drain is one of the main mechanisms like, say, Manin or Kontsevich as National de la Recherche Scientifique: involved in this process. Russians). I do not think that the mathe- [e-mails: [email protected], 3. The Marquise de Pompadour’s spend- matical weight of our school has declined [email protected]] ing on sciences and culture formed about that fast. I explain the result by the same When Arnold says that inviting Eastern one-and-a-half percent of her spending discrimination that I observe in the com- European mathematicians through CNRS on dresses and perfumes etc., but it was mittees of which I am a member. would be ‘extremely difficult’, I am sorry sufficient to create the century of Recently I wrote a letter to the Notices to say that he simply did not try. CNRS Enlightenment, the Encyclopaedia, etc. of the AMS: ‘Is the discrimination against can invite foreign scientists as associate We have no Marquise de Pompadour in the Russian mathematicians politically researchers (chercheurs associés). These Russia, and it seems that a century of correct?’ They have eliminated both the positions are known in France, for some ignorance will come. I published a paper dangerous title and my theory explaining reason which has nothing to do with the on this in the Moscow newspaper Izvestia discrimination against the inventors, Red Army, as ‘postes rouges’, with all due on 16 January 1998; there is an English reproduced below: reverence to those who keep comparing translation of it in the London Mathematical ‘. . . there is a sociological reason why the French educational system with the Society Newsletter 259 (April 1998), 18–20. the American community is always sup- Red Army and CNRS with the Academy of 4. Of course even relatively modest con- porting businesslike development and Sciences of the USSR. tributions to the libraries and funds, publicity rather than invention: the soci- The application procedure can hardly stipends and half-time positions would be ety needs to encourage rather the fast be simpler: all that is required is an invi- extremley useful. Unfortunately the propagation of ideas than their creation. tation letter signed or approved by the European bureaucracy is even worse than, A typical example is the story of the tele- head of the CNRS unit, together with a say, the French one. I can invite some phone (probably unknown to the reader): CV and a research program of the candi- people to Paris using my personal grant the USA Supreme Court decided that Bell date; no form is required, and TeX, RTF, from the Institut Universitaire de France. had appropriated its invention (by pdf or html files are acceptable. It would be extremly difficult if I tried to Meucci) but only at a time when his prior- In the last three years (1996–98), about use the possibility provided by the ity has no longer any practical usefulness one-third of the available positions in University or by the CNRS. And it is com- for the inventor. . . ’ mathematics and theoretical physics have pletely impossible for me to use for an The elimination of discrimination been granted to Eastern European scien- invitation the European system (which against ‘non-Western’ scientists at the tists. The exact figures are the following: had accordingly been called ‘nazi’ in governmental level is perhaps a problem 1996 : 69 months out of 216 (1996 was the French newspapers) independently of the that the mathematical community can’t annus horribilis for the CNRS budget) number of years that I have been paying solve, but to make the nationalistic argu- 1997 : 128 months out of 328 French taxes although I was not born in ments at least morally unacceptable in the 1998 : 124 months out of 364 France. mathematicians’ selection procedures Such figures would suggest affirmative The international mathematical organ- seems to be a reasonable goal. action (according to North American isations should stop the shameful discrim- PS. There were some signs of positive speech, if not practice), rather than dis- ination against Russian scientists (as well development last year. During my first crimination. Actually, no such action, as against other non-Western ones: years in France I was spending more time affirmative or not, was taken by CNRS. Ukrainian, Chinese, Indians, etc.), or at the Prefecture de Police than giving my We just invited the best ones. should at least protest against it. three lecture courses at the University and Finally, I would like to mention that, I suppose that most of our occidental at the Ecole Normale. Last year I was no during the same period, CNRS has hired colleagues can’t imagine the degree of the longer asked to get permission from the 12 mathematicians and theoretical physi- humilations we have to go through at Prefecture to cross the French boundary cists from Eastern Europe on permanent their Consulates and Police stations to and am thus able to move freely, essen- full-time research positions. Moreover, come to their conferences, workshops, tially within the boundary of the Third five of the six available senior research etc. Reich. positions (Directeur de Recherche) have I have the feeling that the Western The English consulate at Paris has been granted to Eastern Europeans, two (French?) idea of human rights is the idea recently asked me by their official paper of which gave an invited lecture at ICM 98 of Human Rights of Western (French?) (among two dozen other documents) to in Berlin.

EMS March 1999 17 ANNIVERSARIES 1999 Anniversaries by June Barrow-Green and Jeremy Gray

Maria Gaetana Agnesi (d.1799) volume be translated into French, and a June Barrow-Green translation appeared The name Agnesi is familiar to most math- in 1775. In 1760 John ematicians through the cubic curve known Colson3 prepared an as ‘the witch of Agnesi’ and described by English translation the equation x2y = a2(a – y). Indeed, those [3], although, partly as unaware of its history may have been a result of his death tempted to speculate as to how the curve the same year, it was acquired its unusual name. Although the not actually published truth is rather more prosaic than might be until 1801. Colson imagined, as will be told below, the name had been so imp- nevertheless serves as a reminder of Maria ressed by Agnesi’s Gaetana Agnesi, the first European woman work that he had mathematician of the modern period. learnt Italian in order Maria Gaetana Agnesi was born in to make the transla- Milan in 1718, the eldest of twenty-one tion; and his transla- children of Pietro Agnesi whose family for- tion was not restricted tune had been made through silk1. She was just to words, he trans- well educated, her father providing the lated the notation too, best tutors locally available in philosophy, from Leibnizian to languages, natural sciences, mathematics Newtonian. and music. By the age of eleven she had However, a closer mastered several languages, including examination of the French, Latin, Greek, German, Spanish sources shows that and Hebrew, and in 1738 a volume was acclaim for the book published containing 191 philosophical was not as widespread theses she was prepared to defend, chal- as it might appear. lenging all comers. Accounts of her skill in Agnesi’s work received disputation show that she had become well almost no attention versed in the sciences, references being from the great mathe- made to her discussions of the theory of maticians of the eigh- tides, the emanation of light, the proper- teenth century, and ties of geometric curves, and her support later historians of for Newtonian philosophy. provides, perhaps, the best instruction and mathematics largely ignored it. As However, Agnesi soon became disen- the greatest light’. The preface also Truesdell has cogently argued, this was chanted with her life as a public display of includes a moving tribute to Rampinelli, as essentially because Agnesi’s book, although prodigious talent and, to her father’s dis- well as an acknowledgement to an earlier an undoubted model of clarity, contained may, decided to enter a convent. After calculus textbook by Reyneau [4]. nothing new or original, nor were there much persuasion she agreed to remain Apart from Rampinelli, one other per- any applications to mechanics. Although it with the family but on the condition that son had a considerable influence over the has been accurately described as ‘an expo- she could abandon the trappings of her Instituzioni Analitiche: the mathematician sition by examples rather than by theory’, former life. Settled at home she devoted Jacopo Riccati (1676–1754). Riccati was it does not include a single example of the herself to the study of religion and mathe- well known to Rampinelli, and on calculus being applied to natural phenom- matics. Her progress in mathematics was Rampinelli’s suggestion Agnesi wrote to ena, in contrast to other Continental books greatly advanced by the arrival in Milan of Riccati asking for advice and comments on of the period. Ramiro Rampinelli (1697–1759), a her work. Thus began a fruitful correspon- The book begins with elementary alge- Benedictine monk and mathematician who dence which lasted from 1745 to 1749 with bra, moves on to the theory of equations had formerly been a professor at Rome Riccati sending Agnesi many corrections and coordinate geometry, progresses in and Bologna. Rampinelli became a regular and annotations. The correspondence also Volume 2 to the differential and integral visitor to the household and soon took on included Riccati’s unpublished ‘method of calculus (including infinite series, as far as the role of Agnesi’s teacher. polynomials’ which he had devised many they were known at the time), and ends Agnesi’s first mathematical work, a com- years earlier, and which, at his behest, with the solution of elementary differential mentary on L’Hôpital’s posthumous trea- Agnesi included in her book with due equations. The discussion of the curve now tise on conic sections2, remains unpub- acknowledgement. known as ‘the witch of Agnesi’ appears lished. However, her second mathematical At first sight it seems that the Instituzioni towards the end of Volume 1 [1, p. 381]. work Instituzioni Analitiche ad Uso della Analitiche was a great success. Maria The curve, which had made its first Gioventù Italiana [1], a textbook on analysis Teresa, Grand Duchess of Austria and a appearance in the work of Fermat, was first which was privately printed in two volumes noted feminist to whom Agnesi had dedi- constructed in 1703 by Guido Grandi in 1748, made her famous. It was written in cated the work, showed her appreciation (1671–1742) who, in 1718, named it ‘ver- Italian (as opposed to Latin), partly for her by sending Agnesi a diamond-encrusted siera’ from the Latin ‘versiora’ meaning own benefit—she preferred writing in box. Pope Benedict IV, who had himself ‘rope that turns a sail’4. In her discussion of Italian—and partly because she wanted her studied mathematics, wrote personally to the curve Agnesi correctly followed Grandi work to be accessible to the Italian youth, congratulate her upon it and shortly after- in writing ‘la curva . . . dicesi la Versiera’. particularly her brothers. Her aim, as she wards appointed her honorary reader of The name ‘the witch’ appeared later, and stated in the preface, was to present the analysis at the University of Bologna; in only then as an error of translation. The material in such a way that it was ‘endowed 1750 he elevated the appointment to a culprit was Colson: in his translation he with proper clarity and simplicity . . . [and] chair of mathematics. In 1749 the French had made the simple mistake of confusing proceeds with that natural order which Academy recommended that the second ‘la Versiera’ with ‘l’aversiera’, and it is the 18 EMS March 1999 ANNIVERSARIES latter which means ‘the witch’ [3, p. 222]. theorem of plane projective geometry The more axioms one has, the more tight- Despite the fact that Agnesi had been (there is a map sending any given quadri- ly the coordinates are constrained. Thus if offered the chair in Bologna, she never vis- lateral to any other)? Could the fundamen- one has enough axioms one can prove ited the city to take up the appointment, tal theorem be derived from Desargues’ Desargues’ theorem in the plane. As although her name did remain on the rolls and Pappus’s theorems instead? In 1898 Hilbert was the first to show (with a need- of the university for forty-five years. Almost Friedrich Schur proved Pappus’s theorem lessly complicated proof that he replaced immediately after the publication of without assuming continuity, and Hilbert’s with one due to Moulton in later editions), Instituzioni Analitiche, possibly as the result insights began to crystallise. He was now at there are plane geometries in which of severe constraints imposed upon her by Göttingen (he had arrived in 1895) and Desargues’ theorem is false, but it follows her father, she began to devote herself from the incidence axioms in wholeheartedly to religion. She took over three or more dimensions. the instruction of her siblings, and Segment arithmetic then engaged herself in helping the poor and showed that the coordinates infirm. After her father’s death in 1752 she must be taken from a number became even more fervent in her religious system that obeys the associa- devotion and charitable work. She estab- tive law. If Pappus’s theorem lished a hospice for old women and spent is also true, then the number all her money supporting it. In 1771 she system must be commutative. became directress of a large poorhouse of In 1905 Hessenberg showed the church and died there, destitute, in that Pappus’s theorem 1799. implies Desargues’, but not 1 The Dictionary of Scientific Biography perpetuates the conversely. myth that Pietro Agnesi was a professor of mathematics The Grundlagen der in Bologna. The correct status of the Agnesi family has Geometrie did indeed exert a been fully documented by Anzoletti [2], see Truesdell major influence on mathe- [5, p.115]. 2 Guillaume de L’Hôpital, Traité analytique des sections matics. His friend Hurwitz coniques, Paris, 1720; according to Truesdell [5, p.123], hailed it as introducing a new this work was of ‘scant importance’ when it was origi- field of axiomatics into the nally published. subject (neglecting, as Hilbert 3 John Colson (1680–1760) held the Lucasian chair at Cambridge from 1739 to 1760. He published little of had, the strong Italian contri- distinction, concentrating most of his efforts on trans- bution during the 1890s). It lation; see his biography in The Dictionary of National inspired a number of prob- Biography and Truesdell [4, p.132 and footnote 42]. lems in the famous list 4 For a history of the curve, see G. Loria, Curve Piane Speciali Algebriche e Transcendenti, Teoria et Storia, Vol. 1, Hilbert presented in 1900 at Milan, 1930. the International Congress of Mathematicians in Paris. Bibliography American mathematicians 1. M. G. Agnesi, Instituzioni Analitiche ad especially were drawn to the Uso della Gioventù Italiana, Vol. 1, Milan, Klein asked him to write a memoir on the axiomatic foundations of many branches of 1748. occasion of the unveiling of the Gauss- mathematics. Its philosophical naïveté 2. L. Anzoletti, Maria Gaetana Agnesi, Weber statue there. Hilbert wrote his drew sharp criticisms from Frege, and Milan, 1900. Grundlagen der Geometrie. however much Hilbert seems to have want- 3. J. Colson, Analytical Institutions, Vol. 1, This booklet of some 90 pages divides ed to brush off Frege’s comments they may London, 1801. the axioms of geometry into five groups: well have alerted him to some of the com- 4. Charles René Reyneau, Analyse démon- incidence, order, parallels, congruence, plexities involved in defining numbers and trée ou la méthode de resoudre les problèmes des and continuity. This is not as transparent clarifying the relationship between mathe- mathématiques, et d’apprendre facilement ces as it might seem. The parallel axiom is not matics and logic, a growing concern of his sciences . . . , Paris, 1707. introduced to facilitate a discussion of non- in later years. Other imperfections, such as 5. C. Truesdell, Maria Gaetana Agnesi, Euclidean geometry; that had to wait for a the obscure talk about a complete system Archive for the History of Exact Sciences 40 separate publication (included in later edi- of axioms, helped Veblen to formulate the (1989), 113–142 and 43 (1991), 385–386. tions of the book) in which Bolyai- concept of categoricity. Subsequent edi- Lobachevskii was specifically described. In tions did not so much smooth this out as June Barrow-Green [j.e.barrow-green@ 1899 a non-Euclidean geometry for paper over the weak points with new expo- open.ac.uk] is a research fellow in the history of Hilbert was simply a geometry that was not sitions and add on numerous extensions. mathematics at the Open University, UK. Euclidean. The vexed issue of continuity Far from being a paradigm, the undoubt- (in 1899) was wrapped around the ed success of Hilbert’s Grundlagen der Hilbert’s ‘Grundlagen der Archimedean axiom: given any three Geometrie owes much to the growing fame points A, A1, and B on a line, construct a of its author and the collaborative and crit- Geometrie’ (1899) sequence of equal segments AA , A A , . . ical nature of work in mathematics. Jeremy Gray 1 1 2 . , An–1An such that B lies between An–1 and The first of what were to prove many edi- An. This last point hints at a possibly unex- Bibliography tions of David Hilbert’s Grundlagen der pected feature of the Grundlagen der D. Hilbert, Grundlagen der Geometrie, in Geometrie appeared in 1899. The novel Geometrie: its focus on non-Archimedean Festschrift zur Feier der Enthüllung des Gauss- character of the work, and its alleged geometries. These had been introduced Weber-Denkmals in Göttingen, Teubner, implications for the move towards abstract (one might say re-introduced) by Veronese Leipzig, 1899. axiomatic formulations of mathematics, in his Italian book of 1891, which Hilbert D. Hilbert, Foundations of Geometry, second are sometimes misunderstood, swallowed probably read in the German translation of English edition (translation of the tenth up in the folk memory of its remarkable 1894, and he footnoted it as a profound edition), Open Court, La Salle, Illinois, author. work in his Grundlagen. 1971. Hilbert had been interested in the founda- Hilbert then set about giving ingenious tions of geometry since lecturing on pro- accounts of what axioms imply what theo- jective geometry at Königsberg in 1891, rems, and which results are independent of Jeremy Gray [e-mail: [email protected]] is a and he followed the debate in the litera- each other. A key tool in this is the intro- senior lecturer in mathematics at the Open ture on the subject. Did one need continu- duction of coordinates, based on what University, UK. ity assumptions to prove the fundamental Hilbert called the arithmetic of segments. EMS March 1999 19 SOCIETIES Societies Section

