CONTENTS

EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY

EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected]

ASSOCIATE EDITORS STEEN MARKVORSEN Department of Mathematics Technical University of Denmark NEWSLETTER No. 44 Building 303 DK-2800 Kgs. Lyngby, Denmark June 2002 e-mail: [email protected] KRZYSZTOF CIESIELSKI EMS Agenda ...... 2 Mathematics Institute Jagiellonian University Reymonta 4 Editorial by Luc Lemaire ...... 3 30-059 Kraków, Poland e-mail: [email protected] Berlingen 2 ...... 5 KATHLEEN QUINN The Open University [address as above] EMS Summer School in Eilat ...... 7 e-mail: [email protected]

SPECIALIST EDITORS Women & men in mathematics ...... 10 INTERVIEWS Steen Markvorsen [address as above] Coping with publishers and copyright ...... 14 SOCIETIES Krzysztof Ciesielski [address as above] Anniversaries - Bento Caraça ...... 17 EDUCATION Tony Gardiner Anniversaries - William Burnside ...... 18 University of Birmingham Birmingham B15 2TT, UK Can you spare books? ...... 21 e-mail: [email protected] MATHEMATICAL PROBLEMS Forthcoming Conferences ...... 23 Paul Jainta Werkvolkstr. 10 Zentralblatt MATH ...... 28 D-91126 Schwabach, Germany e-mail: [email protected] Recent Books ...... 29 ANNIVERSARIES June Barrow-Green and Jeremy Gray Open University [address as above] Designed and printed by Armstrong Press Limited e-mail: [email protected] Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK and [email protected] telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134 CONFERENCES email: [email protected] Kathleen Quinn [address as above] Published by European Mathematical Society RECENT BOOKS ISSN 1027 - 488X Ivan Netuka and Vladimir Sou³ek Mathematical Institute Charles University The views expressed in this Newsletter are those of the authors and do not necessarily Sokolovská 83 represent those of the EMS or the Editorial team. 18600 Prague, Czech Republic e-mail: [email protected] NOTICE FOR MATHEMATICAL SOCIETIES and [email protected] Labels for the next issue will be prepared during the second half of August 2002. Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of ADVERTISING OFFICER Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: Vivette Girault [email protected] Laboratoire d’Analyse Numérique Boite Courrier 187, Université Pierre INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER et Marie Curie, 4 Place Jussieu Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, 75252 Paris Cedex 05, France Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e- mail: ([email protected]). Please include the name and full address (with postal code), tele- e-mail: [email protected] phone and fax number (with country code) and e-mail address. The annual subscription fee (including mailing) is 65 euros; an invoice will be sent with a sample copy of the Newsletter.

EMS June 2002 1 EMS NEWS EMS Committee EMS Agenda EXECUTIVE COMMITTEE 2002 PRESIDENT (1999–2002) 21-26 June Prof. ROLF JELTSCH EURESCO Conference: Seminar for Applied Mathematics ETH, CH-8092 Zürich, Switzerland Discrete Painlevé Equations and the Solvability of Difference Equations e-mail: [email protected] Giens, near Toulon (France) VICE-PRESIDENTS webpage: http://www.esf.org/euresco/02/ Prof. LUC LEMAIRE (1999–2002) Department of Mathematics 1-5 July Université Libre de Bruxelles Congrès de Mathématiques Appliquées à la mémoire de Jacques-Louis Lions C.P. 218 – Campus Plaine Collège de France, Paris (France) Bld du Triomphe B-1050 Bruxelles, Belgium e-mail: [email protected] e-mail: [email protected] webpage: http://acm.emath.fr/congres-jllions Prof. BODIL BRANNER (2001–2004) Department of Mathematics 15 August Technical University of Denmark Deadline for submission of material for the September issue of the EMS Newsletter Building 303 Contact: Robin Wilson, e-mail: [email protected] DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] 28-30 September SECRETARY (1999–2002) Prof. DAVID BRANNAN Executive Committee meeting in Stockholm (Sweden), at the invitation of the Department of Pure Mathematics Swedish Mathematical Society The Open University Walton Hall 30 September Milton Keynes MK7 6AA, UK Deadline for proposals for 2004 EMS Lectures. e-mail: [email protected] Contact: David Brannan, e-mail: [email protected] TREASURER (1999–2002) Prof. OLLI MARTIO Department of Mathematics 15 November P.O. Box 4 Deadline for submission of material for the December issue of the EMS Newsletter FIN-00014 University of Helsinki Contact: Robin Wilson, e-mail: [email protected] Finland e-mail: [email protected] 31 December ORDINARY MEMBERS Deadline for bids for the Fifth European Mathematical Congress, 5ecm, in 2008 Prof. VICTOR BUCHSTABER (2001–2004) Contact: EMS Secretariat, e-mail: [email protected] Department of Mathematics and Mechanics Moscow State University Deadline for Raising Public Awareness Article Competition 119899 Moscow, Russia Contact: Vagn Lundsgaard Hansen, e-mail: [email protected] e-mail: [email protected] Prof. DOINA CIORANESCU (1999–2002) Laboratoire d’Analyse Numérique 2003 Université Paris VI 8-9 February 4 Place Jussieu Executive Committee meeting in Nice (France), by invitation of the local organisers 75252 Paris Cedex 05, France of AMAM2003. e-mail: [email protected] Prof. RENZO PICCININI (1999–2002) Dipartimento di Matematica e Applicazioni 10-13 February Università di Milano-Bicocca AMAM2003: EMS-SMAI-SMF Meeting in Nice (France) Via Bicocca degli Arcimboldi, 8 Mathématiques Appliquées - Applications des Mathématiques (Applied Mathematics - 20126 Milano, Italy Applications of Mathematics) e-mail: [email protected] Contacts: Doina Cioranescu, e-mail: [email protected] Prof. MARTA SANZ-SOLÉ (2001-2004) and Mireille Martin-Deschamps, e-mail: [email protected] Facultat de Matematiques Universitat de Barcelona webpage: http://acm.emath.fr/amam/ Gran Via 585 E-08007 Barcelona, Spain 1 March e-mail: [email protected] Deadline for proposals for 2004 EMS Lectures. Prof. MINA TEICHER (2001–2004) Contact: David Brannan, e-mail: [email protected] Department of Mathematics and Computer Science 7-12 July Bar-Ilan University CIME-EMS Summer School at Bressanone/Brixen (Italy) Ramat-Gan 52900, Israel e-mail: [email protected] Stochastic Methods in Finance EMS SECRETARIAT Organisers: Marco Frittelli and Wolfgang J. Runggaldier Ms. T. MÄKELÄINEN Department of Mathematics P.O. Box 4 2004 FIN-00014 University of Helsinki 25-27 June Finland EMS Council Meeting, Stockholm (Sweden) tel: (+358)-9-1912-2883 fax: (+358)-9-1912-3213 telex: 124690 27 June - 2 July e-mail: [email protected] 4th European Congress of Mathematics, Stockholm website: http://www.emis.de 2 EMS June 2002 EDITORIAL EditorialEditorial The 6th Research and Technology Development Framework Programme of the European Commission LUC LEMAIRE (EMS Vice-President)

The EMS and the EU of the Framework Programmes, he started wide on-line library for mathematics. Most of this text will be a practical guide, building a first project for FP6, and sub- describing how the European mathemati- mitted it to open debate. Needless to say, The structure of FP6 cal community can contribute to, and ben- the EMS took part in that debate through Leaving aside the EURATOM programme efit from, the 6th Framework Programme an initial position paper on research in on nuclear energy and the programme of of the European Commission (known as mathematics, and in the idea of a activities of the Joint Research Centre, FP6 FP6), which starts at the end of 2002 and European Research Area, and by numer- has two main components: applies until 2006. But let me first give ous reactions to the successive proposals – integrating and strengthening the some impression of the interactions issued by the Commission. On various European Research Area; between the European Commission and points, we received very positive reactions, – structuring the European Research the EMS during the preparation of FP6. and it seems in particular that the ‘return Area. Philippe Busquin, the Commissioner for mechanism’ for researchers working The first of these aims at the development Research, was appointed during the sum- abroad was based on an initial suggestion of priority themes: these being quite spe- mer of 1999. A physics graduate from the of the EMS. cific, mathematics per se does not figure in Université Libre de Bruxelles, he brought We are currently examining with all the this part. ambitious ideas for European research – relevant key bodies, societies and compa- Now, mathematics can (or must) play a namely, the European Union political nies, and with the European Commission, role in research on these themes, so math- agenda. Following the four-yearly rhythm the possibilities for developing a world- ematicians need to have a close look at these programmes. The second one is essentially the follow-up of Training and mobility of researchers and Infrastructures, with a large scope and hopefully an increased budget. Mathematics will con- tinue to be part of that programme. Here is a description of these two parts, from the point of view of mathematics. The full documents used at the time of writing this summary can be found on the web site of the Commission, http://europa. eu.int/comm/research/nfp. They are the Amended proposal for council decision of January 30, 2002 (241 pages!), the Introduction to the instruments available and Provisions for implementing networks of excel- lence (February 28, 2002). Documents will continue to appear on this site, and may contain modifications with respect to the present description. Finally, a note on vocabulary to avoid confusion. In the Fifth Framework Programmes, mathematics was present under Research networks, or Research train- ing networks: it is still present in FP6 under the name Marie Curie research training net- works. On the other hand, FP6 now has Networks of excellence that are not related to the training networks, and are a new instrument of the research policy.

Integrating and strengthening the ERA This component, with the large budget of 12855 million euros for four years, aims mostly at seven priority themes: 1.1.1. Genomics and biotechnology of health 1.1.2. Information Society technologies 1.1.3. Nanotechnologies and nano- sciences, knowledge-based multi- functional materials, and new pro- duction processes and devices 1.1.4. Aeronautics and space 1.1.5. Food quality and safety EMS Vice-President Luc Lemaire with European Commissioner Philippe Busquin 1.1.6. Sustainable development, global EMS June 2002 3 EDITORIAL change and ecosystems see how they could be integrated in inter- this programme, not only to the associated 1.1.7. Citizens and governance in a disciplinary projects. Clearly, the building states of the EU, but also to the ‘third knowledge based society up of the networks must start from the countries’ (all other countries world-wide). There is also a line covering a wider field themes as they appear in the list of priori- This opening will take various forms, of research in which mathematics could ties (such as genomics) and not from the already explicit in the host-driven and play a role: general needs of sciences like biology, individual-driven actions described above. 1.2.1. Supporting policies and anticipat- informatics, chemistry or mathematics. On the other hand, specific co-operation ing scientific and technological Priority 1.2.1 (anticipating scientific activities often exclude mathematical needs needs), sometimes nicknamed the eighth development, being restricted to urgent The numbering is that of the official EU priority, could open a new avenue for some problems of food safety, water pollution, documents, and will probably be used sys- mathematicians. Why not, for instance, health and resources. Still, a specific line tematically in all calls for proposals. propose a network of mathematics model- for Russia and the CIS countries includes ling, which would come as support to the ‘stabilisation of R & D potential’, certainly The way that funding by the EU will occur seven main priorities? We can only urge a crucial point for mathematics. here is mostly by two new financial appropriate groups of modelling centres ‘Instruments’: to take this initiative. What next? – integrated projects; For priorities 1.1.1–1.1.7, the Commission – networks of excellence. Structuring the ERA has already concluded a ‘Call for expres- Documents (still open to discussion) This part of the programme, with a sions of interest’, aimed at potential net- define the operation of these instruments. planned budget of 2655 million euros (for works of excellence or organisers of inte- For instance, a network of excellence four years), will be more familiar to the grated actions. This should allow the would be a group of centres working on mathematics community. Indeed, it is an Commission to be more precise when for- some aspect of one of the priority themes enlarged and improved version of Training mulating their calls for proposals (in early and planning to collaborate substantially and mobility, the Commission having recog- 2003), and may hopefully allow interested on that theme. nised the crucial aspect of human researchers to identify on a website the There is a fear that a concentration of resources for the future. interdisciplinary groups planning for the financial support on such networks would So, among this list, let us note: setting-up of networks. It is then up to restrict funding to a small number of very 2.Human resources and mobility interested mathematicians to contact those large laboratories, thereby creating a vacu- (i) Host-driven actions: Marie Curie potential organisers. um in between. Certainly, the administra- research training networks, Marie Concerning the structuring part, the tion of a network will require substantial Curie host fellowships for early stage calls for proposals should come out at the work (and staff). Still, some recommenda- research training, Marie Curie host end of 2002 or in early 2003. tions appear in the 28 February 2002 doc- fellowships for the transfer of knowl- The important point is to check regular- ument of the Commission, only partially edge (allowing for invitation of high ly the websites where calls appear, proba- answering those fears. level researcher), Marie Curie con- bly on http://www.cordis.lu/rtd2002 or In particular, ‘it is important that these ferences and training courses (fund- http://europa.eu.int/comm/research/nfp.html. networks do not act as “closed clubs”, and ing of conferences and of participa- The official launch of FP6 will be each network will be given a mission to tion of young scientists). marked by a large meeting in Brussels on spread excellence across its boundaries’. (ii) Individual-driven actions: Marie 11-13 November 2002. Also, ‘each network of excellence is expect- Curie intra-European fellowships, ed to have ambitions goals and to assemble Marie Curie outgoing international A regular column the critical mass to achieve these goals. fellowships (allowing young scientists Some writers or journalists get to write a The critical mass will vary from topics to from the EU and ‘associated coun- regular column (daily or weekly) in various topics’. This could be good news for math- tries’ to work in third countries (out- newspapers. It now appears that I have ematics (and the social sciences), where the side the EU and associated states) such a four-yearly column (having likewise critical mass is much lower than in the with a mandatory second phase in described FP5 in issue 32 of this Newsletter). experimental sciences. Europe, Marie Curie incoming inter- I look forward to preparing a description To continue with the description of a national fellowships (to attract top- of FP7 for issue 60 in June 2006 – a network of excellence, it would include a class researchers from third coun- renewed adventure for me. programme of jointly executed research, a tries). set of integrating activities (co-ordination (iii)Excellence promotion and recogni- of activities, creation of research facilities tion: grants, prizes and Marie Curie Journal of the of common interest, and perhaps reloca- chairs (to attract top-class tion of staff) and activities for spreading researchers for a period of three European excellence (training of researchers from years). Mathematical Society outside the network and raising public (iv) Return and reintegration mecha- awareness). nisms, directed at researchers having (JEMS) Integrated projects are organised differ- completed a Marie Curie fellowship, ently, and ‘should be directed at obtaining or having spent at least five years The next issue of JEMS (Vol. 4, No. specific results applicable in terms of, for outside Europe. 2) will contain the following instance, products, processes or services’, Then come two more components: articles: so that they will probably be further away 3.Research infrastructures from fundamental research. 4.Science and society Now, where could mathematics fit in? Kai Cieliebak, Handle attaching in Certainly, any application in an EC pro- The EMS will aim at further developing symplectic homology and the Chord gramme must fit the terms and rules of infrastructures like Zentralblatt-MATH (as Conjecture that programme, so this part of FP6 is not was already done with a grant from the suitable to obtain funding for mathematics FP5 infrastructure line) and will also con- in general. tribute to the digitisation of the mathemat- and However, different branches of mathe- ics literature and its distribution on-line. matics have a role to play in the seven pri- A programme on raising awareness of Colette Moeglin, Sur la classifica- ority themes. For groups of mathemati- science is included in Science and society. tion des series discrètes des groupes cians working in these areas, the strategy classiques p-adiques: paramètres de must be to contact the networks that are Opening to third countries already in the process of building up, to We are very happy to see a new opening in Langlands et exhaustivité. 4 EMS June 2002 EMS NEWS BerlingenBerlingen 22 Second EMS Brainstorming Meeting David Salinger (EMS Publicity Officer)