The Union of Bulgarian organisations — the Society of Bulg- ic principles, comprise everything in arian Mathematicians (SBM) and the country which is related to mathe- Mathematicians Society of Bulgarian Physicists. In matics and computer science: holding Sava Grozdev 1977 a Constituent Congress was held, scientific events; supporting the pro- at which the UBM assumed its current fessional training of teachers, The Union of Bulgarian name. researchers and students; analysing Mathematicians (UBM) is a voluntary, In the last 30 years the number of problems of education at all stages; creative, non-political organisation sections of the UBM has been growing organising Olympiads, competitions whose purpose is to bring together swiftly, eventually reaching 71. With a and contests for students and teachers; people who are interested in mathe- fervour characteristic of the popularising Mathematics and matics and computer science or are Renaissance the members of the UBM Computer science among students involved in activities related to those recruit new sympathisers, and broaden and the general public. fields. The UBM is self-funded and and diversify their activities. In 1998, Since 1968 the UBM has been receives no bounty either from the the year of its anniversary, the UBM organising and holding annual Spring state or from any social institutions. had about 5000 members—teachers in conferences with scientific pro- The birthdate of the UBM was 14 mathematics and computer science, grammes that include topics in mathe- February 1898 when a group of enthu- university lecturers, and scholars and matics, computer science, mathemati- siastic lecturers from the Department specialists from all parts of the coun- cal modelling, mechanics, the teach- of Mathematics at the Higher School, try. In its 100 years of existence the ing of mathematics and computer sci- teachers from the two High schools in UBM has been chaired by internation- ence, etc. Problems of the structure Sofia at that time and the Chief ally renowned scholars and established and practice of contemporary educa- Secretary of the Ministry of Education social figures. Among its presidents tion, instructional texts, professional founded, under the leadership of Prof. have been Dr. Ivan Salabashev, Prof. training, etc., are discussed openly at Emanuil Ivanov, the Physical and Emanuil Ivanov, Dr. Stefan Lafchiev these events, and discussions termi- Mathematical Society (PMS), a fore- (for more than thirty years), Acad. nate in proposing solutions of the runner of the UBM. This happened Georgi Nadzhakov, Acad. Bojan most urgent questions. The Spring several months after the First Petkanchin, Assoc. Prof. Petko Ivanov, conferences present an opportunity International Congress of Mathemat- Prof. Alipi Mateev, Acad. Ljubomir for mutually useful contacts between icians at Zürich in August 1897. Thus Iliev (now Honorary President of the high-school teachers and university the UBM is only a few years younger UMB), Assoc. Prof. Ljubomir Davidov, instructors. than the renowned Göttingen Assoc. Prof. Chavdar Lozanov The UBM organises and co-organ- Mathematical Society instituted by F. (President at the time of writing). ises scientific events which cover a Klein and H. Weber in 1892. The activity of the first (and to this wide range of directions in mathemat- Generations of mathematicians, physi- date the only) organisation of mathe- ics and computer science. Among the cists and computer scientists are maticians and computer scientists in most noteworthy ones are the National deeply indebted to their patriotic pre- Bulgaria (whatever its name over the Seminar on Education in Mathematics cursors for the alliance which was years—PMS, BPMS, BMS, UBM) has and Computer Science, the National founded as early as the late 19th cen- been steadily directed towards the ful- Colloquium on Mathematics, the tury and has been bearing fruit for 100 filment and the enrichment of Computer Science Seminar, the years. Paragraph One of the first charter: Stochastics Seminar and the Seminar Since the very beginning of its exis- • to contribute towards the academic on Problems of Education at Technical tence, the UBM has been an open growth of its members and encour- Higher Schools. In the period organisation. As a result of the institu- age them to pursue original 1968–1998 more than 200 scientific tion of sections in many towns of the research; conferences, summer schools, sym- country, the UBM gradually became a • to monitor the progress of scientific posia, seminars, etc., have been held, national enterprise. For this reason at literature in the areas of physics and with over 30000 attendants from more its 40th anniversary the PMS was mathematics; than 40 countries. renamed the Bulgarian Physical and • to raise and discuss questions on One of the major activities of the Mathematical Society (BPMS). education and point out means and UBM is to work with talented students Initially, apart from the mathemati- methods for its improvement in and their teachers. Through its team cians, its membership included physi- general; for out-of-school work in mathematics cists, engineers, military servicemen, • to develop the general and the and computer science, which includes meteorologists, land-surveyors, school instructional Bulgarian terminology scholars from the Bulgarian Academy and college students (for example, the of these sciences; of Sciences, university lecturers and student section in the town of Stara • to critically survey books and text- outstanding school teachers, the UBM Zagora had 120 members in 1939, the books (especially Bulgarian ones) provides scientific guidance for all one in the region of Rajkovo had 200 on physics and mathematics; national olympiads and competitions members in 1940). Mathematicians, • to offer moral and material support as well as preparating Bulgarian rep- physicists, computer scientists and for the publication of independent resentatives at International others researching closely related sci- research work and of good manuals Olympiads, Balkaniads, etc. in mathe- entific issues and problems of educa- and textbooks. matics and computer science. tion worked together in the same soci- At present the activities of the UBM, On the international scene the ety until 1971, when they decided to whose organisation and management UBM cooperates with kindred organi- separate and to form two independent are founded on contemporary scientif- sations in Greece, Luxembourg, the 20 EMS March 1999 SOCIETIES USA, Macedonia, Canada, as well as teenth century individual universities and institutes in onwards. Russell Russia, Rumania, the Czech Republic, is the family Germany, etc. Cooperation is based on name of the direct contacts and exchange of spe- Dukes of cialists. Joint events are also organ- Bedford; ised. The UBM is a member of the Bertrand Russell European Mathematical Society and of was a relative. the American Mathematical Society. The headquar- They style mathematics the Queen ters were formally of Sciences, because the development opened in of any scientific field is unthinkable October 1998, without the tangible participation of and named De mathematics. The 21st century will be Morgan House in the century of mathematics and com- honour of puter science, of computers and com- Augustus De puter technologies, and this is one of Morgan, by Sir the reasons that the year 2000 has Michael Atiyah, been chosen as World Mathematical former President Year by UNESCO—World Year of the of the Society, De Queen of Sciences. Morgan medallist Sava Grozdev [e-mail: savagroz@math. and Fields medal- bas.bg] is General Secretary of the Union of list. He was sup- Bulgarian Mathematicians ported by other Fields medallist London Mathematical Society : home of the Royal Academy; at pre- members of the Society living and sent large crowds are thronging to the working in Britain: Alan Baker, De Morgan House exhibition ‘Monet in the twentieth Richard Borcherds, Simon Donaldson, Ben Garling century’. The Royal Academy is set Timothy Gowers, Daniel Quillen and back from Piccadilly; the wings on Klaus Roth. At the opening, David The London Mathematical Society was either side of the courtyard are occu- Larman, head of the Mathematics founded in 1865 in University pied by learned societies such as the Department at University College, College, London. University College Society of Antiquaries, the Royal presented the Society with two pictures had itself been founded in Astronomical Society, the Royal of De Morgan. The Society has once Bloomsbury, north of central London, Society of Chemistry, the Linnean again become a close neighbour of in 1826, both as a geographical coun- Society and the Geological Society. University College, and uses its lecture terbalance to the Universities of Until recently, the Society occupied a rooms for its meetings. Oxford and Cambridge and as a secu- single room at the top of the Royal What does De Morgan House pro- lar counterbalance to the religious Astronomical Society, and there the vide? Besides offices, it has a spacious restrictions that then existed in Society developed and flourished. The Council Room, called the Hardy Oxford and Cambridge. Royal Astronomical Society were gra- Room in honour of G. H. Hardy, University College had some strong cious hosts; Council met in its Council active member and generous benefac- and argumentative characters, but room, and Society meetings were fre- tor of the Society; this doubles as a none more so than Augustus De quently held in the Linnean Society’s seminar room for up to 40 people. It Morgan, Professor of Mathematics lecture room, next door. has a comfortable and elegant from 1827 to 1831, and from 1836 to It was decided at a retreat that the Members’ Room, called the 1866: he resigned from his Chair Society held in Oxford in April 1997 Verblunsky room after Professor S. twice, on each occasion on a matter of that the Society needed to expand its Verblunsky, whose benefaction was principle. The Society was established activities, and the fundamental deci- used to furnish it. This is a convenient as a result of the efforts of his son sion was made that it should acquire centre for members visiting London George and a friend of his, but premises of its own. The requirements — and please remember that reciproc- Augustus soon became heavily that were imposed were severe: the ity membership is available to mem- involved, and was elected the Society’s headquarters should be centrally bers of the Belgian, Danish, Dutch, first President. placed and easy to reach by visitors Finnish, French, German, Italian, The Society was originally intended from outside London, there should be Norwegian, Swedish and Swiss mathe- to be an internal society of University a suitable room where Council could matical societies (for details, e-mail College, but by the inaugural meeting meet, they should be near suitable lec- [email protected]). But above all, De it had been decided that its scope ture rooms, and the building should Morgan House provides a firm base should be wider, and it was named the have an appropriate presence. from which the London Mathematical London Mathematical Society. To Nevertheless, the Society found such a Society can expand its present activi- begin with it was run from University building, and moved in during ties, and undertake new tasks, in its College, but it very rapidly became a February 1998. endeavours to forward the cause of Society meeting the needs of all The Society’s headquarters are situ- mathematics. British mathematicians, and within ated in Russell Square, the largest of two years it had moved to premises in the squares in Bloomsbury. All this Ben Garling [e-mail: [email protected]] Burlington House. part of Bloomsbury is part of the is Executive Secretary of the London Visitors to London will know Bedford estate, and was developed by Mathematical Society and a Fellow of St Burlington House in Piccadilly as the the Dukes of Bedford from the eigh- John’s College, Cambridge.

EMS March 1999 21 OBITUARY Obituary of André Weil Beyond the frontier of numbers Jeremy Gray André Weil, who has died aged 92, was Weil was scathing about mathemati- Grothendieck and Deligne, were one of the century’s greatest mathe- cians who base conjectures on little awarded Fields medals, the mathemat- maticians. He will be remembered not more than their own failure to prove a ical equivalent of the Nobel prize, but only for his own remarkable achieve- result they would like to be true. His never Weil. This is perhaps because ments, but for his profound conjec- conjectures were precise but profound the first were awarded in 1936, and tures, which helped direct research for generalisations of known results, and the next in 1950, by which time he was a generation. He was also one of the by putting them in the public domain above the notional limit of 40. founders of an encyclopaedic group he carried out the duty of the leading After the second world war, Weil of, largely French, mathematicians, mathematicians of any period: to became a professor at Chicago and jokingly named “Nicolas Bourbaki” shape the future of the subject. In this later at the Institute for Advanced after a general who fought in the enterprise he was greatly helped by Study at Princeton. There he collabo- Franco-Prussian war. Nicolas Bourbaki. rated with a number of famous mathe- Weil was born in Paris and graduat- As a mathematician in his twenties, maticians, and through major books ed from the Ecole Normale Weil had become painfully aware of and papers over many years, contin- Supérieure at the age of 19. He then how many of the older generation of ued to exert considerable influence on travelled extensively, spending two French mathematicians had died in the growth of mathematics in America. years at Aligarh Muslim University in the first world war, and how far, as a In later life he took an interest in the India from 1930 to 1932, before result, France lagged behind Germany history of mathematics. He wrote a returning to France, where he taught in the study of the subject. He drew fine and sensitive study of number the- at Strasbourg until 1939. When the like-minded mathematicians around ory from Babylonian times to 1800, second world war broke out he was a him, and they set themselves the task and edited some of the work of his conscientious objector, and spent four of writing a one-volume book which great predecessors, Jacques Bernoulli months in Bonne Nouvelle prison, would present modern analysis — and Pierre Fermat. Rouen, where, as the son of Jewish essentially the calculus — in a useful In 1994, his lifetime of achievement parents, his life was imperilled. but rigorous form. was acknowledged when he was award- Eventually he was able to make his way Inspired by the comic traditions of ed the Kyoto prize in basic science to America. During this period he the Ecole Normale Supérieure, Weil from the Inamori Foundation of exchanged many letters with his jokingly gave the group the name Kyoto, Japan. His wife, Eveline, died younger sister, Simone Weil, the social Nicolas Bourbaki. The project grew in 1986. He is survived by two daugh- activist and mystical philospher who and came to reflect the interests of its ters and three grandchildren. died in England in 1943. founders, who included such notables It was also in the difficult years of as Claude Chevalley and Jean the early 1940s that Weil began to for- Dieudonné. They were largely dis- mulate his profoundest ideas on math- persed by the second world war, but ematics. His first significant result, reunited afterwards in Nancy and published in 1929, extended the ideas Chicago. of Henri Poincaré, who had indicated By now the project was one of writ- that results in number theory might be ing the equivalent of Euclid’s Elements, obtained by thinking geometrically. an entire encyclopaedia of modern, Weil’s later conjectures drew togeth- largely pure, mathematics. The group er a range of geometric ideas of Italian of seven Bourbaki met regularly and origin with problems in the theory of circulated drafts to heated debate. numbers much studied by German Unanimity was required before any- mathematicians. They extended thing was published. Membership in Poincaré’s ideas from one to any num- Bourbaki lapses at the age of 50, and ber of dimensions, and made sense several generations have been through only by bold analogy with the develop- it. ing field of topology. But while the Because of the eminence of individ- conjectures made sense, and could ual members their encyclopaedia has even be verified in simple cases, none had an extraordinary influence in of the known topological methods France and French-speaking coun- applied, and Weil called for a massive tries, although it is often criticised for extension of topological methods to its abstract style, lacking in motivation the new setting. His four conjectures and application. But pedagogy was André Weil, mathematician were eventually solved by later mem- never the aim of Bourbaki, whose sem- born May 6, 1906 bers of Bourbaki — two by Alexandre inars set the tone for research interna- died August 6, 1998 Grothendieck, and the last by Pierre tionally for many years. In keeping Deligne — in the early 1970s. The with the original joke, Bourbaki methods invented led to the decisive enjoyed a semi-public life, attending [This obituary appeared in The ‘Guardian’ tools by which Fermat’s Theorem and conferences, giving papers, denying on 12 August 1998; the photograph is several other major results in mathe- that he was a collective fiction. reproduced courtesy of the London matics have recently been solved. Several Bourbaki, including Mathematical Society]

22 EMS March 1999 MEETINGS

Oberwolfach Programme 2000 Mathematisches Forschungsinstitut Oberwolfach Lorenzhof, D-77709 Oberwolfach-Walke, Germany

Names of organisers are in square brackets. and Representation Theory [Ulrich Brehm (Dresden), Jacob Participants of the meetings at Oberwolfach [Stephen Kudla (College Park), Goodman (New York), Richard are invited personally by the director of the Joachim Schwermer (Düsseldorf)] Pollack (New York), Jörg Wills institute; the participation is subject to 12-18 March: Mathematische (Siegen)] such an invitation. Interested researchers, Stochastik 4-10 June: Optimale Steuerung in particular young mathematicians, can [Peter Bickel (Berkeley), Simon komplexer dynamischer Strukturen contact the administration of the institute. Tavare (Los Angeles), Anton [Karl-Heinz Hoffmann (München), Since the number of participants is restrict- Wakolbinger (Frankfurt)] Günter Leugering (Bayreuth), Jürgen ed, not all enquiries can be considered. 19-25 March: Functional Analysis Sprekels (Berlin), Fredi Tröltzsch Information is also available on our website and Partial Differential Equations (Chemnitz)] http://www.mfo.de [Wolfgang Arendt (Ulm), Philippe 11-17 June: DMV-Seminars 2-8 January: Kombinatorik Benilan (Besançon), Philippe [organisers to be announced] [Laszló Lovász (New Haven), Hans Clement (Delft), Jan Prüss (Halle)] 18-24 June: Topics in Classical Jürgen Prömel (Berlin)] 26 March-1 April: Algebraic Geometry 9-15 January: Kontinuierliche Nichtkommutative Geometrie [David Eisenbud (Waltham), Joseph Optimierung und [Alain Connes (Paris), Joachim Cuntz Harris (Cambridge), Frank-Olaf Industrieanwendungen (Münster), Marc Rieffel (Berkeley)] Schreyer (Bayreuth)] [Aharon Ben-Tal (Haifa), Arkadii 2-8 April: Arbeitsgemienschaft mit 25 June-1 July: Geometric Analysis Nemirovskii (Haifa), Josef Stoer aktuellem Thema (wird in Heft and Singular Spaces (Würzburg), Jochem Zowe (Erlangen)] 1/2000 der DMV-Mitteilungen [Jean-Michel Bismut (Orsay), Jochen 16-22 January: Modelltheorie bekanntgegeben) Brüning (Berlin), Richard Melrose [Alexander Prestel (Konstanz), Martin [organisers to be announced] (Cambridge)] Ziegler (Freiburg)] 9-15 April Diophantische 2-8 July: Calculus of Variations 23-29 January: Mathematik poröser Approximationen [Gianni Dal Maso (Trieste), Gero Medien [Hugh Montgomery (Ann Arbor), Friesecke (Oxford), Frederic Helein [Cornelius van Duijn (Amsterdam), Yuri Nesterenko (Moscow), Hans (Cachan)] Peter Knabner (Erlangen)] Peter Schlickewei (Marburg), Robert 9-15 July: Harmonische Analysis 30 January-5 February: The History Tijdeman (Leiden)] und Darstellungstheorie topologis- of the Mathematics of the 20th 16-22 April: Gitterlose cher Gruppen Century Diskretisierugen für partielle [Roger Howe (New Haven), Eberhard [Moritz Epple (Mainz), Jeremy Gray Differentialgleichungen Kaniuth (Paderborn), Gerard (Milton Keynes), Jesper Lützen [Ivo Babuska (Austin), Michael Schiffman (Strasbourg)] (Copenhagen)] Griebel (Bonn), Harry Yserentant 16-22 July: Mathematical Aspects of 6-12 February: Medical Statistics: (Tübingen)] Gravitation Current Developments in Statistical 23-29 April: Representation Theory [Gerhard Huisken (Tübingen), James Methodology for Clinical Trials and Complex Analysis Isenberg (Eugene), Alan Rendall [Helmut Schäfer (Marburg), Richard [Jacques Faraut (Paris), Alan (Potsdam)] Simon (Bethesda)] Huckleberry (Bochum), Karl- 23-29 July: Cohomology of Finite 13-19 February: Geometric Hermann Neeb (Darmstadt)] Groups: Interactions and Stochastic Analysis 30 April-6 May: Kodierungstheorie Applications [Kenneth Elworthy (Warwick), Jürgen [Gerard van der Geer (Amsterdam), [Alejandro Adem (Madison), Jon Jost (Leipzig), Karl-Theodor Sturm Henning Stichtenoch (Essen), Vijay Carlson (Athens), Hans-Werner Henn (Bonn)] Kumar (Los Angeles)] (Strasbourg)] 20-26 February: 7-13 May: Stochastic Analysis in 30 July-5 August: Arithmetic Darstellungstheorie endlich-dimen- Finance and Insurance Algebraic Geometry sionaler Algebren [Darrell Duffie (Stanford), Paul [Gert Faltings (Bonn), Günter Harder [Idun Reiten (Dragvoll), Claus Embrechts (Zürich), Hans Föllmer (Bonn), Nicholas Katz (Princeton)] Michael Ringel (Bielefeld)] (Berlin)] 6-12 August: Effiziente Algorithmen 27 February-4 March: Lattices, 14-20 May: Affine Algebraic [Susanne Albers (Paderborn), Torben Polytopes and Tilings Geometry Hagerup (Frankfurt), Giuseppe [Nikolai Dolbilin (Moscow), Rudolf [Hubert Flenner (Bochum), Italiano (Rome), Kurt Mehlhorn Scharlau (Dortmund)] Hanspeter Kraft (Basel), Peter Russell (Saarbrücken)] 27 February-4 March: Sparse (Montreal)] 13-19 August: Jordan-Algebren Approximation of Non-Local 21-27 May: Self-interacting Random [Wilhelm Kaup (Tübingen), Kevin Operators Processes McCrimmon (Charlottesville), Holger [Wolfgang Hackbusch (Kiel), Tobias [Erwin Bolthausen (Zürich), David Petersson (Hagen), Efim Zelmanov von Petersdorff (College Park), Stefan Brydges (Charlottesville), Frank den (New Haven)] Sauter (Leipzig)] Hollander (Nijmegen)] 20-26 August: Mathematical 5-11 March: Automorphic Forms 28 May-3 June: Discrete Geometry Continuum Mechanics

EMS March 1999 23 MEETINGS [John Ball (Oxford), Richard James 3-9 December: The Mathematics of Bernold Fiedler (Berlin), John (Minneapolis), Stefan Müller Discrete Tomography Guckenheimer (Ithaca)] (Leipzig)] [Richard Gardner (Bellingham), Peter 17-23 December: 27 August-2 September: Komplexe Gritzmann (München)] Thermodynamische Analysis 10-16 December: Global Invariant Materialtheorien [Jean-Pierre Demailly (St Martin Manifolds in Dynamical Systems [Wolfgang Bürger (Karlsruhe), Ingo d’Heres), Klaus Hulek (Hannover), [Wolf-Jürgen Beyn (Bielefeld), Müller (Berlin)] Thomas Peternell (Bayreuth)] 3-9 September: Analytical and Statistical Approaches to Fluid Models [Peter Constantin (Chicago), Alexander Mielke (Hannover), Edriss Titi (Irvine)] Call for Proposals for Scientific Meetings in the 10-16 September: INTERNATIONAL MATHEMATICAL BANACH CENTER Komplexitätskontrolle bei starken Abhängigkeiten Warsaw, Poland [Ursula Gather (Dortmung), Wolfgang Härdle (Berlin), Joel Horowitz (Iowa City)] 17-23 September: Niedrigdimensionale Topologie The Institute of Mathematics of the Polish Academy of [Michel Boileau (Toulouse), Klaus Johannson (Knoxville), Heiner Sciences announces a competition for organizing scientific Zieschang (Bochum)] meetings in mathematics and applied mathematics at the 24-30 September: Topologie International Mathematical Banach Center, Warsaw, Poland, [Robion Kirby (Berkeley), Wolfgang Lück (Münster), Elmer Rees for the years 2000-2001. Interdisciplinary meetings related (Edinburgh)] to mathematics are particularly welcome. The meetings can 1-7 October: Geometrie take the form of semesters, mini-semesters, conferences, [Victor Bangert (Freiburg), Yurii Burago (St Petersburg), Ulrich Pinkall workshops or intensive schools for graduate students. The (Berlin)] Banach Center provides essential financial support; inde- 8-14 October: Arbeitsgemeinschaft mit aktuallem Thema (wird in Heft pendently, there are other possibilities for obtaining addi- 3/2000 der DMV-Mitteilungen tional funds. The deadline for applications is 30 April 1999. bekanntgegeben) At the beginning of May the Scientific Council of the [organisers to be announced] 15-21 October: DMV-Seminars Banach Center, chaired by Professor Friedrich Hirzebruch, [organisers to be announced] will consider applications. The selected applications will 22-28 October: Hyperbolic appear in the official program of the Banach Center for Conservation Laws [Constantine Dafermos (Providence), 2000-2001. Dietmar Kröner (Freiburg), Randall Independently of the above meetings, the Banach Center LeVeque (Seattle)] organizes ‘research groups’ (smaller gatherings of 2-15 29 October-4 November: Random Matrices people). Applications for research groups are independent [Philippe Biane (Paris), Andreas of larger conferences or semesters and can be submitted at Knauf (Leipzig), Peter Sarnak (Princeton)] any time, preferably about 4-6 months in advance, and the 5-11 November: acceptance procedure is much simpler. Fortbildungslehrgang für In the age of electronic communication, practically all Studienräte [organisers to be announced] organizational work can be done via e-mail. Because of this, 12-18 November: DMV-Seminars there are no restrictions on the location of the organizers. [organisers to be announced] Additional information, including application procedures, 19-25 November: Complexity Theory can be obtained from the following address and Internet [Joachim von zur Gathen site: (Paderborn), Oded Goldreich Secretary, Banach Center, Mokotowska 25, PO Box 137, 00- (Rehovot), Claus-Peter Schnorr (Frankfurt)] 950 Warsaw, Poland 26 November-2 December: tel: (+48)-22-628-0192; fax: (+48)-22-622-5750 Nichtnegative Matrizen, M-Matrizen und deren Verallgemeinerungen e-mail: [email protected] or [email protected] [Daniel Hershkowitz (Haifa), Volker http://www.impan.gov.pl/BC Mehrmann (Chemnitz), Hans Schneider (Madison)]