In April, the Society organised a brain- However, the new project discussed at Peter Moss & Jean-Pierre Bourguignon storming meeting of the Executive Berlingen is an ambitious one, initiated by Committee, EMS officers and representa- the AMS, but requiring international part- whether we should hold an annual meet- tives from the various national societies ners, to ‘digitise’ all past mathematical lit- ing, in January, rather like that of the who are its corporate members. The place erature. The project, according to a paper AMS, which also serves as a useful place for was Berlingen, on the Swiss shore of Lake by John Ewing of the AMS, is to make the recruiting young members of staff. After Constance. digitised material freely available. But to discussion, the idea was rejected, partly because of the difficulty of finding a time that would be convenient for all European Universities, but also because the condi- tions of the job market are so diverse across Europe that it is doubtful whether an EMS meeting could usefully help recruitment. Nonetheless, there is a noticeable stimulus to the Society’s activi- ties at events like the 3ecm, when the Executive Committee, subcommittee chairs and representatives of the national societies can meet. We hope that the Abel conference in Norway in June will give a similar impetus.

Four topics were on the menu: the future make it useful there will have to be index- EMS Publishing house of Zentralblatt-MATH, European participa- ing systems and search engines: these The EMS Publishing House now has an tion in the world maths digitised library, should be supplied at a commercial rate. independent existence as (part of) a trust the Society’s policy on meetings, and the The EMS wants to be the European part- based in Zürich, with support from the policy of the EMS Publishing House. The ner in this enterprise and, (having taken Technische Hochschule: ETHZ. The meeting was also to draft ‘expressions of advice from the EU) will submit an expres- Publications Committee, which includes interest’ for support for some of these sion of interest ‘parallel to’ the 6th the managing director Thomas activities within the European 6th Framework programme. Hintermann, should have an advisory role Framework Programme (see Luc in the Publishing House’s policy. Lemaire’s editorial in this Newsletter). Meetings One of the purposes of founding the The Society intends to continue its Publishing House was to have a restraining Summer Schools, EMS Lectures and influence on journal prices, which have Diderot Forums, and will seek EU funding been rising well ahead of inflation. It was for them. It is seeking to expand the EMS clear that, in the short term, pricing policy would be subordinate to the practicalities of building a viable operation. However, a preference was stated for having low prices, rather than for generating a large surplus to finance the EMS. It was agreed that there ought to be substantial discounts for EMS members. The Publishing House Renzo Piccinini & Mina Teicher would consider distributing material from small European mathematics publishers, if Zentralblatt-MATH this were commercially viable. A number Currently, Zentralblatt-MATH is run by a Susan Hezlet & Carles Casacuberta of issues, particularly in the area of elec- governing body representing the Society, tronic publishing, were identified for fur- Springer-Verlag, and FIZ Karlsruhe (the ther discussion. latter being a German national organisa- lectures to small conferences centred on tion). To ensure its future, the organisa- the lectures. It is also starting to hold joint Our President, Rolf Jeltsch, worked us tion needs other European partners and meetings with its member societies. The hard, but we were permitted an hour’s walk continuing funding from the European first one will be in Nice next February, up the hillside overlooking the lake, where Union, which the Society will apply for. An held jointly with both French Societies, it narrows into the river Rhein. evolution, already partly under way, was SMF and SMAI: the subject will be Applied envisaged towards a more devolved struc- Mathematics and Applications of ture, with local editorial boards. Mathematics. The following joint meeting will be with the Portuguese mathematical Maths digitised library society, in September 2003. The meetings Various projects are afoot to make back programme will form a bid to the 6th issues of mathematical journals and books Framework Programme. If the bid is suc- available electronically. One such, the cessful, the Society will be able to have an EMIS Electronic Library of Mathematics, is office (possibly in Brussels) to co-ordinate available free at www.emis.de and there are its meetings. several other significant projects in hand. A question raised at Berlingen was

EMS June 2002 5 NEWS International Congress of Mathematicians 2002 This year’s ICM is being held in Beijing, China, from 20 to 28 August.

The twenty plenary lecturers are: Noga Alon (Israel), Douglas Arnold (USA), Alberto Bressan (Italy), Luis Caffarelli (USA), Sun-Yung Alice Chang (USA), David Donoho (USA), Ludwig Dmitrievich Faddeev (Russia), Shafi Goldwasser (USA/Israel), Uffe Haagerup (Denmark), Michael Hopkins (USA), Victor Kac (USA), Harry Kesten (USA), Frances Kirwan (UK), Laurent Lafforgue (France), David Mumford (USA), Hiraku Nakajima (Japan), Yum-Tong Siu (USA), Richard Taylor (USA), Gang Tian (USA/China) and Edward Witten (USA). There are also 167 invited speakers – those from Europe are: Logic: Elisabeth Bouscaren (France), Jan Denef (Belgium), Moti Gitik (Israel), Daniel Lascar (France) Algebra: Alexei Igorevich Bondal (Russia), Dmitri Olegovich Orlov (Russia), Zlil Sela (Israel) Number theory: Henri Cohen (France), Jean-Marc Fontaine (France), Annette Huber (Germany), Ilya Piatetski-Shapiro (Israel), Emmanuel Ullmo (France) Differential geometry: Paul Biran (Israel), Paul Seidel (France) Topology: Yuri Vitalievich Chekanov (Russia), Emmanuel Giroux (France), Ulrike Tillmann (UK) Algebraic and complex geometry: H. Esnault (Germany), Lothar Goettsche (Italy), Richard Pink (Switzerland), Miles Reid (UK), Vadim Schechtman (France), Burt Totaro (UK) Lie group and representation theory: Patrick Delorme (France), Michael Harris (France), Marie-France Vigneras (France) Real and complex analysis: Nicolas Lerner (France), Michael McQuillan (France) Operator algebras and functional analysis: Semyon Alesker (Israel), Philippe Biane (France), Vincent Lafforgue (France), Rafal Latala (Poland) Probability and statistics: Girard Ben Arous (Switzerland), Jean Bertoin (France), Erwin Bolthausen (Switzerland), Kurt Johansson (Sweden), Andrei Yurievich Zaitsev (Russia), Ofer Zeitouni (Israel) Partial differential equations: Luigi Ambrosio (Italy), Tero Kilpeläinen (Finland), Vladimir Maz’ya (Sweden), Tristan Rivière (Switzerland.) ODE and dynamical systems: Alain Chenciner (France), Michael Benedicks (Sweden), Christian Bonatti (France), Eduard Feireisl (Czech Republic), Bernold Fiedler (Germany), Leonid Pavlovich Shilnikov (Russia), Dmitry Treschev (Russia) Mathematical physics: Jean Bricmont (Belgium), Jean-Pierre Eckmann (Switzerland), Nikita Aleksandrovich Nekrasov (France) Combinatorics: Imre Barany (Hungary/England), Aart Blokhuis (Netherlands), Philippe Flajolet (France), Nathan Linial (Israel), Bruce Reed (France/Canada), Günther Ziegler (Germany) Mathematical aspects of computer science: Uriel Feige (Israel), Ran Raz (Israel) Numerical analysis and scientific computing: Albert Cohen (France), Rolf Rannacher (Germany), Christoph Schwab (Switzerland) Application of mathematics in the sciences: Yann Brenier (France), Nicole El Karoui (France), Alexander Mielke (Germany), Felix Otto (Germany), Alfio Maria Quarteroni (Switzerland /Italy) Mathematics education and popularization of mathematics: Jean-Luc Dorier (France), Vagn Lundsgaard Hansen (Denmark), Jan De Lange (Netherlands), Gabriele Kaiser (Germany), Ivan Yaschenko (Russia), Celia Hoyles (UK), Hans Niels Jahnke (Germany), Nitsa Movshovitz-Hadar (Israel) History of mathematics: Umberto Bottazzini (Italy), Moritz Epple (Germany)

Collaborative Research Programmes PESC area each year, with funding on aver- EUROPEAN SCIENCE (EUROCORES), which is a major trans- age at 75k euros per annum over 3 years. national basic research funding pro- Scientific programmes are longer-term FOUNDATION (ESF) grammes activities on specific themes, and typically – networking activities, which provide bring together teams working in 7 to 10 The European Science Foundation is the funds for European scientists to network countries. These activities are funded on European association of over 70 major over a range of time scales. an à la carte basis by ESF member organisa- national funding agencies devoted to scien- In this latter category, three ‘instruments’ tions, with an average budget of 100k euros tific research in 27 countries. The EMS and are available: per annum over 5 years. PESC normally the ESF, through its Physical and Exploratory workshops enable scientists to recommends between 4 and 6 new pro- Engineering Sciences Committee (PESC), come together to discuss topical and grammes each year, and operates a two- have recognised that they share common emerging issues, usually with the objective stage application procedure, with outline interests, and are developing closer links. of identifying future directions and collabo- proposals being sought in October. PESC’s remit covers physics, chemistry, rations. An annual ESF-wide call for pro- PESC has supported a small number of mathematics, information and computer posals is made, with a closing date in May, workshops, networks and programmes in sciences and the engineering sciences. for events to be held during the following various branches of mathematics, but would PESC’s activities can be separated into year. PESC normally supports at least 10 of welcome an increased number of propos- three broad areas: these events at an average budget of 10k als. – giving expert scientific advice on strate- euros. To find more information about PESC gic issues, including undertaking inde- Scientific networks are normally interdisci- and ESF, visit the website www.esf.org/pesc pendent review of major research and plinary and are aimed at coordinating To contact the PESC secretariat, e-mail infrastructure programmes and propos- activities to stimulate and consolidate the [email protected] als community in particular fields. There are To be informed of PESC news, pro- – initiating strategic science activities, such two ESF-wide closing dates (31 May and 30 grammes and closing dates, ask [email protected] as ESF Scientific Forward Looks, which November) each year. Normally between 2 to put you on the PESC electronic mailing are foresight exercises, and ESF and 4 new networks are supported in the list.