24 EMS March 1999 CONFERENCES Forthcoming conferences compiled by Kathleen A S Quinn

Please e-mail announcements of European con- 1998] Note: accommodation at C.I.R.M. is limit- ferences, workshops and mathematical meetings 14-16: BLMS’99 (Joint meeting of the ed; requests by 31 March (preferably elec- of interest to EMS members, to k.a.s.quinn@ Belgian Mathematical Society and the tronically) open.ac.uk. Announcements should be written London Mathematical Society), Brussels, Information: contact Mlle. Bernadette in a style similar to those below, and sent as text Belgium Lacan, Département de Mathématiques, files or MSWord files (not as TeX input files). Topics: algebraic geometry and mathe- Université de Montpellier 2, F-34095 Space permitting, each announcement will matical logic; combinatorics and finite Montpellier 5, France; fax: (+33)-467-14- appear in detail in the next issue of the geometries; differential geometry and 35-58 Newsletter to go to press, and thereafter will be mathematical physics; stochastic mathe- e-mail: [email protected] briefly noted in each new issue until the meeting matics http://www.math.univmontp2.fr/vaque- takes place, with a reference to the issue in which Programme: four plenary lectures; eight rias/homologiques.html the detailed announcement appeared. The pre- 40-minute lectures in each of the above 26-28: Crystallographic Groups and their sent issue includes conferences up to September areas Generalizations, Kortrijk, Belgium 1999. Speakers: plenary lecturers: H. Föllmer Scope: recent developments concerning Organisers:(Berlin), W. T. Gowers (Cambridge), M. crystallographic groups, and their general- April 1999 Kontsevich (IHES), A. Macintyre izations; topics include affine crystallo- 18-24: Spring School on Functional (Edinburgh); algebraic geometry: D. graphic groups and affine manifolds, Analysis, Paseky, Czech Republic Abramovitch (Boston), A. Borovik almost crystallographic groups and infra- Programme: four series of lectures given (Manchester), Z. Chatzidakis (Paris), M. nilmanifolds, polynomial structures on by Isaac Namioka (Seattle), Recent trends in Coppens (Ceel), T. Gardner (Oxford), F. polycyclic-by-finite groups and polynomial Banach spaces, Vladimir Fonf (Negev), Loeser (Paris), T. Scanlon (Berkeley), W. manifolds, discrete subgroups of Lie Polyhedral Banach spaces, Jesus Castillo Veys (Leuven); combinatorics: M. Aigner groups and homogeneous spaces, localisa- (Extremadura), Structure of subspaces and (Berlin), A. E. Brouwer (Eindhoven), F. tion problems for groups, finitely generat- quotients of Banach spaces and Nigel Kalton Buekenhout (Brussels), W. Haemers ed groups, quasi-isometry and rigidity, (Missouri), title to be announced; there will (Tilburg), J. W. P. Hirschfeld (Sussex), H. geometric group theory also be short communications Van Maldeghem (Cent), D. Welsh Organisers: Paul Igodt, Karel Dekimpe Information: contact Jaroslav Lukes, (Oxford), G. Ziegler (Berlin); differential and Wim Malfait (Kortrijk), Yves Felix Department of Mathematical Analysis, geometry: J.-C. Alvarez (Louvain), B. (Louvain la Neuve) Sokolovská 83, 186 75 Praha 8, Czech Bowditch (Southampton), M. Cahen Programme committee: H. Abels Republic (Brussels), R. Dijkgraaf (Amsterdam), B. (Bielefeld), Y. Felix (Louvain la Neuve), F. e-mail: [email protected] Driver (San Diego), M. Gross (Warwick), D. Grunewald (Dusseldorf), P. Igodt http://www.karlin.mff.cuni.cz/katedry/kma/ Joyce (Oxford), A. Reznikov (Durham); sto- (Leuven/Kortrijk) ss chastic mathematics: L. Devroye (McGill), B. Information: contact Paul Igodt, K. U. [for details see EMS Newsletter 30, December Driver (San Diego), P. Embrechts (Zürich), Leuven Campus Kortrijk, Department of 1998] R. Griffiths (Oxford), G. Louchard Mathematics, Etienne Sabbelaan 53, B- 22-24: Inverse Problems in Stratified (Brussels), G. P. Nason (Bristol), D. O. 8500 Kortrijk; tel: (+32)-56-24-61-37; fax: Media, Aarhus, Denmark Siegmund (Stanford/Cambridge), J. (+32)-56-24-69-99 Organiser: MaPhySto: Centre for Teugels (Leuven) e-mail: [email protected] Mathematical Physics and Stochastics Local organising committee: L. Lemaire, http://www.kulak.ac.be/workshop Programme committee: J.-C. Guillot J. Leroy, M. Parker, Campus Plaine ULB 27-29: Mathematics towards the Third (Paris), B. H. Jacobsen (Aarhus), A. Jensen Information: contact Jules Leroy, Campus Millenium, Rome, Italy ( Aalborg) Plaine ULB, C.P. 218/01, Boulevard du Aim: to present a wide spectrum of trends Information: e-mail: [email protected] Triomphe, B-1050 Brussels, Belgium; tel: of current research that might serve as http://www.maphysto.dk/events/InvProbW (+32)-2-650-58-45; fax: (+32)-2-650-58- guidelines for future developments 99/ 67 Speakers: V. Arnold, E. Bombieri, A. Organisers:e-mail: [email protected] Connes, C. Fefferman, P. Griffiths, M. May 1999 http://www.ulb.ac.be/assoc/bms/BLMS Gromov, M. Kontsevitch, E. Lieb, D. 12-20: Advanced Course on Integral ’99html McDuff, D. Mumford, M. Talagrand, K. Operators and Related Problems, Tbilisi, [For details see EMS Newsletter 30, December Uhlenbeck, D. Vogan Georgia 1998] Organisers: S. Abeasis, V. Baldoni, G. M. Programme: the course is suitable for 17-21: Méthodes homologiques, Luminy, Piacentini Cattaneo, E. Prestini, C. Rossi, advanced graduate student or recent France E. Strickland, G. Tarantello Ph.D.s; there are three series of lectures by Scope: Hochschild homology and cyclic Site: Accademia Nazionale dei Lincei, Paolo Ricci (Rome) on Generalised orthogo- homology, algebraic K-theory, theory of Rome nal polynomials of hypergeometric type, classical groups and representations, Hopf Information: contact Dipartimento di Computation of Newton sum-rules for the zeros algebras, Hochschild cohomology and the Matematica, Universita di Roma Tor of orthogonal polynomials, Computation of the theory of representations of algebras of Vergata, Via della Ricerca Scientifica eigenvalues of second-kind Fredholm operators, finite dimension; this colloquium is part of 00133, Roma, Italy; tel/fax: (+39)-6- and one series by Dazmir Schulaia (Tbilisi) the programme of cooperation between 2023507 on Linear theory of integral equations and their France and several Latin American coun- e-mail: [email protected] applications tries: Argentina, Brazil, Chile, Colombia http://www.mat.uniroma2.it/~math2000 Information: contact TICMI, I. Vekua and Uruguay Institute of Applied Mathematics of Tbilisi Organisers: Claude Cibils (Montpellier) Organisers: State University, University Str. 2, Tbilisi and Max Karoubi (Paris) June 1999 380043, Georgia; tel: (+995)-32-305995 Programme committee: T. Lambre 4-9: EURESCO: Geometry, Analysis & e-mail: [email protected] (Orsay), A. Solotar (Buenos Aires/Orsay), J. Mathematical Physics: Analysis & http://www.viam.hepi.edu.ge/others/ Soto-Andrade (Santiago) Geometry, Obernai (near Strasbourg), TICMI Site: C.I.R.M. (Centre Internat. de France [for details see EMS Newsletter 30, December Rencontres Mathématiques) Scope: to review recent developments in EMS March 1999 25 CONFERENCES symplectic geometry, contact geometry algebra; design techniques; numerical Grants: some support will be available for and Floer homology, Gromov-Witten methods; parallel and distributed algo- graduate students invariants and mirror symmetry, rithms; computer modelling in dynamical Site: University of Messina, Sicily, Italy Donaldson and Selberg-Witten invariants, systems; mathematical models in biology, Information: anyone interested in further symplectic analysis in infinite dimensions, medicine, ecology, etc.; applications to information should send to the organisers: moduli spaces physics, electrotechniques, and electronics; name, institution, e-mail address and esti- Organiser: Jean-Michel Bismut (Orsay) dynamic economic models; general macro- mated probability of attending; address: Speakers: D. Auroux (Paris), P. Biran economic models; market models Department of Mathematics, Faculty of (Stanford), Y. Chekanov (Moscow), R. Programme: 1-hour invited lectures and Science, University of Messina Dikgraaf (Amsterdam), R. Fintushel 20-minute presentations of contributed e-mail: [email protected] (Michigan), E. Getzler (Northwestern), E. papers; invited talks will highlight some of http://dipmat.unime.it/caag Giroux (Lyon), V. Giventhal (Berkeley), L. the major accomplishments, trends and 19-25: Dynamics of Patterns, Anogia, Jeffrey (Toronto), Y. Karshon (Jerusalem), problems in the theory Crete, Greece M. Kontsevich (Bures/Yvette), S. Kuskin Working languages: English and Russian [part of the series Euroconferences in (Edinburgh), G. Liu (UCLA), E. Call for papers: papers are selected on the Mathematics on Crete] Meinrenken (Toronto), T. Mrowka (MIT), basis of an abstract (1-2 complete pages, Organisers: N. Alikakos (Athens), J. W. Nahm (Bonn), L. Polterovich (Tel hard copy only), which should include the Ockendon (Oxford), G. Papanicolaou Aviv), Y. Ruan (Wisconsin), M. Schwarz title of the paper, names, addresses and (Stanford) (Stanford), P. Seidel (Bonn), J.-C. Sikorav complete affiliations of all authors, and Main speakers: G. Fusco (L’Aquila, Italy), (Toulouse), K. Uhlenbeck (Austin), S. T. appropriate references W. Jaeger (Heidelberg), J. Ockendon Yau (Harvard) Organising committee: G. S. Osipenko (Oxford), E. Presutti (Rome), M. Soner Information: contact Dr. J. Hendekovic, (chair),Yuri Ivanov (secretary) (Princeton), M. Struwe (Zürich) European Science Foundation, 1 quai Scientific committee: G. Tardivel (UK), A. Fees: registration fee 250 ECU; living Lezay-Marnésia, 67080 Strasbourg Cedex, Kasterin (Russia), D. Dytte (Denmark), M. expenses (accommodation plus meals) per France; tel: (+33)-3-88-76-71-35; fax: Seppala (Finland), G. Picci (Italy), B. person per day about 30 ECU (double (+33)-3-88-36-69-87 Fuchssteiner (Germany), A. Zhizchenko room) or 38 ECU (single room) e-mail: [email protected] (Russia), O. Plechova (Russia), J. Hugger Grants: some funds are available for young http://www.esf.org/euresco (Denmark), F. Topsoe (Denmark), S. researchers; for information, contact 7-11: 11th International Conference on Znamensii (Russia), M. Mrozek (Poland), Susanna Papadopoulou, Department of Formal Power Series and Algebraic V. Tkachenko (Ukraine), L. Belous Mathematics, University of Crete, Combinatorics (FPSAC’99), Barcelona, (Ukraine), V. Zavadskii (Belorussia), V. Heraklion, Crete, Greece; fax: (+30)-81- Spain Malozemov (Russia), A. Petukhov (Russia) 393881; e-mail: [email protected] Scope: algebraic and bijective combina- Proceedings: it is hoped that all invited Site: Anogia Academic Village, a confer- torics and their relations to other parts of talks and papers accepted for presentation ence centre about 45 minutes by car from mathematics, computer science and will be published Heraklion physics Registration fees: participant US$100, Information: contact N. Alikakos, Organiser: Universitat Politecnica de student US$25, participant from the for- Mathematics Department, University of Catalunya mer Soviet Union US$25 Athens, Panepistimiopolis, 15784 Programme committee: G. Almkvist, H. Site: St Petersburg State Technical Zografou, Athens, Greece Barcelo, F. Bergeron, R. Cori (co-chair), J. University e-mail: [email protected] M. Fedou, K. Koike, C. Martinez, A. Deadline: 30 April for abstracts and regis- 21-27: CIME Session on Computational Mikhalev, M. Noy, P. Paule, R. Pinzani, O. tration forms Mathematics Driven by Industrial Serra (co-chair), R. Simion, D. Stanton, S. Information: contact Yuri Ivanov, MATH- Applications, Martina Franca, Italy Sundaram, J. Y. Thibon, V. Welker, N. TOOLS’99, Department of Mathematics, Scientific directors: V. Capasso (Milan), Wormald, J. Zeng State Technical University, H. W. Engl (Linz) and J. Periaux (Paris) Information: contact Marc Noy, Pau Polytechnicheskaya st., 29 St Petersburg Programme: four series of five lectures: R. Gargallo #5, Dept. Matematica Aplicada 195251, Russia; fax: (+7)-812-5343314, Burkard (Graz), Paths, trees and flows: graph II, E-08028 Barcelona, Spain; tel: (+34)- (+7)-812-5341404 optimization problems with industrial applica- 934016927; fax: (+34)-93401728 e-mail: [email protected] or tions; P. Deuflhard (Berlin), New computa- e-mail: [email protected] [email protected] tional concepts, adaptive differential equation www-ma2.upc.es/~fpsac99 16-19: Commutative Algebra and solvers, and virtual labs, J. L. Lions (Paris), 7-11: International Society of The Arts, Algebraic Geometry, Messina, Sicily Mathematical problems in industry; G. Strang Mathematics, and Architecture Aim: to inform participants of recent (MIT), Wavelet transforms and cosine trans- (ISAMA99), San Sebastian, Spain progress in commutative algebra and alge- forms in signal and image processing, and Aim: to relate the arts and architecture braic geometry and to promote interac- series of two lectures by the scientific direc- with mathematics tions between these fields and their combi- tors and by R. Mattheij (Eindhoven), Organiser: N. Friedman natorial aspects Mathematics of glass Information: tel: (+1)-518-442-4621, fax: Programme: 1-hour invited expositions of Information: http://www.math.unifi.it/ (+1)-518-442-4731 recent developments; contributed talks by CIME/ e-mail: [email protected] participants; poster session for young [for details see EMS Newsletter 30, December http://www.sc.ehu.es/ISMA99/ researchers 1998] 14-19: MATHTOOLS’99 (Tools for Speakers: Luchezar Avramov (Purdue), 23-25: Bar-Ilan Symposium on The Mathematical Modelling), St Petersburg, Hyman Bass (Columbia), Winfried Bruns Foundations of Artificial Intelligence Russia (Osnabrück), Luca Chiantini (Siena), Dale (BISFAI99), Ramat Gan, Israel Aim: a multidisciplinary conference on the Cutkosky (Missouri), Joseph Gubeladze Scope: bridging theory and practice, theo- latest advances in the theory of mathemat- (Georgia), Karen Smith (Michigan), ry-based practical implementations and ical modelling and its role in the explana- Giuseppe Valla (Genova), Chuck Weibel commercial applications tion of some non-linear effects arising in (Rutgers) Speakers: to include S. Rosenschein real systems, as well as the demonstration Organisers: Gaetana Restuccia (Messina), (Stanford) and L. Joskowicz (Israel) of up-to-date efficient methods for solving Jürgen Herzog (Essen) Programme committee: L. Aiello, R. Ben- applied technical problems; this is the sec- Scientific committee: L. Ein (Illinois), J. Eliyahu, Y. Choueka, E. Davis, R. Dechter, ond of a series of conferences initiated in Herzog (Essen), T. Hibi (Osaka), G. R. Feldman, N. Friedman, H. Geffner, D. 1996, organized by the State Technical Restuccia (Messina), H. Seydi (Dakar), R. Geiger, S. Kraus, D. Lehmann, S. University of St Petersburg Strano (Catania), P. Valabrega (Torino), Markovitch, J. McCarthy, J. Minker, J. Scope: mathematical modelling; computer W. Vasconcelos (Rutgers) Rosenschein, E. Sandewall, E. Santos, U. 26 EMS March 1999 CONFERENCES Schild, M. Tennenholtz, B. Webber (Paris), J. Hubbard (Cornell), M. Lyubich Slovenia, half-an-hour’s drive from Information: http://www-formal.stanford. (Stony Brook, USA) Ljubljana international airport and the edu/leora/bisfai/ Fees, Grants, Site: see information for 19- Austrian and Italian borders 25-30: EURESCO: Number Theory & 25 June, Dynamics of Patterns Proceedings: to be published as a special Arithmetical Geometry: Arakelov Information: contact S. Bullett, School of issue of Discrete Mathematics Geometry & Applications, Obernai (near Mathematical Sciences, Queen Mary & Deadline: 2 July for submission of papers Strasbourg), France Westfield College, University of London, Information: e-mail: [email protected] Scope: foundational results in Arakelov Mile End Road, London E1 4NS, UK .si geometry: hermitian geometry and analy- e-mail: [email protected] http://bled.ijp.si/or sis on complex manifolds; intersection the- 28-30: International Conference on 28-2 July: Nonlinear Partial Differential ory and Riemann-Roch theorem; applica- Geometry, Porto, Portugal Equations, Besançon, France tions to diophantine approximation; [3rd meeting of the project Algebra, Aim: Stanislav Nikolaevich Kruzhkov Arakelov geometry of abelian varieties and Geometria e Combinatoria (Praxis 2/2.1/ (1936-97), Professor at the M. V. their moduli spaces MAT/63/94)] Lomonosov Moscow State University, Organisers: Jean-Benoët Bost (Orsay) and Organisers: Gabriela Chaves, Peter greatly influenced the theory of non-linear U. Jannsen (Cologne) Gothen, Luisa Magalhaes partial differential equations with many Speakers: A. Abbes (Paris), J.