6 EMS June 2002 EMS NEWS EMSEMS SummerSummer SchoolSchool inin Eilat,Eilat, IsraelIsrael 24-28 February 2002 Mina Teicher

The EMS Summer School Computational phere at the school. The nice weather and Algebraic Geometry and Applications, support- blue sky, the beauties of the Red Sea and ed by the EMS, the EU (under the EAGER the Eilat mountains, and the various resort program), and the Emmy Noether attractions all failed to compete with alge- Research Institute, took place in Eilat braic geometry. One could see students (Israel) from 24 to 28 February 2002. It practising in the lecture room as late as 10 was organised by Mina Teicher and Boris p.m. Kunyavskii (Bar-Ilan University, Ramat The school took place in a beautiful Gan, Israel) and directed by W. Decker resort, right on the beach of the Red Sea! (University of Saarbrücken, Germany). During the long lunch break the students There were about 40 participants: 10 from could dive and wine. On Monday night, Israel, 22 from other EMS member states the participants were invited to a Purim and the rest from other countries (USA, costume party in the hotel hall. The con- Canada, Korea and Vietnam). Almost all ference tour to Corral Island was held on a the participants were young researchers perfect sunny day: this charming island, (Diploma, PhD students and post-doctoral surrounded by deep blue waters, corrals fellows). A few of the participants were and beautiful fish, is located about 15 km researchers and students from computer south of Eilat, in Egyptian territorial science departments, interested in study- waters (we needed a one-day island visa to ing new computational tools for computer Egypt). We arrived there on an old sailing vision based on algebraic geometry. Most Mina Teicher ship (crossing the border in the water). A students brought along a laptop computer; small boat took us to the island where we some computers were available for the problem-oriented software (SINGULAR, hiked to the top of the hill (with its semi- other students. MACAULAY2). From the third day, the restored castle) and saw a spectacular view The school program included morning students were subdivided into two groups, of clear sky, red mountains, deep blue lecture courses given by G. Pfister according to their wishes and their techni- water, curved bays, and our classic ship (University of Kaiserslautern) and W. cal and mathematical level. The beginners with its sails winding in the northern (typi- Decker, as well as afternoon computer group studied Gröbner basis techniques in cal of the Red Sea) wind. From the top one exercise sessions prepared in advance by detail, while the advanced group managed could see four different countries (Israel, the lecturers: beforehand, the students had more sophisticated topics such as sheaf Egypt, Jordan and Saudi Arabia) meeting down-loaded the necessary software and cohomology (including the computation of in a multiple point. The view was breath- scripts from W. Decker’s Internet web-site. Beilinson monads) and the identification taking. The rest of the time was devoted to For the first two days the participants were of complex surfaces using the adjunction diving, snorkelling and a barbecue lunch. briefly introduced to the algebraic-geomet- method. We returned to Eilat and one of the famous ric problems under consideration and the There was a very intense working atmos- red sunsets of the Red Sea.

EMS June 2002 7 EMS NEWS EMSEMS lecturlectureses forfor 20032003 CallCall forfor prproposalsoposals

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

NewNew deadlinedeadline forfor ArticleArticle CompetitionCompetition

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

8 EMS June 2002 5ECM

EUROPEAN CONGRESS OF MATHEMATICS 2008 Call for Bids for the 5ECM

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

General information on ECMs European Congresses of Mathematics are organised every four years: The first Congress was held in Paris in 1992, the second in Budapest in 1996, and the third in Barcelona in 2000. In 2004 the Congress will be held in Stockholm. The next free slot for a Congress is the year 2008. The Congress must be in Europe. Experience of previous Congresses suggests that the attendance might be expected to be around 1000 mathematicians. The dura- tion has so far been 5 days. 10 EMS Prizes to young outstanding European mathematicians are awarded at the opening ceremony. The Congress programme should aimed to present various new aspects of pure and applied mathematics to a wide audience, to offer a forum for discussion of the relationship between mathematics and society in Europe, and to enhance co-operation among mathematicians from all European countries. The standard format of previous ECMs has been: - About 10 Plenary Lectures; - Section Lectures for a more specialized audience, normally several held simultaneously; - Mini-symposia; - Film and mathematical software sessions; - Poster Sessions; - Round Tables. An exhibition space for mathematical societies, booksellers, etc. is required. No official language is specified and no interpreta- tion is needed. Proceedings of the previous ECMs have been published by Birkhäuser Verlag.

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

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

Marta Sanz-Solé and David Brannan

EMS June 2002 9 FEATURE

WWomenomen andand MenMen inin Mathematics:Mathematics: Then and Now – Part 1

Andrea E. Abele, Helmut Neunzert, Renate Tobies and Jan Krüsken

[This article is a translation of ‘Frauen Kaiserslautern, (mathematical and his- a university degree. Staatsexamen grad- und Männer in der Mathematik’ which torical aspects: H. Neunzert and R. uates can become teachers, whereas appeared in DMV-Mitteilungen 2/2001. Tobies) and Erlangen-Nürnberg (psy- diploma graduates cannot usually It is in two parts: Part 2 will appear in chological aspects: A. Abele and J. become teachers but work in other the next issue.] Krüsken) and is supported by the fields. The doctoral exam, which could Volkswagen Foundation. We are follow- previously be passed without a prior Studying mathematics is becoming increas- ing a double strategy by collecting both Staatsexamen, can only be taken today ingly popular with women but the top mathe- historical and present-day data and com- as a second academic degree – after the matical jobs are still filled by men. Why is paring them. From a historical perspec- first academic degree (Staatsexamen or this? Don’t women want these jobs, can’t they tive we look at women and men who diploma) and two or three years of doc- get them or are they hindered from getting chose mathematics as a profession at the toral studies. The doctoral degree exam- them? The Volkswagen Foundation is sup- beginning of the 20th century and ination consists of a written dissertation porting an interdisciplinary project entitled analyse their career paths. The compar- and an oral exam. ‘Women in mathematics: factors determining ative data is drawn from a longitudinal For our analysis we conducted written mathematical careers from a gender compar- study with women and men who gradu- interviews with graduates of mathemat- ative perspective’ which addresses these ques- ated in mathematics in 1998. By juxta- ics from 48 German universities, who tions and endeavours to explain the reasons posing historical and current data, we had either passed a Staatsexamen or a for the divergence between the career paths of hope to gain insights that apply to the diploma. This ‘modern sample’ consists women and men who have graduated in period under investigation, but also of 392 women (178 diploma graduates mathematics. serve to illustrate continuity and change and 214 Staatsexamen graduates) and Mathematics has become more popu- over the years. The focus of our interest 699 men (431 diploma graduates and lar with women. While, for example, in is gender comparison, as well as a gener- 268 Staatsexamen graduates), and is 1925 19%, and in 1950 20%, of first-year al description of career paths in mathe- representative of German mathematics mathematics students in Germany were matics. graduates in 1998. On average, the ques- women [9, 4], this figure had risen to The historical analysis is based on tionnaires were completed nine months 37% in 1987 and 47% in 1998 [8]. The recently discovered material from the after graduation; further interviews are number of women obtaining a doctoral Archive for Historical Education planned three and five years after grad- degree (PhD) in mathematics has dou- Research in Berlin. We analysed person- uation. bled from 11% in 1988 to 22% in 1998. al records of 3040 Prussian mathematics The questionnaire data provided by However, the number of women profes- teachers who passed their mathematics our modern sample and the archive sors is less than 4%, and outside acade- exams between 1902 and 1940, of whom records data of our historical sample are, mia few women hold top mathematical 462 (15.2%) were women. This ‘histori- of course, only partly comparable. In our positions. While the percentage of cal sample’ included Dr. Margarete modern sample we asked questions on women amongst first-year students of Kahn, a student of Hilbert’s (1880- the socio-economic background of the mathematics is the same as that for other 1942), Dr. Clara Löbenstein (b. 1883) students, their parents, their mathemat- subject areas, the percentage of women and the mathematics professors Helmut ical interest development, their courses mathematics professors is less than half Hasse (1898-1979), Erich Kamke (1890- of study, and their plans for career and of the average percentage of women pro- 1961) and Konrad Knopp (1882-1957), private lives: we have no such informa- fessors in all subjects (3.4% to 9%) [8]. and is representative because Prussia was tion on our historical sample. On the To some extent, the low number of the largest of the German states. At that other hand, the teacher records in the women in top mathematical positions is time, students passing a mathematics historical sample contain information on a result of a time lapse compared to exam could either take a Staatsexamen, long-term career development which other subjects. Since the percentage of an examination on one major and one or our modern sample cannot yet deliver. women studying and graduating in two minor subjects taken under the In the historical sample, there is also no mathematics increased later than in supervision of the state which was differentiation between Staatsexamen other subjects, it seems reasonable to (among other things) the entrance exam and diploma, because the latter was not assume that the number of women in top for an occupational career as a teacher, introduced until 1942. This differentia- mathematical positions will also increase or they could pass a doctoral examina- tion, however, is extremely important in later. Extrapolating into the future, tion (an academic degree). Our histori- the modern sample. Some data, howev- there will also be a very small share of cal sample includes persons who passed er, are available for both samples, such women (about 8%) in top mathematical the Staatsexamen as well as those who as father’s profession, the respective positions. Such a low number might elic- passed a doctoral examination. ages of students at the beginning and it questions, that may provocatively be Nowadays, there are two ways of study- end of studies, and examination grades. formulated as: are women not willing to ing mathematics and two different final This paper is a report on some of the pursue top mathematics careers, are exams. Mathematics students can either data analysed so far. Our presentation is they not capable of doing so, or are they pass the Staatsexamen (as in the histori- directed at three comparisons: hindered by external conditions? cal sample) or they can pass the ‘diplo- • the time comparison ‘then and now’; These are the questions we are ma’ (which did not exist prior to 1942). • the degree comparison ‘diploma ver- addressing in an interdisciplinary The diploma is the final exam of a sus Staatsexamen’; research project, which was launched in course of studies that focus primarily on • the gender comparison ‘women versus 1998 at the Universities of one subject, such as mathematics, and is men’. 10 EMS June 2002 FEATURE The gender comparison can be con- sity admission from the Oberlyzeum (pri- at graduation in the modern sample is ducted with all data. The then-now vate secondary schools for girls), where higher than in the historical sample comparison is possible only when com- young women could obtain teaching (27.6 years to 25.8). This is partly due parable data are available from both certificates for intermediate and higher to the fact that nowadays young men samples. The diploma–Staatsexamen secondary girls’ schools in the public usually complete their civil or military comparison is possible only for the sector. The introduction of mathematics service before taking up their studies, modern sample. and natural science courses had reper- whereas in the historical sample, they In Part 1 we consider the first of these com- cussions for the choices of study. usually completed it after graduation. parisons; the others will be discussed in Part According to the figures provided by At the beginning of the 20th century, 2. the Prussian statistics, mathematics was students changed university more often the third most popular choice (after than today. In the historical sample 65% Then and now philology and medicine) between 1909 of the students changed university at Historically, the socio-economic background and 1919 [11, pp. 22ff.]. As the legacies least once, regardless of gender, while of women students was different from that of of several women mathematicians make today’s figure is only 10%. On the other men; today this is not the case. clear, apart from an interest in mathe- hand, the percentage of students who In the historical sample, women more matics the decision was taken because (partially) pursue their studies in anoth- often had fathers with an academic edu- new possibilities opened up for earning er country was a lot smaller in the his- cation than men (45% to 27%). In the a living, as women were now allowed to torical sample than today: (women 20%, modern sample, the parents’ education- take up careers as mathematics or nat- men 16%). A clear change in the way al level is generally higher (40% have ural science teachers at public sec- women and men study can be seen in fathers, and 21% have both parents with ondary education institutions for the fact that in the present sample 93% an academic education) and there is no women. had a part-time job in addition to their difference between women and men Co-education of girls and boys is the studies, whereas in the historical sample with regard to the fathers’ level of edu- norm today. Whether secondary school only 12% of the women and 7% of the cation (42% of women and 39% of men mathematics is less motivating for girls men worked parallel to their studies, or have fathers with an academic educa- than for boys is the subject of much dis- had the chance to do so. However, these tion). However, these figures are not cussion (see [7]), but is not the subject changes are not specific to mathematics, specific to mathematics students but of our project. In the modern sample but are evident in all subjects [5]. apply to students from all subject areas. there are no differences between women In the past, women students came more and men with regard to the types of The achievements of women and men were, often from educated and wealthy back- schools they had attended, or the level and are, equal. grounds than men [3, 5, 6], because an of courses they had completed. 64% Historically and currently women and academic education for a daughter was said that mathematics was their men achieve the same examination costly and not customary. Today the favourite subject at school, and women results (see Table 1 below): the grades general level of education has risen con- said so even more than men (67% versus run from 1 (very good) to 6 (insuffi- siderably and the support given to 61%). Regardless of gender, all respon- cient). In the modern sample there is daughters is more or less equal to that dents in our modern sample attested only a difference between Staatsexamen for sons. that their interest in mathematics dated and diploma exams, which is a result of from an early age: 46% during primary different grading and examination Historically, education opportunities were school, and a further 32% by the middle practices. A comparison of the grades very different for women and men; today, of secondary education. 17% had had a reached in the Staatsexamen in the two they are the same. mathematical role model and for 38% samples show a remarkable similarity at At the beginning of the 20th century the someone had promoted their interest in the beginning and the end of the 20th education system was very different. mathematics (a ‘mentor’). century. Education was sex-segregated, and until In the modern sample we also collect- 1908 the only opportunities open to Study duration has lengthened in recent ed data on school grade point averages. women for a mathematics or natural sci- times and study behaviour has changed. Our sample had a better grade-point ence education were of a private nature. While students in the historical sample average (M = 1.9) than the respective A decree, signed on 18 August 1908, studied less than 10 semesters, study year’s cohort (M = 2.4) indicating that made Prussia the first German state to duration in our modern sample has mathematics students achieve higher introduce mathematics and natural sci- increased to roughly 12 semesters, for grades than other school leavers. There ence courses in its ‘Higher Secondary both women and men. The age at which were only two gender differences: men Schools for Girls’; Bavaria followed in women conclude their studies is nearly reported more informatics and comput- 1910. From 1908, new educational the same in both samples (historically er science experience than women, and opportunities for girls emerged, such as 27.1, today 26.8 years), a result of the women reported more additional quali- colleges offering the humanities (with compensating tendencies to study fications than men, such as speaking Greek and Latin), Realgymnasium (with longer today, and historically to have more than one foreign language and more mathematics and science, plus taken courses prior to entering universi- having further job qualifications. Latin and modern languages) and ty. In the historical sample, for exam- Oberrealschulen (no ancient languages, ple, 44% of the women gained admis- Both historically and at present there are but modern languages and more math- sion to university by taking the ‘fourth slight gender differences in the minors cho- ematics and science courses). After way’, described above, after having sen by women and men with majors in math- 1909, there was also a so-called ‘fourth obtained a teaching certificate: some ematics. way’ to obtain the Matura, the prerequi- even worked as teachers before In the historical sample, teachers with site school-leaving certificate for univer- enrolling at university. The age of men majors in mathematics had degrees in

Table 1. Examination grades in mathematics 1902/1940 1998/1999 Staatsexamen Diploma Women Men Women Men Women Men N=381 N=1864 N=205 N=206 N=176 N=428 Grade* 2.17 2.21 2.14 2.12 1.67 1.60 * Grades with honours weighted with 0.75, others according to grade scale. Rounded to two decimal places.

EMS June 2002 11 FEATURE seems that there is a slight gender dif- ference in interest for application of mathematics to economics (women more interest) or to the natural and technical sciences (men more interest).

The number of women and men obtaining a doctoral degree has remained similar. In the historical sample, 104 women (22.5%) and 676 men (26.2%) were awarded a PhD. Of these, one-third passed the doctoral examination with mathematics as major, and two-thirds with other majors. Men often chose physics as a non-mathematical major, while women chose biology and philoso- phy as often as physics (see Figure 1). Regarding publications after the PhD, there were only small gender differ- ences. The record cards of 12 women (2.6%) and 121 men (4.7%) recorded such work. Of course, participants of our modern sample may not yet have passed their PhD exams yet. We therefore asked them whether they intended to pass a doctoral exam. They indicated their Fig 1 intention on a 5-point likelihood scale ranging from ‘not at all’ to ‘certain’. one to four minors as well. Usually, they try and the private sector. Regarding diploma graduates, 21% of acquired a teaching certificate for three Today there are specific studies and women and 25% of men declared their subjects. Regardless of gender, the most diploma certificates for different orien- intention as ‘certain’, which neatly cor- likely combination was mathematics, tations within mathematics – for responds to the historical data. If we physics and chemistry (women 40%, instance, mathematics directed towards add the answers of ‘certain’ and ‘very men 38%). Women chose physics more applications in technical fields or in probable’, then 24% female diploma often as a minor, men more often as a economics. Within these new diploma graduates and 32% male diploma grad- second major. Today, Staatsexamen stu- courses men more often chose informat- uates intended to pass a PhD. These dents usually take only two subjects and ics (computer engineering) as a minor percentages also correspond very well the most frequent combinations are (men 42%, women 32%). Conversely, with the percentages of doctoral mathematics and physics, or mathemat- women chose economics as a minor degrees actually awarded in recent years ics and chemistry. In contrast to the his- more often than men (women 32%, men (see [8, 10]). Among the Staatsexamen torical sample, Staatsexamen women 25%). graduates, however, only 9% of both today choose physics less frequently as a These slight differences in the choice women and men assessed their inten- minor than Staatsexamen men (women of study minor between men and tion of passing a doctoral exam as ‘cer- 20%, men 45%). However, among the women, both historically and currently, tain’ or ‘very probable’. Irrespective of diploma graduates men and women may be interpreted as pragmatic behav- gender, the most important reason for hardly differed in the percentage of iour. Applied mathematics was not a wishing to take a doctoral exam was physics chosen as a minor (women 16%, promising career perspective for interest in science. There were also no men 17%). women at the beginning of the 20th gender differences in the content area Nowadays, subject areas such as prob- century, and so they chose this speciali- of the dissertation (as the written part of ability theory and statistics are well sation less frequently than men. Today, the doctoral study): probability liked among students, and (indepen- informatics and economics are equiva- theory/statistics, numerics and optimi- dent of gender) many graduates have lent minors with regard to future career sation were the most named areas. This passed their written exams in these prospects, and women and men are contradicts the occasionally heard asser- areas. Historically, they were not avail- comparably pragmatic. However, it tion that women choose future-oriented able at the German universities. In the historical sample there was a great gen- der difference in the choice of ‘applied mathematics’, introduced in 1898 (3% women, 21% men), but this may be due to the fact that women at that time had almost no chance of pursuing a career and earning money in areas outside the educational system. In 1898 mathemat- ics included representative geometry, technical mechanics and geodesy (com- bined with probability). The range of choice of mandatory subjects was extended in the following two decades to include astronomy, insurance and finance mathematics, statistics, hydro- dynamics and aerodynamics [10]. An education in applied mathematics pre- pared students for jobs at higher tech- nical education institutions or in indus- Fig 2

12 EMS June 2002 FEATURE areas of mathematics less often than Women also had to wait longer than Kultur [Statistics on Students], Fachserie men (see [3]). men to obtain a permanent teaching 11, Reihe 4.1: Studenten an position. These Prussian women teach- Hochschulen; Reihe 4.2: Prüfungen an Career entry is similar between women and ers were almost exclusively unmarried Hochschulen; Reihe 4.4: Personal an men. and childless (only 1% of the female Hochschulen, Wiesbaden, 1975 ff. In the historical sample there were no teachers were married then [5]), 9. H. Titze (1987) (ed.). Datenhandbuch gender differences up to graduation because the law decreeing the ‘celibacy’ zur deutschen Bildungsgeschichte [Data (Staatsexamen, PhD), and nor were of female civil servants and subsequent Handbook on German Education there gender differences in the number laws made the combination of career History], Band 1, Vandenhoeck of students working as research assis- with marriage/family virtually impossi- Ruprecht, Göttingen. tants at the university, usually before ble for women [11, p. 38]. An analysis of 10. Renate Tobies, Zur Stellung der ange- graduation (11 women, 2.4%; 93 men, the reasons as to why some of the wandten Mathematik an der Wende vom 3.6%). There were no gender differ- female teachers left their jobs also 19. zum 20. Jahrhundert – allgemein ences either in the Studienassessor exam- shows that career and family were then und am Beispiel der inations taken by 84.2% of the women virtually incompatible. The most impor- Versicherungsmathematik [Applied and 85.7% of the men: this last-named tant reason to quit one’s position was Mathematics at the End of the 19th examination no longer exists. At that marriage (for women) and bad health Century], Panem Circenses time, however, it was an exam at the (for men). In view of the virtual impos- (Mitteilungsblatt des Fördervereins für end of two years’ practical work and sibility of combining work and family, Mathematische Statistik und didactic training as a teacher after grad- few women in the historical sample Versicherungsmathematik, Göttingen), uation. It was thus the first step on the would voluntarily step off the career Beilage zu Heft 2 (1990), 1-11. career ladder of a Gymnasium teacher. ladder. Our data clearly shows that 11. R. Tobies (ed.), Aller Männerkultur zum In the modern sample, nine months women teachers were strongly discrimi- Trotz. Frauen in Mathematik und after their graduation, 77% of the diplo- nated against at the beginning of the Naturwissenschaften [In Spite of all male ma students had a job, 6% had firm 20th century, also with regard to differ- Culture – Women in Mathematics], prospects of work, 8% had a PhD grant, ences in salary (see [3, 5, 6]). Campus, Frankfurt, 1997. 4% were still looking for work and 5% Today’s legislation no longer discrim- were currently not looking for work inates against women; data from our Andrea Abele (-Brehm) and Jan Krüsken, (they intended to go on with further modern sample’s further career devel- Lehrstuhl Sozialpsychologie, Universität courses, had to serve their military or opment will show whether there are Erlangen-Nürnberg, Bismarckstrasse 6, civil service, or had private reasons for other (and perhaps more subtle) forms 91054 Erlangen: [email protected] not wishing to have a job at that time). of discrimination that still hinder gen.de There are no gender differences in women in their careers. Helmut Neunzert and Renate Tobies, FB these numbers, and nor were there gen- Mathematik und Fraunhofer-Institut für der differences with respect to areas of References Techno- und Wirtschaftsmathematik, work (university versus private sector) 1. A. Abele and J. Krüsken, Determinanten Postfach 3049, 67653 Kaiserslautern: or salary (see Figure 2). Our study par- der Promotionsabsicht in Mathematik [email protected] ticipants had an extremely rapid and [Predictors of the Intention to do PhD successful start to their careers. Work], I.V., 2001. There were no gender differences 2. T. Bahne and G. Törner, Fakten, Fakten, either with regard to the Staatsexamen Fakten – Mathematikstudentenzahlen graduates. In the German educational [Facts, facts, facts – numbers of mathe- system, Staatsexamen graduates who matics students], DMV-Mitteilungen H. 2 want to become teachers have to under- (1999), 22-27. go a mandatory second part of practical 3. S. Enzelberger, Sozialgeschichte des training as a schoolteacher, which con- Lehrerberufs. Gesellschaftliche Stellung cludes with the so-called ‘second von Lehrerinnen und Lehrern von den Staatsexamen’. In our sample, three- Anfängen bis zur Gegenwart [Social quarters of the Staatsexamen graduates History of Teaching Professions], were in this second part of practical Juventa, Weinheim, 2001. training, 5% had decided not to work as 4. M. Folkerts (ed.), Algorismus. Studien teachers and had other appointments in zur Geschichte der Mathematik und mathematics, and 17% wanted to Naturwissenschaften [Studies on History become teachers but had decided to of Mathematics and Science], H. 12, postpone the second part of training München, 1994. because they first wanted to realise 5. C. Huerkamp, Bildungsbürgerinnen. other plans. Frauen im Studium und in akademischen Berufen 1900-1945 [Educated Women], Historically, women were discriminated Vandenhoeck Ruprecht, Göttingen, against in their further careers. 1996. Despite achieving the same degree with 6. B. Lohschelder, (1994). Die Knäbin mit the same grades, and despite a similar dem Doktortitel [The ‘female boy’ with transition from university to the work- the Doctoral Degree], Centaurus, ing world, the women’s further career Akademikerinnen in der Weimarer development in our historical sample Republik, Pfaffenweiler, 1994. was less successful than their male col- 7. C. Niederdrenk-Felgner, Die leagues’ career development. For exam- Geschlechterdebatte in der ple, while the careers of 36% of the Mathematikdidaktik [The Gender women mathematicians ended at the Debate in Mathematics Didactics], level of Studienassessor, only 16.3% of Frauenforschung und the men ‘got stuck’ at this level. 59.1% Geschlechterperspektiven in den of the women in our historical sample Fachdidaktiken (ed. H. Hoppe, E. achieved permanent positions in higher Nyssen and M. Kampshoff), Beltz, education institutions, as opposed to Weinheim, 2000. 71.9% of the men. 8. Statistisches Bundesamt: Bildung und

EMS June 2002 13 FEATURE CopingCoping withwith publisherspublishers andand copyrightcopyright Wilfrid Hodges (Queen Mary College London)