-M. Bismut Main speakers: Luis Cordero (Santiago de important and highly original contribu- (Orsay), J. I. Burgos (Barcelona), P. Cohen Compostela), Antonio Costa (Madrid), tions; this international conference pays (Lille), S. David (Paris), R. Ferretti Ron Donagi (Pennsylvania), Teresa tribute to his memory by presenting recent (Zürich), C. Gasbarri (Cologne), H. Gillet Monteiro Fernandes (Lisboa), Ivan Penkov developments in the domains where his (Chicago), K. Köhler (Bonn), J. Kramer (California), John Rhodes (Berkeley) ideas were particularly fruitful (Berlin), S. S. Kudia (Maryland), K. Programme: 1-hour invited lectures and Scope: conservation laws; Hamilton-Jacobi Künnemann (Cologne), J.-H. Everste 30-minute sessions for shorter communica- equations and viscosity solutions; entropic (Leiden), V. Maillot (Paris), M. McQuillan tions solutions and renormalised solutions; non- (Oxford), D. Roessler (Bures/Yvette), L. Sponsor: Fundaçao para a Ciencia e a linear parabolic problems; Korteweg-de Szpiro (Orsay), H. Tamvakis Tecnologia Vries equation (Philadelphia), E. Ullmo (Orsay) Information: contact Peter Gothen, Dep. Steering committee: N. S. Bakhvalov, M. Information: contact Dr. J. Hendekovic, Matematica Pura, Faculdade de Ciencias, G. Crandall, C. M. Dafermos, P.-L. Lions, European Science Foundation, 1 quai 4099-002 Porto, Portugal; tel: (+351)-2- O. A. Oleinik (M. V. Lomonosov Moscow Lezay-Marnésia, 67080 Strasbourg Cedex, 3401441/(+351)-2-2008628 State University) and the European net- France; tel: (+33)-3-88-76-71-35; fax: e-mail: [email protected] works (TMR) ‘Hyperbolic Systems of (+33)-3-88-36-69-87 http://www.fc.up.pt/mp/pbgothen/Congres Conservation Laws’ and ‘Viscosity e-mail: [email protected] sos/agc99htm Solutions and their Applications’ http://www.esf.org/euresco 28-1 July: Coordination in Parallel and Scientific committee: C. Bardos (Paris), G. 26-2 July: EURESCO: Algebra & Distributed Applications and Activities, Barles (Tours), P. Bénilan (Besançon), J. Discrete Mathematics: Infinite France Carrillo (Madrid), V. L. Kamynin Combinatorics & their Impact on Topics: multisites coordination; dynamic (Moscow), F. Murat (Paris), B. Perthame Algebra, Hattingen, Germany architecture management for multi-com- (Paris) Scope: combinatorial methods and results ponent applications; coordination software Secretaries: M. Diguglielmo, C. Pagani in set theory and their application to alge- architecture; coordination models and Programme: plenary lectures will be deliv- bra; recent advances in cardinal arithmetic applications for collaborative work and ered by members of the steering commit- and the interplay between them and vari- CSCW; group decision protocols; coordi- tee and by A. Bressan (Trieste), X. Cabré ous subfields of algebra, particularly com- nation models for programming languages (Barcelona), T. Gallouët (Marseille), A. S. mutative algebra and module theory and application to Java and CORBA; for- Kalashnikov (Moscow), C. E. Kenig Organisers: Saharon Shelah (Jerusalem) mal and semi-formal techniques for coor- (Chicago), S. Luckhaus (Leipzig), F. Otto and Rüdiger Göbel (Essen) dination description and analysis (Santa Barbara), E. Yu. Panov (Novgorod), Speakers: B. Belcar (Prague), A. Blass Organisers: Khalil Drira, Raul Jacinto D. Serre (Lyon), I. V. Skrypnik (Donetsk), (Michigan), J. Brendle (Kobe), M. Droste Montes H. M. Soner (Princeton), P. E. Souganidis (Dresden), M. Dugas (Waco), M. Dzamonja Deadlines: 5 April for draft papers (about (Madison), L. C. Tartar (Pittsburgh), J. L. (Norwich), P. Eklof (Irvine), M. Goldstern 4 pages); acceptance notified by 1 May; 1 Vazquez (Madrid); lectures in parallel ses- (Vienna), R. Grossberg (Pittsburgh), W. July for camera-ready papers sions will be organized on each theme of Hodges (London), E. Hrushovsky Information: contact Khalil Drira, LAAS- the conference (IHES/Jerusalem), T. Hyttinen (Helsinki), CNRS, 7 Av. Colonel Roche, 31077 Call for papers: participants are invited to M. Kojman (Negev), P. Komjath Toulouse Cedex, France; tel: (+33)-5-61- send an abstract of 15-20 lines (Budapest), S. Koppelberg (Berlin), M. C. 33-63-22 Registration fees: FF 500, or FF 600 if Laskowski (Maryland), C. Metelli (Naples), e-mail: [email protected] paid after 16 May D. Monk (Colorado), O. Spinas (Zürich), S. http://www.laas.fr/~khalil/cpdaa Site: Université de Franche-Comté, Thomas (New York), B. Velickovic (Paris), 28-2 July: Fourth Slovene International Besançon M. Ziegler (Freiburg) Conference in Graph Theory, Bled, Deadline: 21 March for submission of Information: contact Dr. J. Hendekovic, Slovenia abstracts European Science Foundation, 1 quai Speakers: Noga Alon (Tel Aviv), Brian Information: contact Mme Diguglielmo, Lezay-Marnésia, 67080 Strasbourg Cedex, Alspach (Canada), Dan Archdeacon Equipe de Mathématiques, Université de France; tel: (+33)-3-88-76-71-35; fax: (Vermont), Marston Conder (Auckland), Franche-Comté, 25030 Besançon Cedex, (+33)-3-88-36-69-87 Michel Deza (France), Henry Glover France; tel: (+33)-3-81-66-63-40 e-mail: [email protected] (Ohio), Pavol Hell (Canada), Joan e-mail: [email protected] or http://www.esf.org/euresco/ Hutchinson (Minnesota), Wilfried Imrich http://pegase.univ-fcomte.fr/Actu/SNK99/ 26-2 July: Holomorphic Dynamics, (Austria), Caiheng Li (Australia), Laszlo 28-6 July: CIME-EMS Summer School in Anogia, Crete, Greece Lovasz (Yale), Crispin Nash-Williams Pure Mathematics: Iwahori-Hecke [part of the series Euroconferences in (Reading), Roman Nedela (Slovakia), Algebras and Representation Theory, Mathematics on Crete] Tomaz Pisanski (Ljubljana), Bruce Richter Martina Franca, Italy Organisers: K. Athanassopoulos (Crete), (Ottawa), Gert Sabidussi (Montreal), Paul Organiser: V. Baldoni and D. Barbash S. Bullett (London), A. Douady (Paris), B. Terwilliger (Wisconsin), Thomas Tucker Information: e-mail: [email protected]. Harvey (London) (New York), Arthur White (Michigan), uniroma2.it Main speakers: K. Astala (Jyvaskyla, Xuding Zhu (Taiwan) 29-9 July: LMS Durham Symposium on Finland), B. Branner (Lyngby), A. Douady Site: Hotel Golf, Lake Bled in the North of Stochastic Analysis, Durham, England EMS March 1999 27 CONFERENCES T. J. Lyons (Imperial, London), E. Fluckiger (Besançon), D. Lewis (Dublin), A. and D. Macpherson); the lectures will Bolthausen (Zürich), L. Grogg (Cornell) Ranicki (Edinburgh) progress from introductory material on Main speakers: G. Ben Arous (Lausanne), Speakers: A. Berge (Bordeaux), J. J. permutation groups and model theory to D. Dawson (Toronto), B. Driver (San Boutros (Paris), J. H. Conway (Princeton), recent research and open problems Diego), S. Evans (Berkeley), H. Föllmer D. Hoffmann (Besançon), C. Kearton Information: http://www.science.unitn.it/ (Berlin) T. Kurtz (Madison), E. Perkins (Durham), M. Kreck (Mainz/Oberwolfach), ~puglisi/workshop.html (Vancouver), L. Saloffe-Coste (Cornell), S. R. Parimala (Bombay), M. Rost 12-18: Third International Conference Watanabe (Japan) (Regensburg), W. Scharlau (Münster), J.-P. on Symmetry in Nonlinear Mathematical Support: this research symposium, organ- Serre (Paris), M. Taylor (Manchester), C. Physics, Kiev, Ukraine ised under the auspices of the London T. C. Wall (Liverpool) Topics: classical Lie analysis of equations Mathematical Society, is supported by a Organiser: TMR network project ‘K-theo- of mathematical physics; reduction tech- research grant from EPSRC ry, linear algebraic groups and related niques and exact solutions of non-linear Information: Prof. T. J. Lyons, Depart- structures’ partial differential equations; non-classical ment of Mathematics, Imperial College, Site: University College, Dublin conditional and approximate symmetry; 180 Queen’s Gate, London SW2 2BZ, UK Note: some financial support is available symmetry in non-linear quantum mechan- e-mail: [email protected] for young researchers from EU states ics, quantum fields, gravity, fluid mechan- Information: contact Prof. D. Lewis, ics, mathematical biology, mathematical Organisers:Department of Mathematics, University economics; representation theory; q-alge- July1999 College, Dublin; tel: (+353)-1-706-8373 bras and quantum groups; symbolic com- 3-9: Computer Vision and Speech e-mail: [email protected] putations in symmetry analysis; dynamical Recognition: Statistical Foundations and http://mathsa.ucd.ie/TMR/quadconf.html systems, solitons and integrability; super- Applications, Anogia, Crete, Greece 5-9: Fourth International Conference on symmetry and parasupersymmetry [part of the series Euroconferences in Industrial and Applied Mathematics Programme committee: A. Nikitin and A. Mathematics on Crete] (ICIAM 99), Edinburgh, Scotland Samoilenko (co-chairs, Ukraine), J. Organisers: B. Gidas and D. Mumford Information: http://www.ma.hw.ac.uk/ Beckers (Belgium), G. Bluman (Canada), (Brown University, USA) iciam99/ J.-M. Cervero (Spain), P. Clarkson (UK), Main speakers: Y. Amit (Chicago), O. 8-24: XXIXth Probability Summer H.-D. Doebner (Germany), G. Goldin Catoni (Paris), P. Diakonis (Stanford), O. School, Saint-Flour, Cantal, France (USA); B. K. Harrison (USA), N. Faugeras and J. Zerubia (INRIA Sophia Speakers: Erwin Bolthausen (Zürich), Ibragimov (SAR), R. Jackiw (USA), M. Antipolis, France), D. Geman (Palaiseau, Edwin Perkins (Vancouver), Aad van der Lakshmanan (India), P. Olver (USA); M. France), S. Geman (Brown University, Vaart (Amsterdam) Shkil, I. Skrypnyk, I. Yehorchenko, R. USA), I. Johnstone (Stanford), J. Malik Information: contact P. Bernard, Zhdanov and V. Boyko (Ukraine) (Berkeley), C. Regazzoni (Genoa), S. Université Blaise Pascal, Mathématiques Organisers: Institute of Mathematics of Ullmann (Israel) Appliquées, F63177 Aubiére Cedex, the National Academy of Sciences of Fees, Grants, Site: see information for 19- France; tel: 04-73-40-70-52 or 04-73-40- Ukraine and Ukrainian Pedagogical 25 June, Dynamics of Patterns 70-50; fax: 04-73-40-70-64 University Information: contact B. Gidas, Division of e-mail: [email protected] Information: contact A. Nikitin, Institute Applied Mathematics, Brown University, 9-17: Symposium on Computation in of Mathematics, National Academy of Providence, Rhode Island 02912, USA Group Theory and Geometry, Coventry, Sciences of Ukraine, 3 Tereshchenkivska e-mail: [email protected] England Street, Kyiv 4, Ukraina; tel: (+38)-044- 4-11: Paul Erdös and his Mathematics, Organisers: David Epstein and Derek Holt 224-63-22 or (+38)-044-250-08-96; fax: Budapest, Hungary Site: University of Warwick, Coventry (+38)-044-225-20-10 Scope: all the fields to which Paul Erdös Information: contact Ms. Peta McAllister, e-mail: [email protected] or contributed: number theory, analysis, com- Mathematics Institute, University of [email protected] binatorics, probability theory, set theory Warwick, Coventry CV4 7AL, England; tel: http://www.imath.kiev.ua/~appmath/first_ Programme committee: V. T. Sós (chair), (+44)-1203-524403 in.html A. Sali (secretary), L. Babai, L. Lovász, B. e-mail: [email protected] 16-18: ESA’99: Seventh Annual European Bollobás, A. Hajnal, G. O. H. Katona, M. http://www.maths.warwick.ac.uk/~dbae/sy Symposium on Algorithms, Prague, Laczkovich, P. Revesz, A. Sárközy, M. mposium99html Czech Republic Simonovits, J. Szabados 12-16: 17th British Combinatorial Scope: research in the use, design and Information: contact A. Sali, Mathematical Conference, Canterbury, England analysis of efficient algorithms and data Institute of HAS, Budapest, P. O. Box 127, Main speakers: W. T. Tutte (Rado lectur- structures as carried out in computer sci- H-1364 Hungary er), Simeon Ball (Eindhoven), Jeff Dinitz ence, discrete applied mathematics and e-mail: [email protected] (Vermont), Martin Dyer (Leeds), Klaus mathematical programming http://www.math-inst.hu/~erdos99 Metsch (Giessen), Janos Pach (New York), Topics: approximation algorithms, combi- 5: CEMRACS: Centre d’été de mathéma- Robin Thomas (Georgia), Carsten natorial optimisation, computational biol- tique et de recherches avancées en calcul Thomassen (Lyngby), Nick Wormald ogy, computational geometry, databases scientifique, Orsay/Luminy, France (Melbourne) and information retrieval, graph and net- Topics: hyperbolic system of conservation Organisers: D. A. Preece and J. D. Lamb work algorithms, machine learning, num- laws; kinetic equations (Boltzmann, Vlasov, (University of Kent at Canterbury) ber theory and computer algebra, on-line Fokker-Planck); numerical methods, scien- Programme: nine 1-hour lectures and con- algorithms, pattern matching and data tific computing, probability (Monte-Carlo tributed talks in parallel sessions compression, symbolic computation methods); plasma physics Information: http://speke.ukc.ac.uk/cbs/ Information: e-mail: [email protected]. Organisers: ASCI, GdR SPARCH, TMR ms/bcc17/ cuni.cz ‘hyperbolic’ and TMR ‘kinetic’ 12-17: Workshop on Model Theory and http://www.ms.mff.cuni.cz/esa99/ Site: ASCI, Orsay and C.I.R.M. Luminy Permutation Groups, Trento, Italy 19-29: LMS Durham Symposium on Deadline: 31 March Aim: to give an overview of some common Quantum Groups, Durham, England Information: e-mail: [email protected] ground between model theory and permu- Organisers: A. N. Pressley (King’s, http://www.asci.fr/cemracs/ tation groups London), A. Sudbery (York), S. Donkin 5-9: Quadratic Forms and their Programme: three overlapping series of (QMW, London) Applications, Dublin, Ireland lectures: A short course on permutation groups Main speakers: J. Bernstein (Tel Aviv), E. Aim: to bring together mathematicians (Peter M. Neumann, Oxford); An introduc- Effros (UCLA), E. Frenkel (Berkeley), T. who are specialists in quadratic forms and tion to model theory (David M. Evans, Koorwinder (Amsterdam), P. Littlemann related topics or use them in their research Norwich, and Dugald Macpherson, Leeds); (Strasbourg), M. Kashiwara (Kyoto), A. Programme committee: E. Bayer- Research topics and open problems (D. Evans Varchenko (Chapel Hill) 28 EMS March 1999 CONFERENCES Support: this research symposium, organ- Travel grants: contact Prof. W. Hodges Petersburg, chairman), A. D. Alexandrov ised under the auspices of the London (address above) (St Petersburg), V. Arnold (Moscow/Paris), Mathematical Society, is supported by a Information: Association for Symbolic M. Gromov (Paris), F. Hirzebruch (Bonn), research grant from EPSRC Logic, 1409 West Green Street, Urbana, IL S. Novikov (Moscow/Maryland), Ya. Sinai Information: Prof. A. N. Pressley, 61801, USA; tel: (+1)-217-244-7902; fax: (Moscow/Princeton), S. Smale (Berkeley), Department of Mathematics, King’s (+1)-217-3339576 V. Turaev (Strasburg), O. Viro (St College, Strand, London WC2R 2LS, UK e-mail: [email protected] Petersburg/Uppsala) e-mail: [email protected] http://www.math.uiuc.edu/~asl/ Organisers: St Petersburg State 24-30: Groups of Tree Automorphisms 1-7: EQUADIFF 99, Berlin, Germany University, St Petersburg Mathematical and Lattices, Anogia, Crete, Greece Scope: one of a series of conferences Institute of Russian Academy of Science, St [part of the series Euroconferences in devoted to all mathematical aspects of dif- Petersburg Mathematical Society and Mathematics on Crete]; the dates given in the ferential equations Euler International Mathematical Institute first announcement of this conference have Organisers: B. Fiedler, H-G. Bothe, P. Local Organisers: N. Netsvetaev and A. been changed Deuflhard, K. Doppel, F. Duzaar, H. Vershik Main speakers: H. Bass (Columbia, USA), Gajewski, K. Gatermann, K. Groeger, R. Sponsors: support from RFBR (Russia) M.Burger (Zürich), P. de la Harpe Kornhuber, R. Lauterbach, K. Schneider, and Intas (EC) is expected (Geneva), A. Lubotzky (Israel), S. Mozes R. Seiler, J. Sprekels Proceedings: the proceedings will be pub- (Israel), F. Paulin (Paris) Information: contact Mrs. R. Loehr, Freie lished Organisers: H. Bass, A. Lubotzky, S. Universität Berlin, Mathematisches Site: Euler International Mathematical Mozes, M. Picardello (Rome) Institut I, Arnimallee 2-6, D-14195 Berlin, Institute, St Petersburg Mathematical Fees, Grants, Site: see information for 19- Germany Institute of the Russian Academy of 25 June, Dynamics of Patterns e-mail: [email protected] Science Information: contact S. Mozes, http://www.math.fu-berlin.de/~equadiff/ Deadline: 1 April for submission of talks Department of Mathematics, Hebrew 2-6: Fifth International Conference on Information: contact M. Zvagel’skii, University of Jerusalem, Givat Ram, 91904 Finite Fields and Applications, 191011 Steklov Institute of Math. (POMI), Jerusalem, Israel Augsburg, Germany nab. reki Fontanka 27, St Petersburg, e-mail: [email protected] Information: http://www.Math.Uni- Russia 26-6 August: Structure Formation in the Augsburg.DE/fq5/ e-mail: [email protected] Universe, Isaac Newton Institute, 9-14: György Alexits Memorial http://www.pdmi.ras.ru/EIMI/1999/ Cambridge, England Conference, Budapest, Hungary rokhlin/ Topics: inflation; cosmic defects; high red- Topics: function series, Fourier analysis, 20-26: Eleventh International Congress shift observations; cosmological parame- summability, approximation and expan- of Logic, Methodology and Philosophy of ters; large scale galaxy and mass distribu- sions, interpolation, inequalities Science, Krakow, Poland tion; quantum cosmology; baryon and Organiser: János Bolyai Mathematical Information: http://www.uj.edu.pl/Phils/ dark matter content; CMB experiments Society congress/ and statistics Programme committee: K. Tandori (hon- 22-29: Summer School on Quantum Organisers: R. G. Crittenden, V. A. orary chair), L. Leindler, F. Schipp and J. Groups, Hesselberg, Germany Rubakov, P. J. Steinhardt, N. G. Turok Szabados (co-chairs), S. Fridli (secretary), Topics: Hall algebras of quiver algebras, Speakers: A. Albrecht, R. Bond, F. F. Msricz, V. Totik, P. Virtesi quantum groups, crystal and canonical Bouchet, A. Doroshkevich, G. Efstathiou, Information: contact S. Fridli, bases R. Ellis, M. Fukugita, A. Guth, S. Hawking, Department of Numerical Analysis, Eötvös Programme: the meeting is in two parts: in C. Hogna, R. Juskiewicz, N. Kaiser, E. L. University, Muzeum krt. 6-8, Budapest, the first part the participants lecture on Kolb, T. Kibble, O. Lahav, A. Lasenby, J. H-1088 Hungary; tel: (+36)-1-2669-833, introductory topics; the second part is a Ostriker, L. Page, J. Peacock, M. Rees, V. ext. 3113 workshop where specialists in the area lec- Rubakov, P. Shellard, J. Silk, A. e-mail: [email protected] ture on recent topics Starobinsky, A. Szalay, P. Steinhardt, M. 10-15: International Conference on Organisers: K. Erdmann (Oxford), D. Turner, N. Turok Mathematical Logic, Novosibirsk, Russia Happel (Chemnitz), S. Koenig (Bielefeld) Deadline for applications: 31 March Scope: model theory, computability theo- Support: provided by the TMR scheme Information: e-mail: [email protected]. ry, proof theory, logic foundation of com- Information: contact Steffen Koenig, ac.uk puter science Fakultät für Mathematik, Universität http://www.newton.cam.ac.uk/programs/ Programme committee: Yu. L. Ersdhov Bielefeld, D-33501 Bielefeld, Germany sfu.html (chair), S. I. Adiyan, B. Cooper, E. Engeler, e-mail: [email protected] S. S. Goncharov, A. Macintyre, L. L. http://www.mathematik.uni- Organisers:Maksimova, Yu. V. Matiyasevich, A. bielefeld.de/~sek/summerseries.html August 1999 Nerode, H. Ono, E. A. Palyutin, M. G. 23-4 September: Generalized Dirac 1-6: 1999 ASL European Summer Peretyatkin, A. Prestel, A. A. Razborov, H. Operators and their Geometric Scattering Meeting (Logic Colloquium ’99), Utrecht, Schwichtenberg, R. Soare, M. A. Taitslin Theory, Warsaw, Poland The Netherlands Deadline: abstracts (at most 1 page in 12- Aim: to bring together researchers from Scope: logic broadly; a featured topic will point font) should be sent by 1 June to A. both the mathematical physics and the be computational logic N. Ryaskin, Conference on Mathematical geometric analysis branch of scattering Programme committee: C. G. Jockusch Logic, Institute of Mathematics, theory, in order to compare methods and (chair), E. Barendsen, J. van Eijck, S. Novosibirsk, 630090, Russia get an overview of the most recent results Goncharov, W. Hodges, D. de Jongh, A. Information: tel: (+7)-383-2-356237; fax: in both fields Kechris, P. Koepke, M. Lerman, D. (+7)-383-2-357808 Topics: scattering and spectral theory on Marker, J. van Oosten, A. Pitts, A. Visser e-mail: [email protected] complete non-compact manifolds; har- Local organisers: J. van Eijck (chair), P. 19-25: Topology and Dynamics: Rokhlin monic analysis on locally symmetric Blok, P. Dekker, M. de Rijke, Y. Venema Memorial, St Petersburg, Russia spaces; Hodge and de Rham cohomology Invited speakers: S. Abramsky, L. [in memory of Vladimir A. Rokhlin (1919-84)] of complete non-compact spaces; scatter- Beklemishev, D. Haskell, D. Miller, J. Scope: algebraic and differential topology; ing theory for N-body Schrödinger opera- Rutten, P. Speissegger, A. Weiermann algebraic, real algebraic, and Riemannian tors; distribution of resonances Deadline: 2 April for abstracts of con- geometry; smooth and symplectic dynam- Programme committee: B. Bojarski, J. tributed papers, to Prof. W. Hodges, ics, ergodic theory; applications Bruening, J. Eichhorn, T. Friedrich, E. School of Mathematical Sciences, Queen Programme: 1-hour talks and 25-minute Melrose, W. Mueller Mary and Westfield Colleges, London E1 communications Organiser: Banach Centre of the Polish 4NS, UK; e-mail: [email protected] Programme committee: A. Vershik (St Academy of Science, together with the EMS March 1999 29 CONFERENCES above committee Information: contact Francisco J. Craveiro cations Site: Banach Centre, Warsaw, Poland de Carvalho, Universidade de Coimbra, Proceedings: it is hoped to publish these Information: contact Prof. Thomas Portugal in the journal Integral Transforms and Friedrich, Institut für Mathematik, e-mail [email protected] Special Functions Humboldt-Universität zu Berlin, Ziegel- 5-11: XX International Seminar on Information: contact AMADE, Depart- strasse 13a, Unter den Linden 6, D-10099 Stability Problems for Stochastic Models, ment of Mathematics and Mechanics, Berlin, Germany; tel: (+49)-30-2093- Lublin-Nalczów, Poland Belarusian State University, Fr. Skaryny 1825; fax: (+49)-30-2093-1824 Scope: limit theorems of probability theo- Avenue 4, 220050 Minsk 50, Belarus e-mail: [email protected] ry and mathematical statistics, characteri- e-mail: [email protected] or amade99@ http://www-irm.mathematik.hu- sations of probability distribution and their mmf.bsu.unibel.by berlin.de/~pahlisch/Banach-99html stability, theory of probability metrics, 15-19: GD’99 Seventh International 29-4 September: Linear series and lower limit theorems and characterisation prob- Symposium on Graph Drawing, Prague, dimensional varieties, Bedlewo, Poland lems in stochastic analysis, stochastic Czech Republic Aim: to present recent progress in linear processes and queueing theory, applied Scope: algorithms, graph theory, geome- series, centred around the Fujita statistics, actuarial and financial mathe- try, topology, order theory, graphic lan- Conjecture and the classification of alge- matics guages, perception, applications, practical braic varieties Programme: invited and contributed talks systems Organisers: T. Bauer, S. Di Rocco, T. and poster sessions Topics: algorithms, models and tech- Szemberg Organising committee: V. M. Zolotarev niques for drawing graphs, visualisation of Programme committee: E. Ballico, Y. (chair), M. Arato, A. Balkema, V. E. structural information, perception issues Kawamata, R. Lazarsfeld, A. J. Sommese, J. Bening, R. Jajte, V. V. Kalashnikov, A. V. relating to diagram understanding, geo- Wisniewski Kolchin, V. Yu. Korolev, V. M. Kruglov, K. metric and topological graph theory, pla- Conference fee: 300 PLN Kubacki, E. Omey, A. Plucinska, Z. narity issues, intersection and visibility rep- Notes: the number of participants is limit- Rychlik, L. Stettner, D. Szynal, K. Urbanik resentations of graphs, tools and systems ed to 50, and early registration is recom- Publication: to appear in two volumes in for graph drawing, user interfaces for view- mended; grants covering living expenses the Journal of Mathematical Sciences series ing graphs, interactive exploration of large are available; participants wishing to give a (Plenum) graphs, applications of graph drawing talk should submit an abstract with their Registration fee: US$50; accommodation Organiser: J. Kratochvil (Prague) application and meals are about US$30 per person per Deadlines: 26 May: submission of papers; Information: e-mail: [email protected] day (double room) 15 July: notification of acceptance; 31 July: http://www.im.uj.edu.pl/~workshop/ Information: K. Kubacki, Institute of registration; 15 September: final version of 30-1 September: Sixth International Mathematics UMCS, Pl. Marii Curie- papers Symposium on Generalized Convexity Sklodowskiej 1, 20-031 Lublin, Poland Site: Stirin Castle, Prague, Czech Republic and Monotonicity, Karlovassi, Samos, e-mail: [email protected] Information: e-mail: Greece http:stabil.umcs.lublin.pl/ or [email protected]. cuni.cz Topics: problems related to theoretical, http://bernoulli.mi.ras.ru/ http://www.ms.mff.cuni.cz/gd99/ algorithmic, computational and modelling [for details see EMS Newsletter 30, December 16-22: Fourth International Workshop on issues in connection with generalisations of 1998] Differential Geometry and its convexity and monotonicity, as they arise 6-13: Advanced Course on Function Applications, Brasov, Romania in mathematical programming, econom- Spaces and Applications, Tbilisi, Georgia Topics: Riemannian and pseudo- ics, management science, engineering, Programme: the course is suitable for Riemannian geometry, complex and numerical mathematics, variational advanced graduate student or recent quaternionic geometry, symplectic and inequalities, equilibrium problems Ph.D.s; there are two series of lectures: contact geometry, foliation theory, topo- Invited speakers: J. Jahn (Erlangen), P. Alois Kufner (Czech Republic) on New logical aspects Pardalos (Florida), A. Prekopa (Rutgers) aspects in weight theory and George Jaiani Organising committee: R. Iordanescu, Deadlines: 31 March: early registration; (Tbilisi) on Hardy’s inequality and related top- Gh. Pitts, D. Papuc, D. Acu 30 June: late registration and titles and ics Programme: 50-minute and 30-minute abstracts of talks; 30 September: submis- Information: contact TICMI, I. Vekua invited talks; short oral communications sion of manuscripts Institute of Applied Mathematics of Tbilisi and poster sessions Information: contact T. Vigli-Papadaki, State University, University Str. 2, Tbilisi Deadline: 1 July for receipt of abstracts Department of Mathematics, University of 380043, Georgia; tel: (+995)-32-305995 Grants: there are fifteen grants (to cover the Aegean, Karlovassi 83200, Samos, e-mail: [email protected] meals and accommodation) for partici- Greece; tel: (+30)-273-33914/34750; fax: http://www.viam.hepi.edu.ge/other/TICMI pants under 35 (+30)-273-33896 [for details see EMS Newsletter 29, September Information: e-mail: [email protected]. e-mail: [email protected] 1998] ro, [email protected], danpapuc@info. http://kerkis.math.aegean.gr/~gc6/GC6. 6-21: EMS Summer School in Applied uvt.ro or [email protected] htm Mathematics: Numerical Simulation of 20-26: International Symposium on Flows, Heidelberg and Freiburg, Classical Analysis, Kazimierz Dolny, Organisers:Germany, and Zürich, Switzerland Poland September 1999 Organiser: Gabriel Wittum (Heidelberg) Topics: several complex variables, 3-7: Summer School on Differential Information: e-mail: [email protected] Riemannian and Hermitian geometry, Geometry, Coimbra, Portugal berg.de spectral theory in Hilbert space, probabili- Programme: courses on Geometry of sub- 14-18: International Conference on ty, mathematical physics manifolds, Analytic Methods of Analysis and Invited speakers: K. Goebel, J. Kisyñski, J. Dirk Ferus (Berlin) and Poisson and symplec- Differential Equations (AMADE), Minsk, Lawrynowicz, E. Ligocka, J. Siciak, M. tic geometry, I. Vaisman (Haifa); 1-hour lec- Belarus Skwarczyñski tures by David R. J. Chillingworth Scope: integral transforms and special Programme: invited lectures and 45-min- (Southampton), Sheila Carter (Leeds), functions; differential equations and appli- urte scientific communications in English Jean Pierre Francoise (Paris) and Bernd cations; integral, difference, functional Information: contact T. Mazur, Depart- Wegner (Berlin); 20-minute contributed equations and fractional calculus ment of Mathematics, Technical Univer- talks Organising committee: I. V. Gaishun and sity, Malczewskiego 29, 26-600 Radom, Organisers: Joana M. Nunes da Costa, F. A. V. Kozulin (Belarus) and V. A. Il’in Poland; fax: (+48)-48-26333 or (+48)-48- J. Craveiro de Carvalho, A. M. d’Azevedo (Russia) 23969 Breda, Bernd Wegner Programme: 45-minute plenary talks; 20- e-mail: [email protected] or krupa Site: Universidade de Coimbra, Portugal minute reports and 10-minute communi- @alpha.sggw.waw.ps 30 EMS March 1999 RECENT BOOKS Recent books edited by Ivan Netuka and Vladimír Soucek