Executive summary for authors of from you. The checklist below may help research papers in journals you to make sure that you have not missed The number of mathematical papers that any important points. are stored or circulated as electronic files is The agreement is a bargain struck increasing steadily. It is important that between your interests and those of your copyright agreements should keep in step publisher. For example, both you and your with this development, and not inhibit publisher have a common interest in stop- mathematical authors or their publishers ping your work being plagiarised by other from making best use of the electronic people. But if your publisher is expected to medium together with more traditional take plagiarists to court at his expense, he media. While most mathematicians have may well feel entitled to redress the balance no desire to learn the subtleties of copy- by asking you for something else that he right law, there are some general principles wants but you may not. that they should keep in mind when dis- Changes in the law and technology are cussing copyright for research papers with continually altering the balance between their publishers. author and publisher. So you shouldn’t 1. A copyright agreement with your pub- feel inhibited about telling your publisher if lisher is a bargain struck between his you feel that some change in the copyright interests and yours. You are entitled to form sent to you by your publisher would look out for your interests. Most journal make it a fairer deal. (Your publisher is not publishers have a standard copyright inhibited about changing his form where form, and may be unwilling to vary it for he feels it’s appropriate.) Because of the individual authors. But nothing pre- costs involved, the publisher is more likely vents you from asking, if you see room - You promise your publisher that you to be willing to discuss the contract for a for improvement. Pressure from have taken all reasonable steps to ensure book than for a journal article; but even for authors may lead publishers to change that your paper contains nothing that is journal articles, pressure from authors may their standard contracts. libellous or infringes copyright. lead a publisher to change his standard 2. Three groups of people have an interest - Your publisher will authorise reprint- contract. in your paper: ing of your paper in collections and will So far as possible, we have avoided legal - Yourself and your employer (who may take all reasonable steps to inform you terminology in the checklist. This is for two in some countries be automatically the when he does this. reasons. The first is to make the points original copyright holder and hence a 4. Should you grant full copyright to the clearer and more direct. The second is that party to the copyright agreement); publisher? In some jurisdictions it is there are still enormous differences - The journal publisher; impossible to transfer full copyright between one legal system and another, - Users of paper who are not parties to from author to publisher; instead the though the differences are gradually nar- the copyright agreement, including author gives the publisher an exclusive rowing under the pressure of international readers and libraries. right to do the things that publishers trade. For example ‘copyright’ in the USA One of the main purposes of your copy- need to do, and these things need to be and its nearest equivalent in France, ‘droit right agreement is to control how your spelt out in the agreement. This way of d’auteur’, are really quite different con- publisher or you make the paper avail- proceeding is possible in all jurisdic- cepts; and the German and British legal able to this third group. Publishers will tions, and it has the merit of being clear systems make different assumptions about hardly allow individual authors to dic- and honest about what is allowed or who is the initial owner of a work. Different tate agreements with libraries. But if required. legal systems have different ways of deliver- you know that a certain journal publish- The copyright checklist was written by ing the balance that you want. er makes life hard for libraries, you can Wilfrid Hodges, was approved and is rec- We assume you are a mathematician and take this into account when choosing ommended by the Committee on not a lawyer. So how can you draft a clause where to submit your paper. Electronic Information and Commun- that gets the effect you wanted? You can 3. There is no ideal copyright agreement ication of the International Mathematical start from what your publisher proposes, for all situations. But in general your Union (IMU). The executive summary was using your common sense. The points in agreement should contain the following endorsed by the Executive Committee of the checklist below all carry notes about features: the IMU in its 68th session in Princeton, things to look out for, and in several cases - You allow your publisher to publish the NJ, 14-15 May 2001. we point out things that matter in particu- paper, including all required attach- lar countries. We hope these resources will ments if it is an electronic paper. What do you want from your publisher? be enough for you; if not, you may need to - You give your publisher rights to An annotated checklist for mathematical authors find a friendly lawyer. authorise other people or institutions to A copyright agreement with your publisher copy your paper under reasonable con- is a signed undertaking that he will do or P is Publisher (assumed male). ditions, and to abstract and archive your not do certain things, and you will do or 1. Things you might allow P to do paper. not do certain other things. If you are won- Publish your work. - Your publisher allows you to make dering how to get a fair deal in this agree- Make sure that it’s clear what the ‘work’ is, reprints of the paper electronically avail- ment, you should start by asking what you especially if it involves electronic items. able in a form that makes it clear where want your publisher to do for you, and what There is also a question whether it is the paper is published. you are prepared to let your publisher ask ‘your’ work. Of course you will know if you 14 EMS June 2002 FEATURE stole it from someone. But even if you But creating an abstract, or quoting more chance of conviction is low. Also, as it wrote the paper entirely on your own, you extensively than is required for purposes of stands this is an obligation into the indefi- may not realise that your employer can scholarly comment, may fall outside these nite future (or at least until the copyright claim ownership of your mathematical rules. If you grant P the right to handle lapses, which in North America is normally work. such matters, dealing with requests for uses 70 years after the death of the author); why In France and Germany this can’t arise. such as these will generally fall to P’s ‘rights should P lumber himself with this? You But in any English-speaking country you and permissions’ department. should rest in the knowledge that plagia- would be wise to check your contract of rism is a threat to P as well as to you. employment to see what it says about the 2. Things you might require P to do Note that in most countries P will not be copyright in works that you wrote as part of Pay you in any position to take plagiarists to court if your employment, particularly if you are This normally applies only to books. There P doesn’t have a legal interest in the work. working for a government agency. Be are some journals and conference proceed- But the details vary from country to coun- warned also that your contract of employ- ings for which you have to pay P. try. ment need not be the end of the story, because the law in different countries Anything under 1 above 3. Things you might require P not to do makes different assumptions about copy- It’s up to P what he will accept along these Alter your work. right ownership if your contract of employ- lines; but he will not usually accept an By international agreement you as author ment is not specific about it. For example, obligation to publish without a clause that have a moral right to claim authorship of in Canada the assumption is that your the work must be of acceptable quality. But your work and to object to any distortion, employer holds the copyright unless your in any case you and P have a common mutilation or other modification of it which contract of employment says otherwise; interest in having people or libraries buy would be prejudicial to your honour or rep- though as author you have certain rights the work. utation. Like all moral rights, this stays over the publication of articles written by with you for ever and it doesn’t need to be you. If you are a US public servant and the Advertise the publication of your work adequate- stated in the copyright agreement; but dif- work was done as part of your official ly ferent countries have taken different steps duties, then there is no copyright in it with- This applies to books rather than journal to safeguard this right. in the US, though there may be outside the papers. It is not a thing that publishers will In any event the moral right is rather US; if you are in this position you probably normally accept as an obligation. vague. You may want to demand some- know where to seek advice on the matter. Nevertheless one does meet authors who thing stricter, for example that no change In France it is essential that your copy- have a grievance about the way their work is made in the text of your paper. Don’t be right agreement says explicitly that P is was advertised. There is nothing to pre- surprised if P puts restrictions. For exam- allowed to publish the work. vent you asking for such a clause, particu- ple, P has to protect himself against possi- larly if P is one of those charming publish- ble libel or plagiarism by you; he may insist Distribute free copies under certain conditions. ers who threaten to give your book less on being able to make alterations that are This raises no legal problems. favourable treatment if you don’t go along necessary for legal reasons, and he won’t with their other requests on the copyright want to be delayed by having to check with Authorise other people or institutions to publish form. you first. (This arises particularly with elec- copies of your work. tronic files that P keeps on his website. He For example, you probably want to allow Let you know when other people ask for or are can hardly alter journals already delivered offprint services to distribute offprints of given permission to republish the work to libraries.) In return you can reasonably your work, and to charge a fee for copies. You can reasonably ask to be informed if a insist that any such emergency alteration is chapter of your book is going to appear in approved by an academic editor. Authorise other people or institutions to make someone’s collection; you can’t reasonably Don’t be surprised either if P insists on copies of your work under certain restricted con- ask to be informed every time an offprint is being able to make purely electronic or for- ditions. issued. matting adjustments; this is reasonable. This is a very important clause. Students Also P will be a fool to give you a cast-iron and researchers need to be able to make guarantee in this clause. By the time P 4. Things P might want you to do photocopies of your written papers or parts needs to send you the information, you Guarantee that the work has not previously of your books. If your work is electronic, may have left the country and be impossi- been published, and that you are not simul- then nobody can load it onto their comput- ble to trace. Any clause of this kind should taneously offering it to another publisher. er or bring it up on their screen without require P only to use ‘best endeavours’ (or As it stands, this prevents P from pub- copying it (from disk or Internet to RAM, some similar phrase) to get the information lishing a work of yours which has already from RAM to screen); so for electronic to you. been published, even when the person who works this clause is absolutely essential. holds the necessary authority has autho- Usually P takes responsibility for negoti- Update the electronic format of electronic mater- rised P to republish. But if P knows that ating licences for colleges and libraries; ial as the advance of technology requires this is the situation and still wants to pub- though P may contract this out to an You are in uncharted territory here. It is lish, P will presumably withdraw the clause. agency. Your contract must give P permis- more sensible to require this for electronic There can be a tricky scenario when the sion to do this, though P will notice if you material in a standard text format than it is previous publication was on paper, very ask him to accept a contract that doesn’t. for graphics files that may need some par- likely before electronic publication was You should try to avoid details at this point, ticular software application to run them. P invented, and the proposed new publica- because there are many subtleties that you may reasonably insist on a ‘best endeav- tion is electronic. Both you and P need to probably aren’t aware of. (For example, ours’ clause in any case. be sure that the previous publisher can’t should electronic access from the college be Some publishers say explicitly that they stop you making the new publication. This controlled by password, IP address or will not patch up your files if these are may depend not only on the text of the ear- domain name?) Librarians and publishers incompetently written. This is a very rea- lier copyright agreement, but also on the both complain bitterly that the other side sonable requirement, and you should legal system of the country in question. often makes unreasonable demands; it’s assume too that P will not sort out the mess Unless you are extremely sure of your situ- best that you keep out of these fights. if you have used an outdated format (for ation, find the copyright agreement with example, an obsolete version of TeX). the previous publisher and show it to a reli- Authorise other people to make derivative uses of able lawyer. your work, such as reviewing or indexing. Take legal proceedings against plagiarists Guarantee that you are legally entitled to For normal scientific reviewing, fair use or P would be stupid to accept this obligation give P the rights that you are claiming to equivalent rules will usually allow the small without very severe restrictions. Legal pro- give him. amount of copying that may be involved. ceedings are expensive and sometimes the Caution here. Unless you are very sure of EMS June 2002 15 FEATURE the full facts, you should never do more licence to publish under certain condi- another publisher to include some of the than guarantee that you have taken all rea- tions. Recently many publishers have work in a published collection, and you sonable steps to make sure you are entitled. been moving towards this arrangement, update the work for this new publication. For example, an electronic paper may that you assign copyright but receive a If you do retain copyright and P is asking contain software that some company issued carefully circumscribed exclusive for a restriction of this kind, you will need as freeware, but later the company changed licence, as a way of heading off to agree with P a way of drawing a line its mind and demanded that users of the demands from authors that they should between the kinds of revised publication software should pay for a licence. You (and retain copyright. A typical clause of this that will devalue P’s version unacceptably hence P) may still be legally liable, though kind might allow you and those that won’t. You are on your own you may be able to plead in mitigation that - to make copies for classroom teach- here – there are no standard agreed for- you didn’t know about the change. This is ing, mulations. (But some may emerge as it very uncommon, but the fact that it can - to make copies for distribution to col- becomes commoner for authors to retain happen at all should warn you to take care leagues in your own institution, copyright.) with a clause like (b). - to use the work in later publications Guarantee that the work contains no libel of your own (including lectures), Publish (or authorise someone else to publish) the or other material that shouldn’t be pub- - to keep the work on your own web- work without its including an acknowledgment lished. site. that the first publication was by P, with a full ref- You can agree to this more safely than erence to that publication. (b), but you should still be careful, particu- In Germany, (iii) is technically impossi- This is a common clause in contracts that larly in Britain where the libel laws are stiff. ble, but German publishers sometimes allow you to publish the work yourself. It Include a confidentiality clause, or ask refer to (i) as ‘transfer of copyright’. seems very reasonable. Sometimes P will for part of the agreement to be by a verbal In the US (where the terminology of (i)- require that the acknowledgment is in a understanding rather than a written con- (iii) does apply), your legal rights and those suitably prominent place, for example on tract. of P don’t depend on copyright being reg- the first page. There might be a good reason for these, istered with the Copyright Office. But if but common sense suggests you should be you are a US resident and want to use your Revoke the contract. extremely suspicious. If you do have copyright as a basis for suing someone, you It’s normal to make copyright agreements grounds for suspicion, you might ask for a must have registered; moreover, if you irrevocable by either party. But if you and clause saying that no oral statement should want to sue for statutory damages and the publisher agree, there is nothing in the be taken into account apart from the text, attorney’s fees, you must have registered law to prevent you granting copyright or which should be taken to constitute the either before the plagiarism occurred, or licence for a limited period or in a restrict- entire agreement. within three months of first publication. In ed area of the world, or simply leaving it cases (i) and (ii), you hold the copyright open for either party to revoke the contract 5. Things P might want you not to do and you will need to register it yourself. In after first publication. Publish the work yourself. case (iii), P holds the copyright and may ask This includes keeping the work on a public you to state in the contract that you allow P 6. Other considerations website after P has published it. If you have to register it. Which country’s laws apply? given somebody else an explicit licence to A copyright contract should contain a include it in their website, then in general Authorise someone else to publish or copy the ‘jurisdiction clause’, saying what jurisdic- you can’t prevent them keeping the work work. tion applies; sometimes it does this by say- on their site; but usually in such cases the This has become a real problem, where a ing where the parties can sue. If both pub- licence is implicit, so that you can write to publisher holds the copyright on a book lisher and author are in the same country the owner withdrawing the licence, and the that is out of print and is unwilling to (or the same legal jurisdiction, e.g., a state owner is then obliged to remove the work republish it (or to republish it with changes of the US, or Scotland), the law makes the from the site. that you want to make), though other pub- default assumption that the laws of that The legal terminology of most countries lishers are willing. So in case (a)(iii) you country or jurisdiction apply. The legal sit- allows three possibilities: should consider insisting on a clause that P uation is very complicated if publisher and (i) If you have given an ‘exclusive licence’ will agree to grant a licence to another pub- author are in different countries and the to P, then this prevents you from pub- lisher on reasonable terms if the book goes contract contains no jurisdiction clause. lishing the work yourself or authorising out of print. Define your terms. There are any num- anyone else to publish it. P on the If you insist on being able to authorise ber of anecdotes about authors getting other hand can do with your work what further publication or copying yourself, caught out by not realising how a word in you license him to do, and nothing bear in mind that for people who want to the contract might be interpreted. For more. publish or copy, P may be much easier to example, your contract should probably (ii) If you give P a ‘non-exclusive licence’, find than you, particularly if P is a famous define what it counts as ‘publication’, or this entitles you to publish the work publishing house. You can make yourself a avoid the word altogether; otherwise you yourself and authorise other people to little easier to reach by entering into a col- may find in US law that a free distribution publish it; but in this case P may very lective licensing scheme, such as those run doesn’t count as publication. Your defini- well ask you to promise not to authorise by the UK Copyright Licensing Agency or tions don’t have to agree with some stan- third parties to publish the work, except the US Copyright Clearance Center, or any dard legal definition; they do their job if under strict conditions (see (c) below). similar Collection Society. Some publishers they make clear what the parties to the con- Again P can do whatever you license specifically exclude registration with a tract had in mind. him to do. (Don’t be bullied by pub- licensing agency even if you retain copy- lishers who warn you that if you opt for right; this is a bit of a cheek and you might Acknowledgements: My thanks to Eva this kind of agreement they will be want to press them on it. Bayer-Fluckiger, John Ewing, Susan inhibited in disseminating your book. Hezlet, Gary Lea, Ulf Rehmann, Laurent With their agreement, you can license Publish a revised or upgraded version of the Siebenmann and Bernd Wegner, for their them to do whatever you want them to work yourself. comments on an earlier version, though do.) This possibility arises very easily if the work they are not responsible for any mistakes of (iii)If you have ‘assigned copyright’ to P, is published electronically; you are bound fact or judgement. then all authority over the work passes to be tempted to correct false theorems, to P. This prevents you from publish- and maybe to attach relevant programs Wilfrid Hodges, School of Mathematical ing the work yourself or authorising when they become available. But it can also Sciences, Queen Mary, University of London, anyone else to publish it; except that P arise with printed work, for example if you Mile End Road, London E1 4NS, UK; e-mail: may give you in return a (non-exclusive) retain copyright, and then later you allow [email protected] 16 EMS June 2002 ANNIVERSARIES context as a product of human social activ- ity. BentoBento CaraçaCaraça (1901-48):(1901-48): Caraça also wrote biographies of notable and inspiring people, such as Abel, A beautiful mind Galois, Galileo, Leonardo da Vinci, A beautiful mind Romain Rolland and Rabindranath Tagore, and philosophical texts about cul- Natália Bebiano (Coimbra) ture. Caraça was a gifted speaker. He con- tributed to newspapers and magazines and promoted relevant cultural events in Portugal, artistic meetings, scientific con- ferences and courses, with the main pur- pose of promoting people’s culture. Most of these events took place at the Universidade Popular Portuguesa, an insti- tution where progressive intellectuality and enlightened members of the working classes could discuss cultural and scientific topics. Bento Caraça was president of Universidade Popular for many years, and his activity here was very emblematic, focused on the culturalisation of people and on the defence of democratic values. Another remarkable responsibility was the Biblioteca Cosmos, one of the most signifi- cant cultural achievements of the twentieth century in Portugal. Under Caraça’s lead- ership Cosmos published over 114 titles cov- ering different fields of knowledge in about eight years. He introduced methods of Econometrics in Portugal. In 1938, he founded Centro de Estudos de Matemática Aplicados à Economia, of which he was chair- man. In 1940 he founded the Sociedade Portuguesa de Matemática, of which he was president for two years (1942-44), and founded and edited the journal Gazeta de Matemática. In 1946, Caraça was expelled from his university teaching position. He was perse- cuted by the political police under the dic- tatorship and imprisoned at Aljube. There were many cases of political persecution, and victims included university teachers – in particular, mathematicians. Bento Caraça died on 25 June 1948. Crowds of people of all social classes joined together in the streets of Lisbon in a spontaneous tribute to the Master and to the citizen. Caraça was a man of culture devoted to the pursuit of knowledge, and a talented teacher. In his classes he had a singular style, his fascinating way of presenting sub- jects was so rare that he was seen in the academic community as an idol. He was a pioneer of Portuguese organisations for peace and international movements Bento de Jesus Caraça was born in Vila For the first time, mathematics has been present- against World War II. He participated in Viçosa, Alentejo, Portugal. He studied eco- ed by someone who lives the profession with the an artistic and literary movement known as nomics at the Instituto Superior de soul of an apostle and of an artist. neo-realism. His scientific and philosophic Ciências Económicas e Financeiras, Caraça was also the author of Conceitos work can be characterised by a question- University of Lisbon, where he later taught Fundamentais da Matemática (1942), which ability of the man himself and his position infinitesimal analysis as Assistant (1919), has become a central reference for scientif- in a contemporary world, putting complex becoming Extraordinary Professor (1927) ic popularisation in Portugal. This remark- demands to human existence. He is one of and Full Professor of Higher Mathematics able best-seller, also very popular in Brazil, the personalities who marked Portuguese (calculus, analytical geometry, probabilities aims to provide a core of knowledge for a life in the twentieth century. and applications) in 1929. wide audience of non-specialists, who In mathematics, he published influen- could be fascinated by the ideas, concepts Natália Bebiano is Full Professor of the tial undergraduate textbooks, Interpolação e and beauty of mathematical topics. The Department of Mathematics at the University of Integração Numérica (1933), Cálculo Vectorial book consists of three parts, entitled Coimbra, Portugal; this article is based on a lec- (1937), and Lições de Álgebra e Análise Numbers, Functions and Continuity. The ture commemorating the centenary of Bento (1935-40). About these books, the mathe- genesis of the concepts is analysed, and Caraça’s birth, given at the University of Évora matician Sebastião e Silva wrote: mathematics is presented in an historical on 23 November 2001. EMS June 2002 17 ANNIVERSARIES £600 per annum – and had time to pursue his own mathematical interests. He seems to have maintained his links with Cambridge, sometimes attending Henry The 2002 Ferran WWilliamilliam Frederick Baker’s Saturday seminar or ‘tea party’, and he remained highly regarded at Pembroke where he became an Sunyer i BurnsideBurnside Honorary Fellow in 1900. On the death of Sir George Gabriel Stokes in 1903 he was Balaguer prize (b. 1852) offered the Mastership of Pembroke, which he declined, either for financial rea- Tony Mann (Greenwich) sons or because he wished to avoid the con- awarded to comitant administrative responsibilities. He took an active part in the London Alexander Mathematical Society, serving on Council for many years and being President 1906- Lubotsky, Dan 08, and was elected Fellow of the Royal Society in 1893. Burnside remained at the Royal Naval Segal and André College until his retirement in 1919. He lived in south-east London and on his Unterberger retirement moved to West Wickham, where his house Cotleigh in High Street is now The lnstitut d’Estudis Catalans has the HSBC Bank. His wife Alexandrina awarded the 2002 Ferran Sunyer i Urquhart came from Poolewe in Ross-shire Balaguer Prize to Alexander (north-west Scotland) and they regularly Lubotzky (Jerusalem, Israel), Dan visited the family croft there, where Segal (Oxford, UK), and André William could indulge his love for fishing. Their five children (there were no grand- Unterberger (Reims, France) for children) are still remembered in Poolewe. their monographs entitled Subgroup There are hints that that Burnside could Growth and Automorphic Pseudo- present a rather stern personality when differential Analysis and Higher-level people did not come up to the high stan- Weyl Calculi. This year’s prize is dards that he set for himself and others, exceptional since it has been award- but he was held in affection by his naval ed ex-aequo to two manuscripts. This year marks the sesquicentenary of the students, who on his retirement presented The members of the Jury — birth in London on 2 July 1852 of William him with a handsome illuminated address Hyman Bass (Michigan), Antonio Burnside, who today is known principally (now in Pembroke College Library). Córdoba (Madrid), Warren Dicks for his contributions to group theory. (He Initially an applied mathematician, (Barcelona), Paul Malliavin (Paris) Burnside published his first paper on is inevitably sometimes confused with his and Alan Weinstein (Berkeley) — contemporary, the Irish mathematician group theory in 1893. His Theory of groups William Snow Burnside (1839-1920), of finite order (1897) was the first book in point out that Subgroup Growth, by author with A. W. Panton of a Theory of English on group theory: a considerably Lubotzky-Segal, is a highly original Equations: our Burnside was of Scottish revised second edition appeared in 1911. book reporting the state of the art in descent.) The death of his father in 1858 Burnside wrote in the first edition: an important and still rapidly devel- left the family in straitened circumstances. No simple group of odd order is at present oping area of asymptotic group the- William was educated at Christ’s Hospital, known to exist. An investigation would ory, while Automorphic Pseudo- the ‘Bluecoat School’, where he was top undoubtedly lead to results of importance. differential Analysis and Higher-level pupil in the mathematical school, and in It was almost seventy years before Feit Weyl Calculi, by Unterberger, is an 1871 he was awarded a mathematical and Thompson would show that indeed all excellent exposition of a sophisticat- scholarship to St John’s College, groups of odd order are soluble. This was ed area of analysis with deep con- Cambridge. typical of Burnside’s ability to identify nections to analytic number theory. In his first year at Cambridge, Burnside fruitful problems: another example was was a member of the St John’s Boat Club the ‘Burnside Problem’ (is a finitely-gener- Both books are very well written and which was Head of the River. For reasons ated group of finite exponent necessarily will be attractive to new as well as that are unclear, during his second year he finite?) which he proposed in 1902 and mature researchers in each field. moved to Pembroke College, where he which also led to significant areas of twen- The prize consists of 10000 euros contributed to the Boat Club as coach and tieth-century mathematics. and the monographs will be pub- oar (usually Seven) for the rest of his time Towards the end of his life, Burnside lished in Birkhäuser Verlag’s series in Cambridge: it is not considered entirely became interested in probability theory, Progress in Mathematics. coincidental that in this time the writing a book, Theory of Probability that was The Ferran Sunyer i Balaguer Prize Pembroke boat rose from twenty-fifth to published posthumously in 1928. is granted by the Ferran Sunyer i fourth in the May races. William Burnside died on 21 August Balaguer Foundation (http://www. Burnside was joint second wrangler in 1927 and is buried in West Wickham crm.es/info/ffsb.litm) and is awarded Parish Church, where his grave is marked 1875, and came first in the Smith’s Prize each year to a mathematical mono- Examination. He was then awarded a fel- by a Celtic cross. His collected papers, lowship at Pembroke, where he remained edited by Peter M. Neumann, A. J. S. graph of an expository nature pre- until the summer of 1885, when he became Mann and Julia Tompson and including a senting the latest development in an Professor of Mathematics at the Royal number of essays about Burnside’s mathe- active area of research in mathemat- Naval College at Greenwich. He resigned matics by distinguished scholars, will short- ics, in which the applicant has made his Pembroke fellowship on his marriage ly be published by Oxford University Press. important contributions. in 1886. The awarding ceremony took place At Greenwich Burnside taught mathe- Tony Mann [[email protected]] is at the on April 24 at the Institut d’Estudis matics to seamen and naval architects. He University of Greenwich, UK, which is located Catalans in Barcelona. was well paid – the professors’ salary was at the Royal Naval College. 18 EMS June 2002 EMS June 2002 19 CIME SUMMER COURSES CIME summer courses 2002 The CIME (International Mathematics Summer Centre) has organised the following courses for summer 2002.