Books submitted for review should be sent gence of sequences of functions, Wr Ha (I) and the author’s solution of to together with the Stone-Weierstrass one of the most celebrated problems Ivan Netuka, MUUK, Sokolovská 83, theorem. of real analysis—the Kolmogorov 186 75 Praha 8, Czech Republic. All topics are explained with great problem of sharp inequalities for care and with full details that could M. Alber, B. Hu and J. Rosenthal intermediate derivatives in the Hölder help less experienced readers, but on r a r a (eds.), classes W H (R+) and W H (R). Current and Future Directions the other hand only readers with a Birkhäuser, This book has seventeen chapters in Applied Mathematics, good background and some knowl- Boston, 1997, 261 pp.; DM 78, ISBN 0- and two appendices. It is warmly rec- edge of technical matters will really be 817-63956-X and 3-764-33956-X ommended to mathematicians special- able to appreciate them. Sometimes This book contains survey articles and izing in approximation theory, func- topics are done in reverse order: first tional and convex analysis, optimiza- general thoughts and views on applied in a very general setting and then for a mathematics by the plenary speakers tion, topology and integral equations. special case. Of course, it helps to save (kn) and panellists of a Symposium on some space and time but beginners Current and Future Directions in could have difficulties in coping with H. G. W. Begehr, H. Koch, J. Applied Mathematics, held at the this approach. It is good that the Kramer, N. Schappacher and E.-J. University of Notre Dame in the ‘divorce’ of real and complex variable Thiele (eds.), Mathematics in Berlin, Spring of 1996. The first part of the parts does not take place here and that Birkhäuser, Berlin, 1998, 200 pp., DM book consists of reflections by several all material is accompanied by many 28, ISBN 3-7643-5943-9 and 0-8176- participants at the Symposium (R. remarks, examples, exercises, etc. The 5943-9 Brockett, Ch. I. Byrnes, A. Friedman, pictures are nice and instructive, and This book contains twenty-two short J. Gunawardena, D. Holm, M. Ali well-organized indices help the reader articles on leading personalities in Khan, B. Marcus, J. E. Marsden, C. F. to find easily the required parts of German mathematics living and work- Martin) on changes and important text. The book can be recommended ing for some time in Berlin. Two intro- trends in both research and education. for libraries, teachers and students ductory overviews are devoted to In the second part, the plenary speak- who want to reach a deep level of mathematics at the Prussian Academy ers (A. M. Bloch, J. E. Marsden and G. understanding from the very begin- of Sciences from 1700 to 1810 and in Sanchez, R. Brockett, C. I. Byrnes, H. ning. There are more condensed Berlin from 1810 to 1933, but the J. Landau and A. Lindquist, P. courses covering more or less the same period covered extends up to the pre- Constantin, N. M. Ercolani, R. E. (traditional) material; this one will be sent day. This period is one of the Ewing, M. A. Khan and Y. Sun, J. E. appreciated by those who like to have most interesting parts of the history of Marsden and J. M. Wendlandt) pro- things done in detail. (jve) mathematics; the book helps the read- vide surveys in their research fields, as er to understand the events which so well as new research results. S. Bagdasarov, Chebyshev Splines and influenced world history. This book will be a useful guide to Kolgomorov Inequalities, Operator Contributions cover the foundation research workers, students and teach- Theory, Advances and Applications, Vol. of Berlin University, the ‘golden age’ ers involved with the applications of 105, Birkhäuser, Basel, 1998, 205 pp.; of mathematics, the competition mathematics. (kn) DM 178, ISBN 3-7643-5984-6 and 0- between Berlin and Göttingen, the 8176-5984-6 Nazi period, the post-war develop- H. Amann and J. Escher, Analysis I, This monograph gives an extensive ment of mathematics in a divided Grundstudium Mathematik, Birkhäuser, account of structural, limiting and Berlin and the situation after the Basel, 1998, 445 pp., ISBN 3-7643- extremal properties of perfect ω- reunification. 5974-9 and 3-7643-5976-5 splines generalizing standard polyno- This book will be of considerable inter- This textbook is the first volume of a mial perfect splines in the theory of est not only for the historians of math- planned three-volume course of analy- Sobolev classes. Special attention is ematics but also for the whole mathe- sis. It contains five chapters. The first paid to the qualitative description of matical community. (jve) one is devoted to basics like logic, set Chebyshev ω-splines and ω-polynomi- theory, mappings, relations and oper- als associated with the Kolmogorov J. Bertoin, Lévy Processes, Cambridge ations, and also to an introduction of problem of n-widths and sharp addi- Tracts in Mathematics 121, Cambridge the real and complex number systems, tive inequalities between the norms of University Press, 1998, 266 pp.; £17.95, linear and affine spaces and algebras. intermediate derivatives in functional ISBN 0-521-56243-0 / 0-521-64632-4 The combined approach to elemen- classes with a bounding modulus of Lévy processes are processes with tary and relatively advanced parts continuity ω. The author pursues independent and stationary incre- appears also in the following chapters; three main goals: (i) to introduce the ments. They include as important the second one starts with elements of notion and give the formulae for the examples Poisson, Wiener and Cauchy metric and normed spaces and deals perfect ω-splines in WrHω; (ii) to processes and, more generally, stable also with basics studied traditionally in describe various extremal properties processes. They constitute an impor- elementary courses. In such a way it is of perfect ω-splines by emphasising tant class of space-time homogeneous possible to include in the third chapter new phenomena and old features Markov processes and of semimartin- the study of continuous functions and inherited from polynomial perfect gales. The probabilistic modelling the notion of topology, in the fourth splines; and (iii) to show examples of applies Lévy processes in the study of the Lagrange mean-value theorem applications of the general theory of queues, insurance risks, in mathemati- and the Banach fixed point theorem, perfect splines in examples related to cal finance, etc. They should be met by and in the fifth the pointwise conver- the computation of N-widths of classes anybody interested in potential theory. EMS March 1999 31 RECENT BOOKS The monograph fills a gap in mod- the next part the Jacobson radical, systems; the Buchberger algorithm for ern probabilistic literature and pro- simple modules and chain conditions Gröbner bases; the Ritt-Wu character- vides an updated and concise refer- are related to a torsion theory. The istic set method for ordinary differen- ence text, in as self-contained way as classical Hopkins-Lewitzki theorem tial equations, and the Riquier-Janet possible. Standard probability and stating that right artinian rings are method for partial differential equa- Fourier analysis are the only prerequi- right noetherian is generalized in the tions. sites required by the author, but a third part. The fourth part is devoted This book is a collection of fourteen reader familiar with more sophisticat- to the relative injectivity, projectivity papers on symbolic rewriting tech- ed presentations of Markov processes, and flatness, with special emphasis on niques, presented at a workshop at the with continuous stochastic analysis, generalized Baer and Fuchs condi- Centro Stefano Franscini in Ascona in will undoubtedly gain more from the tions. Injective hulls, and projective April 1995. The workshop brought text. and torsion free covers relative to a together forty researchers from vari- The preliminary material presents torsion theory are treated in part 5. ous areas of rewriting techniques, the an elementary treatment of infinitely The last part investigates the relative main goal being the investigation of divisible distributions, Poisson and versions of some classical properties of common threads and methods. The Wiener process, and martingales. rings—namely, simple, semisimple, papers are on the following topics: Chapter I presents Lévy processes in primitive, semiprimitive, prime and parallel completion techniques; connection with the Markov property, semiprime rings. (lbi) Gröbner bases, an alternative algo- and the related potential theory is rithm; symmetrization based comple- G. Brewka, J. Dix and K. Konolige, summarized in Chapter II. The tion; reduction of G-invariant polyno- increasing Lévy processes-subordina- Nonmonotonic Reasoning: An mials for a permutation group G; non- , Lecture Notes , CSLI tors are studied in Chapters III and Overview 73 commutative Gröbner freaks; imple- Publications, Stanford, 1997, 179 pp.; IV. The next two chapters are devoted menting non-commutative Gröbner £14.95, ISBN 1-881-52683-6 and 1- to local times and fluctuation theory, basis systems; string rewriting and 881-52684-4 while Chapter VII is a fascinating Gröbner bases for monoid and group Non-monotonic reasoning leads to study of Lévy processes with no posi- rings; Gröbner fans and projective conclusions which do not grow monot- tive jumps. The text concludes in schemes; normalized rewriting; syn- onically with increasing information. A Chapter VIII by listing consequences tactic termination orderings; iterated formalization of this reasoning, non- of the scaling property of stable Ore extensions; torsion group of ellip- monotonic logics, is treated in processes. Each chapter is accompa- tic curves; finite group presentation; Chapters 2–5 of this book. Model pref- nied by a set of exercises and com- and degree four identities for alterna- erence logics (such as the closed-world ments that provide additional infor- tive rings. assumption, the minimalization of cir- mation on the topic. (jste) Some of the papers are of interest to cumscription and modal conditional both algebraists and computer scien- A. Beutelspacher and U. Rosenbaum, logics) are discussed in Chapters 2 and tists: for example, the techniques Projective Geometry: From Found- 3, while Chapter 4 is concerned with described in the paper on string Cambridge ations to Applications, fixed-point logics, including default rewriting, or that on non-commutative University Press, Cambridge, 1998, 258 logics and auto-epistemic ones. Gröbner freaks. Other papers may be pp.; £15.95, ISBN 0-521-48364-6 and Abductive inference methods are of interest to specialists in computer 0-521-48227-1. treated in Chapter 5. In Chapter 6, science. (tk) As the authors write in the preface, semantics for programs from the view- projective geometry is a jewel of math- point of logic programming (nega- J.-Y. Chemin, Perfect Incompressible ematics. The first four chapters of this tion-as-finite-failure) and from the Fluids, Oxford Lecture Series in book are devoted to classical projective viewpoint of non-monotonic reason- Mathematics and its Applications 14, and affine geometry, including finite ing are presented. A relationship Clarendon Press, Oxford, 1998, 187 pp.; spaces. They cover synthetic projective between these semantics and non- ISBN 0-19-850397-0 geometry, analytic geometry, monotonic logics is discussed in This book is concerned with some collineations, quadratic sets and Chapter 7. The book is an interesting recent mathematical results obtained quadrics. The next chapter describes overview of the topic described; proofs for perfect incompressible fluids. The applications of projective geometry in of assertions are not presented. A very Euler equations are derived from a the theory of codes, and the last chap- extensive bibliography is included. variational principle. The following ter presents an introduction to cryp- (jml) topics are presented: Littlewood-Paley tography. In this way the book con- theory, Biot-Savart’s law, resolution of tains both the foundations of the pro- M. Bronstein, J. Grabmeier and V. the Euler equations with smooth initial jective geometry and also some appli- Weispfenning (eds.), Symbolic data, the study of solutions with cations of this theory. It is interesting Rewriting Techniques, Progress in bounded vorticity, a presentation of that the first author was responsible Computer Science and Applied Logic 15, vortex patches problem, the problem for introducing the code for numbers Birkhäuser, Basel, 1998, 288 pp.; DM of vortex sheets, wave fronts, analytic on German bank notes. (lbo) 148, ISBN 3-7643-5901-3, ISBN 0- and Gevrey regularity of solutions of 8176-5901-3 the Euler equations, and singular vor- P. E. Bland, Topics in Torsion Theory, Symbolic rewriting techniques are tex patches. All results are treated for Mathematical Research 103, Wiley-VCH, methods for deriving consequences the Euler equations in two- or three- Berlin, 1998, 160 pp.; DM 128, ISBN 3- from systems of equations. They are of dimensional space. The flow problems 527-40131-8 great use when investigating the struc- in domains with non-empty bound- This booklet is devoted to some ture of the solutions. Such techniques aries are not investigated. aspects of ring and module theory appear in many areas of research with- The book contains a number of very related to a (hereditary) torsion theo- in computer algebra: the Knuth- interesting results, but reading it ry. The first part is a survey of the Bendix completion for groups, requires a deep knowledge of various basic properties of torsion theories. In monoids and general term-rewriting areas of mathematics. It will be of 32 EMS March 1999 RECENT BOOKS interest mainly to specialists in partial duced. It turns out that uniformly rec- example, the wave equation with dif- differential equations. (mf) tifiable spaces are exactly those BPI ferent kinds of non-linearities is con- spaces that are BPI equivalent to sidered. In the contribution of J.-P. D. Cvetkovic, P. Rowlinson and S. Euclidean space. BPI equivalence is an Gossez, Some remarks on the antimaxi- Simic, Eigenspaces of Graphs, equivalence relation that gives rise to mum principle, a relation between the Encyclopedia of Mathematics and its many natural questions: what is the antimaximum principle and the Fucík Applications , Cambridge University 66 number of different equivalent class- spectrum of differential operator is Press, 1997, 258 pp.; £45, ISBN 0-521- es?, how do they behave with respect exhibited and the extension of this 57352-1 to different deformations?, and so on. principle to the case of p-Laplacian This book describes how the spectral An interesting relation between BPI operator is given. S. I. Pohozhaev, The theory of finite graphs can be spaces of the same dimension is the fibering method in nonlinear variational strengthened by exploiting properties property of ‘looking from one space problems, gives in his lectures a detailed of the eigenspaces of adjacency matri- down to the other’, which means that a explanation of the one-parametric ces associated with a graph. One objec- non-trivial piece of the latter space is fibering method in the context of tive is to describe graphs by algebraic the Lipschitz image of a closed piece another methods of non-linear analy- means as far as possible. The book of the first one. A challenging problem sis. He presents its applications to deals mainly with eigenspaces of is whether the equivalence defined existence problems: the existence of graphs, and the emphasis is on those naturally using this relation is the multiple solutions, lower bounds on a parts of spectral theory where the same as BPI equivalence. Many ques- number of solutions, and questions of structure of eigenspaces is a dominant tions remain open concerning proper- non-existence of solutions. The mater- feature. For the most part, the eigen- ties of the order on the BPI spaces ial presented by A. Szulkin, Index theo- spaces considered are those of a (0,1)- induced by this relation. ries for indefinite functionals and applica- adjacency matrix of a finite undirected Besides basic notions, the book tions, is concerned with different index graph. The discussion of graph spec- gives a number of examples of BPI theories and their application to the tra in the first chapter reveals the lim- spaces, counter-examples to some ‘too problem of determining the number itations of the spectrum as a means of optimistic’ conjectures, and partial of periodic solutions to certain systems characterizing a graph, and motivates answers to many questions. Used and of ordinary differential equations. The the search for further algebraic invari- developed methods include the study contribution of I. V. Skrypnik, ants such as the graph angles in of various covering and cutting prop- Topological characteristics of fully nonlin- Chapters 4 and 5. erties of spaces. The reader needs no ear parabolic problems, presents applica- Angles also have a role in Chapter more preparation than some basic tions of topological approach devel- 6, where the theory of matrix pertur- knowledge of metric spaces and mea- oped by the author to the local solv- bations is applied to adjacency matri- sures on them. (ph) ability and conditional solvability of ces. Graph angles arise from a geo- the initial-boundary value problem for P. Drábek (ed.), metric approach to eigenspaces and Topological and an arbitrary T for fully non-linear par- lead to the notion of a star partition of Variational Methods for Nonlinear abolic equations. (oj) vertices, an important concept which is Boundary Value Problems, 20th relevant to the current study of the Seminar in Partial Differential Equations, A. Engel, Problem-Solving Strategies, graph isomorphism problem. Pitman Research Notes in Mathematics Problem Books in Mathematics, Springer- Specialists in graph theory and mathe- Series 365, Addison Wesley Longman, Verlag, New York, 1998, 403 pp.; DM matical chemistry will welcome this Harlow, 1997, 155 pp.; $45, ISBN 0- 68, ISBN 0-387-98219-1 treatment of important new research. 582-30921-2. All over the world there are mathe- (mloe) This volume contains the proceedings matical competitions for high-school of the International Spring School on students and there is also the G. David and S. Semmes, Fractured non-linear analysis, function spaces International Mathematical Olymp- Fractals and Broken Dreams: Self- and applications, held in Cholin. It iad. The author often led the German Similar Geometry through Metric and was the 20th conference in the series delegation at the IMO and was also Measure, Oxford Lecture Series in of seminars organised each year in the Chairman of the Jury at the 30th Mathematics and its Applications 7, various parts of the Czech Republic by IMO. In all such contests the partici- Oxford University Press, Oxford, 1997, the Department of Mathematics of the pants solve some problems in elemen- 212 pp.; £35, ISBN 0-198-50166-8 University of West Bohemia and by the tary mathematics. This book is an introduction to an Union of Czech Mathematicians and This book contains about 1300 interesting and well-motivated topic Physicists. Every four years (since problems. They are divided into four- with many open questions. The central 1978), this seminar transforms into an teen chapters on the box principle, notion is a kind of self-similar metric International Spring School. The inequalities, sequences, functional space called a BPI (‘big pieces of main goal of the seminar is to present equations and geometry. In each itself’) space. The class of BPI spaces a complete survey of some particular chapter there are some problems with includes the usual examples of fractal recent topics in PDEs to a wider math- solutions and then a lot of problems sets and is intended to include also a ematical audience, including non-spe- with hints leading to the solution. The variety of their deformations. Roughly cialists. The preface contains a list of problems are selected from competi- speaking, an Ahlfors regular space of speakers and topics since 1976. tion problems from the USSR, dimension d is BPI if, for any pair of There are five contributions in this Hungary, Germany and other coun- balls, there exist pieces of them of sub- volume. J. Berkovits, Some extensions of tries, and also from the IMO. As the stantial proportion (with respect to the topological degree theory with applications author writes in the preface, there can d-dimensional Hausdorff measure) to nonlinear problems, gives three differ- never be enough problems for train- which are in some sense uniformly ent extensions of degree theory which ing for such mathematical competi- bilipschitz equivalent. can be applied to different types of tions. The book is designed not only A corresponding notion of the BPI problem. The basic use of degree the- for trainers and pariticipants of con- equivalence of two spaces is intro- ory in applications is explained; as an tests, but also for high-school teachers EMS March 1999 33 RECENT BOOKS wishing to enrich their teaching with In fact, the book covers two ‘sub- The four-colour map problem, river some interesting non-routine prob- courses’. The first presents the mod- crossings, dinner-guest problems, the lems, and for individuals who are ern theory of dynamical systems, in finite group problem, the Dirichlet interested in solving challenging prob- Chapters 1, 2, 8 and 9, introducing drawer principle and many more are lems. (lbo) topological dynamics and ergodic the- explained with their history of success- ory; the other provides a complete ful, as well as erroneous, solutions. If K. Engel, Encyclopedia Sperner Theory, exposition of smooth actions, vector the origin of a new theory is connected of Mathematics and its Applications 65, fields, Lie groups, Lie algebras and with a solution of a problem (such as Cambridge University Press, 1997, 417 semisimple groups, including the the theory of knots or non-Euclidean pp., £50, ISBN 0-521-45206-6 structure theory, in Chapters 3, 5 and geometry) or if a theory is used to This book presents Sperner theory 7. A special role is played by Chapters solve some puzzle, its basic facts are from a unified point of view. The pre- 4 and 6, which offer an elementary explained in a very lucid way. Though sentation is very good and the book survey of algebraic geometry and alge- many parts of the book demand the should be understandable for a non- braic actions, and the development of reader’s full concentration, no special- specialist. It brings combinatorial invariant geometric structures. The ist knowledge of mathematics is need- methods together with various other use of differential-geometric language ed for an understanding. methods, and the covered area is very is one of the interesting features of this All essential facts are accompanied large. The main emphasis is on the book. The main rigidity theorems are by references and each of the twenty- main results and methods, and most of stated and proved in Chapter 10. three chapters ends with a list of refer- the results are given with complete The exposition is based on courses ence books and articles. While reading proofs. taught by the author at Pennsylvania about problems and puzzles, the read- The book is divided into eight chap- State University and Washington er will meet many outstanding person- ters. Chapter 1 starts with Sperner’s University, St Louis. The book can be alities who have entered the history of theorem which answers the question: recommended for a wide audience, mathematics. The philosophy of math- ‘what is the maximum possible size of including anyone interested in dynam- ematics is also discussed whenever a family of pairwise unrelated (with ical systems, Lie theory and differen- appropriate. All is flavored by respect to inclusion) subsets of a finite tial geometry. (jsl) Gardner’s special way of narrating the set?’; this chapter also contains main natural sciences. (jtro) examples of Sperner theory. Chapter Y. Fong, U. Knauer and A.V. 2 deals with extremal problems for Mikhalev (eds.), First International J. Gunawardena (ed.), Idempotency, finite sets and describes basic methods Tainan-Moscow Algebra Workshop, Publications of the Newton Institute, to solve these problems; Chapter 3 Proceedings of an International Cambridge University Press, Cambridge, 1998, considers profiles of families of subsets Conference held at National Cheng Kung 443 pp.; £55, ISBN 0-521-55344-X of [n] belonging to certain classes, University. Tainan, Taiwan, 23 July–22 The aim of this volume is to provide from the point of view of linear pro- August, 1994, Walter de Gruyter, Berlin, an up-to-date survey on various areas gramming. Chapter 4 deals with the 1996, 349 pp.; DM248, ISBN 3-110- of mathematics where semirings with flow-theoretic approach in Sperner 14864-1 an idempotent addition operation theory; it starts with Dilworth’s theo- The volume begins with three invited appear. Most of the papers record the rem followed by the max-flow min-cut survey articles by leading experts on workshop organized by Hewlett- theorem, the first of several min-max current trends in their areas: P. M. Packard’s Basic Research Institute in theorems described in this chapter. Higgins on Ramsey’s theorem in algebra- the mathematical sciences, but there Chapter 5 is on matchings and sym- ic semigroups, A. A. Mikhalev on are also some others, written especial- metric chain orders, and the partition Combinatorial aspects of the theory of Lie ly for this book. It has become widely lattice approach in Chapter 4 and the superalgebras, and A. V. Mikhalev on known only recently that linearization algebraic approach in Sperner theory Isomorphisms and anti-isomorphims of of certain non-linear optimization can be considered as a link between endomorphism rings of modules. The sec- problems is possible over semirings the flow-theoretic material which is ond part of the volume consists of with idempotent addition, but not described in detail in nearly 100 pages twenty-two original research papers over the standard number systems. in Chapter 6. Chapter 7 deals with which present new results including These methods appear, for example, limit theorems and asymptotic esti- solutions of some long-standing prob- in the theory of computation, pure mates. Chapter 8 on Macaulay posets lems in rings and near-rings, Lie alge- and applied probability and mathe- describes a theory based on the bras, quantum groups, semigroups matical physics, and a systematic study Kruskal-Katona theorem. (jval) and combinatorics. (jtu) of the subject has emerged. The full list of the contributions R. Feres, Dynamical Systems and M. Gardner, The Last Recreations. reflects the diversity of the research: J. Semisimple Groups: An Introduction, Hydras, Eggs, and Other Mathematical Gunawardena, An introduction to idem- Cambridge Tracts in Mathematics 126, Mystifications, Springer-Verlag, New potency; J.-E. Pin, Tropical semirings; D. Cambridge University Press, 1998, 245 York, 1997, 392 pp.; DM 39.90, ISBN 0- Krob, Some automata-theoretic aspects of pp.; £35, ISBN 0-521-59162-7 387-94929-1 min-max-plus semirings; F. D’Alessandro The author develops in a detailed and The name of Martin Gardner, a and J. Sakarovitch, The finite power self-contained way many aspects of Lie columnist of Scientific American and property for rational sets of a free group; theory, topological dynamics and author of many excellent publications H. Leung, The topological approach to the ergodic theory, while the prerequisites on recreational mathematics, suggests limitedness problem on distance automata; involve just a first-year graduate the likelihood of an exceptional book G. Mascari and M. Pedicini, Types and course in mathematics. The main pur- in its genre and indeed, the book dynamics in partially additive categories; pose of the book is to introduce the comes up to the reader’s expectations. S. Gauber and J. Mairesse, Task rigidity theorems of Margulis and It touches almost all the main prob- resource models and (max,+)-automata; Zimmer at a level addressed primarily lems which have inspired mathemati- G. Cohen, S. Gaubert and J.-P. at non-experts and graduate students. cians in the last two centuries or more. Quadrat, Algebraic system analysis of 34 EMS March 1999 RECENT BOOKS timed Petri nets; F. Baccelli and J. erties of solutions—are studied as an gradually explained and applied to Mairesse, Ergodic theorems for stochastic introduction to non-linear results important topics in a clear and self- operators and discrete event networks; B. obtained for small and smooth data. consistent form, accompanied by a Gaujal and A. Jean-Marie, The last chapters are devoted to a huge number of examples and exercis- Computational issues in recursive stochas- study of microlocal analysis of singu- es. tic systems; R. D. Nussbaum, Periodic larities of solutions of non-linear dif- The first chapter deals with finite points of nonexpansive maps; A. Göurel, ferential equations by means of the systems and opens the world of states, O. C. Pastravanu and F. L. Lewis, A sys- paradifferential calculus. entropy and equilibrium of physical tem theoretic approach for discrete-event This handy monograph is well writ- systems. Gibbs measures and the control of manufacturing systems; D. D. ten and its concise style will be appre- famous Ising model are introduced in Cofer and V. K. Garg, Idempotent struc- ciated both by postgraduate students their special form for finite systems. tures in the supervisory control of discrete and by specialists in the field. (mr) The ergodic theory and ergodicity of event systems; R. A. Cuninghame- measures preserving dynamical sys- J. W. Jerome (ed.), Green, Maxpolynomials and discrete- Modelling and tems are discussed in the following event dynamical systems; V. N. Computation for Applications in chapter. Two chapters are then devot- Kolokoltsov, The stochastic HJB equation Mathematics, Science, and Engin- ed to an explanation of entropy, infor- , Numerical Mathematics and and WKB method; S. Samborskii, The eering mation, pressure, free energy and Scientific Computation, Clarendon Press, Lagrange problem from the point of view of equilibrium states for general systems, Oxford, 1998, 215 pp.; £55, ISBN 0- idempotent analysis; V. N. Kolokoltsov and many results from the first chap- 198-50080-7 and V. P. Maslov, A new differential ter are here generalized and This book contains articles based on a equation for the dynamics of the Pareto sets; explained in a geometrical way. In the workshop held at Northwestern M. Akian, J.-P. Quadrat and M. Viot, fifth chapter, the relationship between Duality between probability and optimiza- University in May 1996. It includes the Gibbs measures and equilibrium states following papers: Mathematics, compu- tion; P. Del Moral, Maslov optimization is discussed and the equilibrium states tational chemistry and battery building (M. theory: topological aspects; P. Del Moral for the general Ising model are stud- Ratner), Transport of multispecies conta- and G. Salut, Random particle methods in ied as an important case. Applications minants with biological and chemical kinet- (max,+)-optimization problems; E. of the general theory to Sinai-Bowen- ics in porous media (M. F. Wheeler, C. Wagneur, The geometry of finite dimen- Ruelle measures, fractals generated by Dawson and J. Eaton), Equidistribution sional pseudomodules; E. A. Walkup and iterated function systems, and pres- and extremal energy of N points on a G. Borriello, A general linear max-plus sure of systems and maximal dimesion sphere (Y. M. Zhou), Some reduced- solution technique; V. P. Maslov, measures are the subjects of the last dimension models based on numerical Axiomatics of thermodynamics and idempo- chapter. The mathematical prerequisi- methods (T. F. Dupont and A. E. tent analysis; and G. L. Litvinov and V. ties used in the main part of the book Hosoi), Viscous approximation to transon- P. Maslov, The correspondence principle are summarized in the appendix. ic gas dynamics: flow past profiles and for idempotent calculus and some computer This book is intended as a guide for charged-particle systems (I. M. Gamba applications. a one-semester course on equilibrium and C. S. Morawetz), Two-carrier semi- The articles cover both practical states and ergodic theory, but will also conductor device models with geometric and theoretical aspects and the whole be of use to many students and structure and symmetry properties (G.-Q. volume seems to be essential reading researchers in the field. (dh) Chen, J. W. Jerome, C.-W. Shu and D. for everybody interested in the area. Wang), Approximation issues for applica- S. Kotz and N. L. Johnson (eds.), (jsl) tions in optimal control and parameter esti- Breakthroughs in Statistics, Vol. III, L. Hörmander, Lectures on Nonlinear mation (H. T. Banks and R. H. Springer Series in Statistics, Springer- Hyperbolic Differential Equations, Fabiano), Zero distribution, the Szegö Verlag, New York, 1997, 559 pp.; DM Mathematics and Applications 26, curve, and weighted polynomial approxi- 114, ISBN 0-387-94989-5 and 0-387- Springer-Verlag, Berlin, 1997, 290 pp.; mation in the complex plane (I. E. 94988-7 DM 48, ISBN 3-540-62921-1 Pritsker and R. S. Varga), and Existence N. L. Johnson and S. Kotz have co- This book is a revised and enlarged and the singular relaxation limit for the edited the internationally acclaimed version of lecture notes given by the inviscid hydrodynamic energy model (Gui- ten-volume Encyclopedia of Statistical author at the University of Lund dur- Qiang Chen, J. W. Jerome and Bo Science, published by J. Wiley. Their ing 1986–87. The nature and the Zhang). work inspired them to publish a notion of ‘hyperbolicity’ is studied, From this survey we see that the chronicle of lives and achievements of starting from the basic concepts of book contains a large amount of inter- the most influential personalities in existence and uniqueness for systems esting material. It will be of interest to the field, spanning nearly four cen- of ODEs where the ‘hyperbolic behav- researchers and students of applied turies. This book collects more than iour’ of these—namely, the property mathematics, scientists and engineers 110 names with texts partially written of blowing up in finite time—is engaged in applied mathematics and by 75 experts from around the world, emphasised. Through the classical scientific computing. (mf) and contains many authentic photos examples connected with Burgers’ and illustrations. I find the book equation, the reader is driven into the G. Keller, Equilibrium States in extremely useful for students; it wild world of first-order systems of Ergodic Theory, London Mathematical enables them to find when and in conservation laws in one dimension. Society Student Texts 42, Cambridge which situations famous results con- The Young measure technique and University Press, 1998, 178 pp.; £13.95, nected with names of individual per- compensated compactness are studied ISBN 0-521-59534-7 and 0-521-59420-0 sons were found. in the context of these. Further, non- This book may serve as a guide or ref- It is interesting to see that many linear perturbations of the linear wave erence book for both mathematicians persons considered as Americans were equation and of the Klein-Gordon and physicists working with dynamical of European origin and that many of equation are studied. The linear systems. The theory of equilibrium them had a wide range of scientific results—namely, the asymptotic prop- states and its mathematical tools are interests, being originally educated as EMS March 1999 35 RECENT BOOKS pure mathematicians, physicists, polynomials can be found almost in all and graduate students. The only pre- astronomers, economists, biologists books dealing with computational or requisities are a knowledge of the fun- and geneticists. This fact again illus- applied mathematics. All numerical damental group and simple homology trates that statistics as a science has methods for the solution of non-linear theory. (mc) deep roots in other sciences. Statistical equations can also be used for polyno- R. Lowen, personalities have been classified into mial equations. But the special and Approach Spaces: The seven sections: forerunners (23 per- easy case of polynomials has inspired Missing Link in the Topology- , Oxford sons), statistical inference (24), statisti- many mathematicians and engineers Uniformity-Metric Triad Mathematical Monographs, Clarendon cal theory (19), probability theory (17), to create new and special methods. Press, Oxford, 1997, 253 pp.; £ 60, ISBN government and economic statistics Thus polynomials have been studied 0-198-50030-0 (17), applications in medicine and for a long time and the collected This book is a result of ten years work agriculture (8), and applications in sci- knowledge on this area is comprehen- of the author and his coauthors in the ence and engineering (6); some per- sive. The classical methods, such as the investigation of approach spaces (sets sons belong in several of these cate- Lehmer-Schur algorithm combined together with a function measuring gories. Individual entries are more with Newton’s method and those of distances from points to sets). The cat- concerned with lives of persons than Bairsow, Laguerre, etc., are widely egory of approach spaces (morphisms with technical details of their work, used methods for successively deter- are ‘contractions’) contains naturally which can be found more easily in the mining all roots. embedded categories of topological literature. Only four women are This book concentrates on further spaces, uniform spaces and metric included, some of them contributing iterative procedures which are often spaces (with contractions as mor- pioneering work in their periods (e.g. based in the theory of non-linear phisms). The approach structures Florence Nightingale). I find the book equations. The author describes the allow us to refine some known con- fascinating and recommend it to every Weierstrass method and its various cepts to get (for example) a measure of statistician and probabilist. As Karl modifications, applies the Euler- compactness and a measure of con- Pearson says in the preface: ‘It is Chebyshev algorithm on polynomials, nectedness, giving the right concepts impossible to understand a man’s investigates two-sided and multi-point for all three basic subcategories. At the work unless you understand some- methods, deals with choosing initial end, the author explains completions thing of his environment.’ (jju) approximation and discusses multiple and compactifications of approach roots. I appreciate that the author did R. Kress, spaces. Two appendices are included, Numerical Analysis, not avoid multiple and clustered com- Graduate Texts in Mathematics , one about the theory of categories, 181 plex zeros during numerical tests. Springer, New York, 1998, 326 pp.; DM and the other about some concrete This book is designated for gradu- 78, ISBN 0-387-98408-9 structures used earlier in the text. ate students in computational and The book is useful for those inter- This excellent book is intended as an applied mathematics, for mathemati- ested in generalizations of continuous introduction to numerical analysis for cians, engineers and research workers. structures and their categorical behav- students in mathematics, physics and (jzi) engineering. The first part, Chapters iour, or in finding open problems on 2 to 7, covers numerical linear algebra W. B. R. Lickorish, An Introduction to categories of continuous structures. and is concerned with the solution of Knot Theory, Graduate Texts in (mh) systems of linear and non-linear equa- Mathematics 175, Springer-Verlag, New tions. The necessary functional analyt- York, 1997, 201 pp., 114 fig.; DM 89, Y. I. Manin, Gauge Field Theory and ic tools are presented in Chapter 3. ISBN 0-387-98254-X Complex Geometry, 2nd edn., The second part of the book, Chapters This book is a clearly written introduc- Grundlehren der mathematischen 8 to 12, covers numerical analysis and tion to the theory of knots and links of Wissenschaften 289, A Series of deals with interpolation, numerical simple closed curves in three-dimen- Comprehensive Studies in Mathematics, integration, and the numerical solu- sional space. Since knot theory is a Springer-Verlag, Berlin, 1997, 346 pp.; tion of differential and integral equa- rapidly developing branch of mathe- DM 174, ISBN 3-540-61378-1 tions. Each chapter concludes with a matics and it has expanded enormous- This is the second edition of an excel- set of problems, intended as exercises ly, such an introduction cannot pre- lent and fundamental book on the and applications of the material in the sent all the latest developments. The Radon-Penrose transform in the chapter. book under review contains the follow- framework of complex geometry and The reader is encouraged to test all ing topics: basic notions, Seifert sur- on its supersymmetric extension. The the algorithms in this book on a com- faces, the Jones and bracket polynomi- main body of the book is the same as puter. The references at the end of the als, Seifert matrices and the Alexander in the first edition. The first two chap- book are intended as a possible guide polynomials, covering spaces, the ters treat in detail the geometry of flag to some of the literature covering the Conway polynomials, cyclic branch spaces and double fibrations of such topics of individual chapters more covers, connections between the Arf spaces, together with the Radon- exhaustively. The book is written in a invariant and the Jones polynomial, Penrose transform. A systematic nice style. The text is presented in a fundamental groups, obtaining 3- description of superalgebras and concise and easily understandable manifolds by surgery on S3, 3-mani- superspaces can be found in Chapters fashion and can be successfully mas- fold invariants from the Jones polyno- 3 and 4. The last chapter is devoted to tered in a one-year course. (kn) mials, and the Kauffman and HOM- supersymmetry and gravitation. FLY polynomials. Almost all the pre- Recent developments in the field N. V. Kyurkchiev, Initial Approximat- sented results are proved. The meth- are described in the new part—an ions and Root Finding Methods, ods used are basic differential topolo- appendix (45 pages) written by Sergei Mathematical Research 104, Wiley-VCH, gy, algebraic topology and combina- Merkulov. It consists of two sections: Berlin, 1998, 180 pp.; DM 128, ISBN 3- torics. the first describes several analogues of 527-40132-6 The book is directed towards a the Penrose non-linear graviton con- Chapters on the calculation of roots of broad audience of research workers struction; the second contains two new 36 EMS March 1999 RECENT BOOKS examples (Riemannian supermani- 0-521-57294-0 R. Remmert, Classical Topics in folds in dimension 3/2 and quater- The authors have chosen four non- Complex Function Theory, Graduate nionic supermanifolds in dimension trivial results as an invitation to mod- Texts in Mathematics 172, Springer- 4k/(2k+2)), illustrating well a general ern dynamical systems theory: J. Verlag, New York, 1998, 349 pp..; DM theory explained in the book. Franks’ version of the Poincaré- 79, ISBN 0-387-98221-3 The book should certainly be a part Birkhoff theorem on the fixed points This short review is not aimed at those of the library of anybody interested in of an area-preserving homeomor- who already know Remmert’s Theory of recent substantial interactions between phism of an annulus, the variational Complex Functions, the translation of complex geometry and mathematical principle for topological entropy, the second or third edition of physics. (vs) Fustenberg’s conjecture on ergodic Funktionentheorie I (FI) by the same measures for commuting transforms author. The book under review is a C. Müller, Analysis of Spherical of the circle and Szemeredi’s theorem translation of Funktionentheorie II (FII). Symmetries in Euclidean Spaces, on arithmetic progressions. The book is a very carefully written Applied Mathematical Sciences 129, Most of this book is devoted to classical advanced course on complex Springer-Verlag, New York, 1998, 223 topological dynamics and ergodic the- function theory. Although FII can be pp.; DM 128, ISBN 0-387-94949-6 ory on a level required for under- read independently of FI, it is highly The orthogonal group is clearly the standing proofs of the above-men- recommended that FI is available; the most important symmetry group tioned main results. Three working references in FII refer to the third edi- because of its principal role in examples (interval maps, homeomor- tion of FI. As stated in the Preface, the Euclidean geometry. The fact that the phisms of the circle and shifts) are choice of material is rather classical Laplace equation is invariant with explained in detail. The book is suit- (the theorems of Weierstrass and respect to rotations led from the very able for beginning graduate students, Mittag-Leffler, the Riemann mapping beginning to an extended use of spe- since only basic facts from topology, theorem, Runge’s theorem), but the cial functions (associated with repre- measure theory and linear algebra are reader will also find many other inter- sentations of the group of rotations) in needed. The absence of exercises is a esting topics. mathematics and mathematical main defect of the book. (jmil) As with FI, great care is taken to physics. explain the historical background and This book presents a systematic dis- J. Ramanathan, Methods of Applied to relate the treatment to the theory of cussion of a general theory of such Fourier Analysis, Applied and several complex variables. Thus the functions, based on a direct elemen- Numerical Harmonic Analysis, name index contains more than 150 tary computational approach. It is not Birkhäuser, Boston, 1998, 327 pp.; DM names (for 29 of them a short biogra- restricted to the physical dimension 3, 138, ISBN 0-8176-3963-2 and 3-7643- phy is also provided) and all chapters but treats the case of a general dimen- 3963-2 contain fairly representative bibliogra- sion. The Fourier and Radon trans- The aim of this book is to provide a phies (mostly involving references to forms are intertwining maps for the mathematical introduction to harmon- original works). The author presents action of the orthogonal group, it has ic analysis, with special emphasis on the material from many aspects, with direct consequences for the theory of those topics that find direct applica- clear compact proofs and numerous special functions treated in this book. tion in engineering and the sciences. historical remarks all over the text. The main topics discussed are sperical Basic material on Fourier series, Thus the book is a truly ideal source harmonics, Legendre and Gegenbauer Hardy spaces and Fourier transform for both teachers and students. For a polynomials, and Bessel and Hankel are interweaved with material that dis- mathematician who collects books that functions. The theory is extended to cusses discrete Fourier transform and represent the classical parts of mathe- the complex unit sphere and a com- fast algorithms, spectral theory of sta- matics, it is a book which should not be plexification of the Funk-Hecke for- tionary processes, control theory, and overlooked. (jve) mula is given. The last part contains a wavelets. The book consists of nine discussion of several integral trans- chapters on periodic functions, Hardy World Directory of Mathematicians, forms (the Fourier, Gauss, Weierstrass spaces, prediction theory, discrete sys- 11th edn., The International and Radon transforms), together with tems and control theory, harmonic Mathematical Union, Providence, 1998, a lot of examples and explicit formu- analysis in Euclidean space, distribu- 1093 pp. las. Recently, a very efficient and sys- tions, functions with restricted trans- In 1100 pages this book presents a pic- tematic approach to the theory of spe- forms, phase space, wavelet analysis; ture of the world of mathematicians. cial functions using the representation there are two appendices on the dis- In this 11th edition, 53911 mathe- theory was developed by N. Ja. crete Fourier transform and on maticians are listed, with their Vilenkin and others. In this book, tools Hermite functions. Problems of vary- addresses and (sometimes) e-mail coming from the representation theo- ing difficulty are given at the end of addresses. This is the main part of the ry of the orthogonal group are not each chapter; some ask the reader to publication (936 pages). Other very used. fill in details while others explore top- useful data are presented: the list of This book is well adapted to the ics related to those presented in the members of the International needs of applied mathematicians, text. Mathematical Union, the list of math- physicists and engineers, is written in This book is an excellent text/refer- ematical organizations and a geo- their usual language and certainly will ence for graduates and professionals graphical list of mathematicians from be very useful for them. (vs) in mathematics, engineering and the 69 countries. Needless to say, this is an physical sciences. It is also suitable as a extremely useful publication for every M. Pollicott and M. Yuri, Dynamical general self-study resource for profes- mathematical department or library. Systems and Ergodic Theory, London sionals and practitioners in harmonic (in) Mathematical Society Student Texts 40, analysis, fast Fourier transforms, algo- Cambridge University Press, 1998, 179 rithms, signal processing, electrical pp.; £14.95, ISBN 0-521-57599-0 and engineering and scientific computing. (kn)

EMS March 1999 37 UNIVERSITY OF CAMBRIDGE KUWAIT PROFESSORSHIP OF NUMBER THEORY AND ALGEBRA NOTICE

The Board of Electors to the Kuwait Professorship of Number Theory and Algebra invite applications for this Professorship, which will be newly established from 1 October 2000, following a generous benefaction from the Kuwait Foundation for the Advancement of Sciences. It is hope that the successful candidate will take up appointment on 1 October 2000 or as soon as possible thereafter.

The appointment will be subject to the Statutes and Ordinances of the University.

Candidates for the Professorship should send their applications, marked ‘Confidential’, together with the names of two referees to the Secretary General of the Faculties, from whom further information is available, at the University Offices, The Old Schools, Cambridge, CB2 1TT, so as to reach him no later than 31 May 1999.

Informal enquiries should be made to Professor John Coates ([email protected], Tel +44 (0)1223 337994, Fax +44 (0)1223 337920).

The University follows an equal opportunity policy.

38 EMS March 1999 EMS March 1999 39