Course 1: 30 June to 6 July, at Martina Franca (Taranto) Real Methods in Complex and CR Geometry Scientific direction: Dimitri Zaitsev [[email protected]] and Giuseppe Zampieri [[email protected]] 4 lectures in English for each course (a) Angular derivatives in several complex variables Marco Abate, Università di Pisa, Italy [[email protected]] (b) Real methods in complex dynamics John Erik Fornaess, Univ. of Michgan, Ann Arbor, USA [[email protected]] (c) On the Chern-Moser theory and rigidity problem of holomorphic maps Xiaojun Huang, Rutgers Univ., New Brunswick, USA [[email protected]] (d) Theory of analytic functionals, and boundary values in the sense of hyperfunctions Jean Pierre Rosay, Univ. of Wisconsin, Madison, USA [[email protected]] (e) Extremal analytic discs and the geometry of CR manifolds Alexander E. Tumanov, Univ. of Illinois at Urbana-Champaign, USA, [[email protected]]

Course 2: 10-19 July, at Cetraro (Cosenza) Analytic Number Theory Scientific direction: C. Viola (Università di Pisa) [[email protected]] and A. Perelli (Università di Genova) [[email protected]] The abstracts of the courses are available at the (CIME) address http://www.math.unifi.it/cime/ where the announcement of the course is given. (a) Producing prime numbers via sieve methods (4 lectures) John Friedlander, Toronto, Canada (b) Exponential sums, uniform distribution and cryptographic applications (2 lectures) John Friedlander, Toronto, Canada (c) Counting rational points on algebraic varieties (6 lectures) Roger Heath-Brown, Oxford Univ., England (d) Automorphic L-functions (6 lectures) Henryk Iwaniec, Rutgers University, New Jersey, USA (e) Axiomatic Theory of L-Functions: the Selberg class (6 lectures) Jerzy Kaczorowski Poznan, Poland

Course 3: 15-21 September, at Martina Franca (Taranto) Theory and Applications of Imaging Scientific direction: George Papanicolau (Univ. of Stanford, USA) [[email protected]] and Giorgio Talenti (Univ. di Firenze, Italy) [[email protected]] (a) Array imaging in noisy environments George Papanicolau, Stanford Univ., USA (b) Tomographic imaging Frank Natterer, Univ. of Münster, Germany (c) Diffuse imaging for medical diagnoses Simon R. Arridge, University College, London, UK (d) Experimental methods and results in laser-tissue imaging Robert R. Alfano, Institute for Ultrafast Spectroscopy and Lasers, CUNY, New York, USA (e) Seismic imaging William W. Simes, Rice Univ., USA

Applications As soon as the abstracts of the courses have been sent to CIME, the information will appear on the CIME webpage. Those who wish to attend the session should send an application to the Director of CIME at the address below, as soon as possible. For any further information, please contact Fondazione C.I.M.E. c/o Dipartimento di Matematica ‘U. Dini’ Viale Morgagni, 67/A - 50134 Firenze, Italy Tel: +39-55-434975 or +39-55-4237123 Fax: +39-55-434975 or +39-55-4222695 e-mail: [email protected] Direttore del CIME: Prof. Pietro Zecca [[email protected]] Segretario del CIME: Prof. Elvira Mascolo [[email protected]] Further information appears on the CIME webpage: http://www.math.unifi.it/cime/

This CIME activity is made possible thanks to the generous support received from the European Commission, Division XII, TMR Programme Summer Schools, Consiglio Nazionale delle Ricerche, Ministero Affari Esteri italiano, Ministero dell’ Università e della Ricerca Scientifica e Tecnologica, UNESCO-ROSTE, Venice Office.

20 EMS June 2002 SPARE BOOKS? CanCan youyou sparsparee books?books?

Tsou Sheung Tsun and Herbert Fleischner (EMS Committee for Developing Countries)

Some of you may be sitting on books, or the USA, Canada, Australia, etc., who mathematics and related disciplines, such some of your books may be sitting on would be prepared to donate books within as computer science) that you wish to shelves, although you may not need them this scheme. And maybe, you can get your donate to a developing country, please let any more: these books collect dust. At the university to pay for the transportation us know, with a short description of the same time, many universities in develop- costs of the books you have collected. material available. Please contact either of ing countries are in dire need of scientific Again, experience in a different frame- us: literature – from undergraduate and grad- work has shown that some universities (or Tsou Sheung Tsun, uate texts to journals. maybe private donors) may have funds e-mail: [email protected] The EMS Committee for Developing available for such purposes. Herbert Fleischner, Countries (CDC) considers the collecting So, if you have books or journals (in e-mail: [email protected] of books from you and their shipment to various universities in developing coun- tries as one of its central activities. Moreover, although being a committee of the EMS, the CDC turns not only to European colleagues, but takes this oppor- tunity to call upon colleagues in any devel- oped country, to join us in our efforts. We are looking mainly for scientific literature published in English or French. As experience has shown, the problem is not to find books for donations to such universities, nor the identification of uni- versities in DCs that are interested in receiving such donations. The problem lies in the shipping expenses and in the logistics. With some cooperation by the various players in this (truly international) action, the CDC will be in a position to ful- fil this task. The CDC hopes to liaise with the International Centre for Theoretical Physics (ICTP) at Trieste, Italy, to organise a book donation scheme. We shall try to identify recipients for donated books and journals. We know, for example, that the University of Zimbabwe not only would gladly accept such donations (it has done so in the past in a different framework), but is also prepared to act as a centre for distribution of donated books to universi- ties in the SADC region, which comprises member states as diverse as South Africa, Zambia, Malawi, Tanzania, Angola and Mozambique. In order to take care of the shipping of donations to the respective places, CDC will apply to the Book Donation Scheme which the ICTP runs, to pay for the trans- port subject to their regulations. We, or the donors, might also try various National Commissions for UNESCO to help with shipping costs. A minimum of 40-50 books constitutes a reasonable consignment. We hope that some of you will not only give away some of your own books, but will also involve yourselves actively in collecting books/journals from other colleagues in your respective departments. Maybe some European colleagues know of colleagues in EMS June 2002 21 THEATRE REVIEW tisement for the shampoo her sister would like her to use (‘hair can’t be healthy, they are dead tissues’). PPrroofoof The author also shows understanding of what a proof is, how it can be elegant, how ideas are essential, how new angles of by David Auburn thought on known question produce new results – with lots of work. Certainly, math- Theatre review by Luc Lemaire ematics is central in the play, and charac- ters of mathematicians are not reduced to caricatures. In August 2001, I had the opportunity to resents an external view of the mathemat- When a mathematician appears in a film attend in New York a performance of ics community. or a book, mistakes or misconceptions are Proof, by David Auburn, and to read the Finally, Hal is a former student of often striking. If I ask here: are those peo- play. Robert, who has now a lecturing position at ple mathematicians like those I have Both the play and performance are bril- university. He doesn’t have the genius of known for many years in many countries, liant – and can be highly recommended to Robert, and is plagued by self-doubt. He the answer is a resounding yes. They look, any audience, mathematical or not. In feels that his research is trivial, without big talk and behave like real-life mathemati- fact, the play, the director (Daniel Sullivan) ideas, and he keeps going with the fact that cians (with, of course, the anomaly of the and main actress (Mary-Louise Parker) got he likes teaching. extreme character of Robert). Ben an avalanche of awards, including a The detective story aspect of the play is Schenkman, in the role of Hal, could go Pulitzer Prize for the author. Moreover, it about that famous proof: is it in the note- unnoticed in any mathematical depart- is a public success and the theatre was books? Could Robert really have written it ment or meeting. packed every evening. during remission of his illness? Can it be The questions raised about mathemati- The play is both serious and funny, very recovered or published? I find it remark- cal creation, or careers, and the descrip- well organised, and talks about many prob- able that the author could interest – or tion of the mental processes involved, are lems encountered in life – notably, rela- thrill – the audience and the critics with absolutely relevant – and (apart from two tions and duties in a troubled family. As those questions, when we so often have the remarks, to be precise) I can agree with various critics noted, it works like a detec- impression that the general public doesn’t everything, and recognise the real-life tive story, and various twists in the play even know that mathematical research mathematicians. leave the audience gasping (notably, the exists. At the same time, it is a great play, and it last three words of Act One!). But three of Some short scenes cleverly introduce lots is remarkable that both audience and crit- the four characters are mathematicians, of facts about the characters, mathematical ics can take as an obvious starting point and the play is also about genius, about life and mathematics themselves. In a sin- that research is going on today in operator mathematical research and teaching, and gle page – or a few minutes on stage – the theory or modular forms. about life in the mathematics community. characters mention (without giving The book is available (but comparing it Without revealing any twist of the tale, a answers) some of the clichés about research with the performance it appears that read- description of the characters will set the in mathematics: ‘Really original work – it’s ing a play does not necessarily do justice to scene and give an idea of some real life all young guys ... men mostly’. So the it – it is meant as a play and the tempo, the models that the author has obviously stud- model for Catherine is Sophie Germain, silences, the quality of direction and acting ied. who went into hiding during the French are necessary ingredients). The play con- Robert is around 50. Before he was 30, Revolution, solved questions on prime tinues on Broadway with a new cast (the ‘he made major contributions to three numbers and wrote to Gauss signing as a role of Catherine being taken over by fields: game theory, algebraic geometry, man. We even get in two lines the defini- Jennifer Jason-Leigh), and is currently and non-linear operator theory’ – and ‘the tion of Germain primes – and an impres- running in London with Gwyneth Paltrow economists have been milking his tech- sion of two characters. Indeed, Hal tells in that role. niques for Nobels ever since’. When he was Catherine (and the audience): ‘Germain We keep feeling that mathematical 30, he developed a serious mental illness primes are famous. Double them and add research is unknown, and try to build up which stopped his career altogether – one and you get another prime. Like two. various ‘mathematics awareness pro- except possibly during some intervals of Two is prime, doubled plus one is five: also grammes’. It seems that we now have some remission. Meanwhile, he has filled 103 prime’. To which Catherine immediately solid and unexpected help. notebooks with notes and computations, retorts: ‘Right, or 92,305 times 2 to the which may or may not contain the proof of 16,998 plus one’ – which puts Hal back one The play is published as: an essential theorem on prime numbers step. David Auburn, Proof, Faber and Faber, ISBN (whose proof involves elliptic curves and There are indeed a number of pure com- 0-571-19997-6. modular forms). So the author has con- edy scenes, when Claire ‘does some serious The theatre has a web site with various com- centrated onto Robert the headlines of drinking with the theoretical physicists’, or ments and pictures: mathematics in recent years, combining when Catherine applies logic to the adver- www.proofonbroadway.com. the life of John Nash with Andrew Wiles’s proof of the Fermat theorem, and maybe a hint of Ramanujan’s notebooks. However, there is no claim anywhere of describing the life of an existing person – Robert rep- Help needed! resents a very extreme type of mathemati- cian – and the question of the precision of Kathleen Quinn is retiring as Conferences editor at a biography does not arise. the end of 2002. Catherine, the main character in the play, is his 25-year old daughter. She may have inherited his genius – or maybe his Volunteers are needed to take on this task. tendency to mental illness. She started studying mathematics, but left university to care personally for her father – as she has If you are interested in helping, please contact now done for years. Claire, the eldest daughter, lives in Kathleen Quinn or the Editor-in-Chief. another city, is a financial analyst, and rep- 22 EMS June 2002 CONFERENCES ate students and postdoctoral researchers in mathematics and physics to secondary calcu- lus. Secondary calculus is the result of a nat- ural evolution of the classical geometrical FForthcomingorthcoming conferconferencesences theory of partial differential equations (PDE) originated by Sophus Lie. In particular, it Compiled by Kathleen Quinn allows the construction of a general theory of PDE, in the same manner as algebraic geom- etry does with respect to algebraic equations Format: courses for beginners and advanced Please e-mail announcements of European confer- (Roma), A. Sossinskii (Moscow), A. M. participants; research seminars ences, workshops and mathematical meetings of Vinogradov (Salerno), O. Viro (Uppsala) Topics: 1. Differential calculus over commu- interest to EMS members, to k.a.s.quinn@ Scientific committee: E. Arbarello (Roma), tative algebras and smooth manifolds (sug- open.ac.uk. Announcements should be written in a F. Baldassarri (Padova), U. Bruzzo (Trieste), gested for beginners); 2. Infinite jets and style similar to those here, and sent as Microsoft C. Ciliberto (Roma), A. Collino (Torino), M. diffieties (suggested for more experienced Word files or as text files (but not as TeX input Cornalba (Pavia), C. De Concini (Roma), B. participants) files). Space permitting, each announcement will Dubrovin (Trieste), L. van Geemen (Pavia), Research seminars: 1. ‘Einstein’; 2. Singular appear in detail in the next issue of the Newsletter P. Griffiths (Princeton), V. Kac (Boston), K. Lagrangians and Hamiltonian formalism; 3. to go to press, and thereafter will be briefly noted O’Grady (Roma), C. Procesi (Roma), E. Differential invariants: Theory and applica- in each new issue until the meeting takes place, Sernesi (Roma), J. Stasheff (Chapel Hill), A. tions; 4. Towards differential algebraic with a reference to the issue in which the detailed M. Vinogradov (Salerno) geometry announcement appeared. Organising committee: A. De Paris (Napoli), Lecture notes: available at the website (see G. Rotondaro (Napoli), G. Sparano below) (Salerno), A. M. Vinogradov (Salerno), R. Main speakers: A. De Paris (Naples), S. Igonin (Independent University of Moscow), July 2002 Vitolo (Lecce) Sponsors: Istituto Italiano per gli Studi F. Pugliese (Salerno), A. Verbovetsky Filosofici, Naples; Universita’ degli studi di (Independent University of Moscow, Diffiety 1-5: Congrès de mathématiques appliquées Salerno; Gruppo Nazionale per le Strutture Institute), A. Vinogradov (Salerno, Diffiety à la mémoire de Jacques-Louis Lions, Algebriche, Geometriche e le loro Institute), M. Vinogradov (Moscow, Diffiety Paris, France Applicazioni; Dipartimento di Matematica ed Institute), R. Vitolo (Lecce, Diffiety Institute) Information: website Applicazioni dell’Universita’ degli Studi di Organising committee: D. Catalano http://acm.emath.fr/congres-jllions/ Napoli ‘Federico II’ Ferraioli, A. De Paris, C. Di Pietro, G. [For details, see EMS Newsletter 43] Location: Palazzo Serra di Cassano, Naples Manno, R. Piscopo, F. Pugliese, G. Notes: there is no participation fee Rotondaro, F. Strazzullo, R. Vitolo 1-6: Advanced Course on Mathematical Deadline: 15 June Sponsors: Diffiety Institute of the Russian Finance: Models, Bellaterra, Barcelona, Information: e-mail [email protected], Academy of Natural Sciences, Istituto Spain website http://www.diffiety.org or Italiano per gli Studi Filosofici, Municipality Information: website http://diffiety.ac.ru of Santo Stefano del Sole (AV), Italy http://www.crm.es/matfin Location: S. Stefano del Sole (AV), near 7-14: 6th WSEAS CSCC Multiconference Naples 1-6: 2nd International Conference on the on Circuits; Systems; Communications; Notes: the participation fee is 100 euros, Teaching of Mathematics at Undergraduate Computers; Applied Informatics; Signal reducible in a few special cases Level, Chersonissos, Crete, Greece Processing and Computational Geometry Deadline: 15 June Information: website and Vision; Scientific Computations and Information: e-mail [email protected], http://www.math.uoc.gr/~ictm2 Soft Computing, Rethymna Beach, Crete website http://diffiety.ac.ru or [For details, see EMS Newsletter 42] Information: website http://www.wseas.org/ http://www.diffiety.org conferences/2002/crete 1-6: 2002 Workshop on Wavelets and 22-25: IEEE Symposium on Logic in Applications, Barcelona, Spain 8-26: School and Conference on Algebraic Computer Science (LICS’02), Copenhagen, Information: website K-theory and its Applications, Trieste, Italy Denmark http://www.imub.ub.es/wavelets Information: Information: [For details, see EMS Newsletter 43] website http://www.ictp.trieste.it/www_users website http://www.dcs.ed.ac.uk/home/grohe /math/maths2002.html /lics/lics02/ 2-6: 2002 Barcelona Conference on [For details, see EMS Newsletter 43] [For details, see EMS Newsletter 43] Algebraic Topology (a EuroConference), Barcelona, Spain 10-13: VISIT-ME-2002 (Vienna 22-26: ICCAM 2002, International Information: website International Symposium on Integrating Congress on Computational and Applied http://www.crm.es/2002bcat Technology into Mathematics Education), Mathematics, Leuven, Belgium [For details, see EMS Newsletter 43] Vienna, Austria Aim: to bring together those working on the Information: analysis and application of computational 2-6: 5th Conference of the European website http://www.acdca.ac.at/visit-me-2002 techniques for solving real scientific prob- Society of Mathematics and Theoretical [For details, see EMS Newsletter 43] lems Biology on Mathematical Modelling and Main speakers: Chris Budd (U.K.), Adhemar Computing in Biology and Medicine, 15-18: Modular Curves and Abelian Bultheel (Belgium), Volker Schulz Milano, Italy Varieties (EuroConference), Bellaterra, (Germany), Ben Sommeijer (Netherlands), Information: website Barcelona, Spain Masaaki Sugihara (Japan), Paul Van Dooren http://ecmtb.mat.unimi.it Information: (Belgium) website http://www.crm.es/mcav02 Deadline: already passed for abstracts of 4-6: Current Geometry 2002, Naples, Italy short communications Theme: problems and trends of contempo- 16-22: 7th International Spring School: Proceedings: will be published in the rary geometry Nonlinear Analysis, Function Spaces and ‘Journal of Computational and Applied Aim: to establish a periodic update about Applications (NAFSA 7), Prague, Czech Mathematics’ Italian and international advances in geome- Republic Information: try Information: website http://www.cs.kuleuven.ac.be/ Main speakers: E. Arbarello (Roma), B. website http://www.math.cas.cz/~nafsa7 conference/iccam2002/iccam.htm Dubrovin (Trieste), E. Ferapontov (Moscow), [For details, see EMS Newsletter 40] L. van Geemen (Pavia), S. Gindikin 19-31: V Diffiety School – A School on the 22-26: Universal Algebra and Lattice (Rutgers), V. Kac (Boston), J. Kollar Geometry of Differential Equations, S. Theory, Szeged, Hungary (Princeton), M. Mella (Ferrara), P. Piazza Stefano del Sole (AV), Italy Information: Aim: to introduce undergraduate and gradu- website http://www.math.u-szeged.hu/confer/ EMS June 2002 23 CONFERENCES algebra/2002/ 11-18, 2002 XIII Conference on Analytic Universität zu Berlin, (Unter den Linden 6, [For details, see EMS Newsletter 43] Functions, Bêdlewo, Poland 10099 Berlin) Motivation: an international conference on Grants: participants from special circum- August 2002 analytic functions, with 60 to 100 foreign stance countries and students are supported participants from 20 to 30 countries, and 40 Deadlines: 1 June for standard registration, to 90 Polish participants, has been organised 24 August for late registration 3-9: Logic Colloquium 2002 (ASL European in Poland every fourth year since 1954 Information: e-mail [email protected], Summer Meeting), Münster, Germany Topics: real and complex analytic geometry, website www.compstat2002.de [change of date] extremal problems related to one and sever- Information: al complex variables, approximation prob- 25-30: Wireless and Optical website http://www.math.uni-muenster.de/ lems related to one and several complex Communications (WOC’02), Miedzyzdroje, LC2002/ variables, complex mapping and related Poland [For details, see EMS Newsletter 41] structures, real and complex potential theo- Information: website http://www.wseas.org/ ry, generalised complex (in particular, conferences/2002/miedzyzdroje/gown 4-11: International Conference on the Ideas Clifford) structures, quasiconformal geome- of Albert Abraham Michelson in try and dynamics, complex dynamical sys- 25-30: Nanoelectronics, Nanotechnologies Mathematical Physics, Bêdlewo, Poland tems and fractals (NN’02), Miedzyzdroje, Poland Motivation: to commemorate the 150th Organising Committee: Zbigniew Information: website http://www.wseas.org/ anniversary of the birthday of A. A. Jakubowski (£ódŸ), Jan Krzy¿ (Lublin), Julian conferences/2002/miedzyzdroje/nn Michelson on 19 December 1852 at Strzelno, £awrynowicz (£ódŸ), Olli Martio (Helsinki), near Inoworoc³aw. The importance of Dariusz Partyka (Lublin), Feliks Przytycki 25-30: WSEAS International Conference on Michelson’s measurements of the velocity of (Warszawa), Józef Siciak (Kraków), Jan ElectroMagnetic Compatibility (EMC’02), light, ether drift, standard meter and stellar Stankiewicz (Rzeszów), Promarz Tamrazov Miedzyzdroje, Poland diameters had a great influence on modern- (Kyiv) Information: e-mail [email protected], day physics and mathematical physics. Since Fees: 120 zlotys (c. US $30) per day full website http://www.wseas.org/conferences/ Michelson was the first American citizen to board; the registration fee is 160 zlotys (US 2002/miedzyzdroje/ec win a Nobel prize, and since he was born $40) into an Israelite family, the organisers will be Grants: full support for twenty participants 27-2 September: Third International in contact with the Polish, American, and (full board, travel excluded) School-Symposium: Symmetry and Israeli Physical Societies Information: contact Julian £awrynowicz Cosymmetry Applications in the Theory of Topics: historical aspects of Michelson’s dis- Institute of Mathematics, Polish Academy of Bifurcations and Phase Transitions, Big coveries, contemporary success and status of Sciences Banacha 22, 90-238 £ódŸ, Poland, Sochi, Russia special relativity, contemporary experiments e-mail [email protected] Information: website http://www.math.rsu.ru/ stimulating special relativity, special relativity mexmat/kvm/school2002 versus quantum mechanics and optics, super- 24-28: XV Compstat Conference of the [For details, see EMS Newsletter 43] luminal propagation in anomalous media, International Association for Statistical classical and quantum synchronisation of Computing, Berlin, Germany 29-31: Eleventh International Workshop on clocks, relations to stochastic spaces, astro- [the latest in a series of biannual confer- Matrices and Statistics, Lyngby, Denmark physics and cosmology ences; this conference is in cooperation with [in celebration of the 65th birthday of Organising committee: Julian £awrynowicz the 29th Annual Meeting of the European George P. H. Styan] (£ódŸ), Yuval Ne’eman (Tel Aviv), Roberto D. Finance Association (21-24 August) and the Location: Technical University of Denmark Peccei (Los Angeles), Jakub Rembieliñski Computational Finance Research Conference (Section of Image Analysis and Computer (£ódŸ), Ireneusz Strza³kowski (Warszawa), (24-25 August)] Graphics) Józef Szudy (Toruñ), Michael Turner Theme: computational statistics Aim: to stimulate research and foster inter- (Chicago), Edward Witten (Princeton), Topics: statistical risk management, multi- action between researchers in the interface Leszek Wojtczak (£ódŸ) variate and robust analysis, Markov chain between matrix theory and statistics. The Fees: 140 zlotys (c. US $35) per day, full Monte Carlo methods, statistics of E-com- workshop will provide a forum through board; the registration fee is 200 zlotys (US merce, new strategies in teaching (multime- which statisticians working in the fields of $50) dia, internet), computer based linear algebra and matrix theory may be bet- Grants: full support for twenty participants sampling/questionnaires, analysis of large ter informed of the latest developments and (full board, travel excluded) databases (with emphasis on computing in newest techniques, and may exchange ideas Information: contact Julian £awrynowicz memory), graphical tools for data analysis, with researchers from a variety of countries Institute of Mathematics, Polish Academy of classification and clustering, new statistical Deadline: 3 June for submission of abstracts Sciences, Banacha 22, 90-238 £ódŸ, Poland, software, historical development of software Registration fee: 240 euros before 29 July; e-mail [email protected] Main speakers: S. Brooks (USA), C. Chen 280 euros after that date (Taiwan), T. Hastie (USA), G. Kitagawa International organising committee: R. 5-9: International Conference on Ill-Posed (Japan), J.S. Marron (USA), J. Symanzik William Farebrother (Victoria Univ. of and Inverse Problems, Novosibirsk, Russia (USA), M. Valderrama (Spain), Th. Yee (New Manchester, UK), Simo Puntanen (Univ. of Information: Zealand), K. Yoshioka (Japan) Tampere, Finland), Hans Joachim Werner website www.math.nsc.ru/conference/mml Call for papers: submission period expired (Chair; Univ. of Bonn, Germany) [For details, see EMS Newsletter 42] Scientific programme committee: J. Antoch Local organising committee: Knut (Czech Republic), A. Bowman (UK), M. Conradsen (Chair), Bjarne K. Ersbøll, Per 9-11: Colloquium Logicum 2002, 2nd Delecroix (France), W. Härdle (Germany), P. Christian Hansen, Allan Aasbjerg Nielsen (all Biannual Meeting of the DVMLG, Münster, van der Heijden (Netherlands), W.G. DTU, Lyngby) Germany Manteiga (Spain), J. Nakano (Japan), M. Information: contact Helle R. Welling, Information: Schimek (Austria), A. Unwin (Germany) Workshop Secretary, Bldg. 321, Informatics website http://wwwmath.uni-muenster.de/ Local organising committee: Y. Boztug, H. and Mathematical Modelling, DTU, DK- LC2002/CL2002.html Büning, W. Härdle, L. Hildebrandt, U. 2800 Lyngby; fax: +45 45 88 13 97; [For details, see EMS Newsletter 43] Küchler, D. Pabst, B. Rönz, P. Schirmbacher, e-mail [email protected], B. Schüler, V. Spokoiny, H. G. Strohe, J. website http://www.imm.dtu.dk/matrix02 10-11: Colloquium Logicum 2002, Münster, Wolters, U. Ziegenhagen Germany Sponsors: StatSoft (Europe) GmbH, 31-6 September: European Women in [satellite conference of Logic Colloquium Insightful S-Plus Team, VSN International Mathematics International Workshop on 2002] Limited, Scopeland GmbH, ProGAMMA, Groups and Graphs, Varna, Bulgaria Information: SUN Microsystems, John Wiley & Sons Ltd., Topics: groups and graphs and their appli- website http://wwwmath.uni-muenster.de/ IBM, Minitab Ltd., Springer-Verlag cations in different sciences, discussions on LC2002/ Heidelberg, Cambridge University Press, some problems of women mathematicians [For details, see EMS Newsletter 41] Design Science Inc., NAGLtd Invited speakers: Bettina Eick (Germany), Proceedings: published by Physica-Verlag Wendy Myrvold (Canada), Valerie Berthe Location: main building of Humboldt- (France), Sarah Rees (UK), Karin 24 EMS June 2002 CONFERENCES Gatermann, (Germany), Rita Vincenti (Italy), broids and groupoids, quantum field theory Linz, Hagenberg/Linz, Austria Faina Solov’eva (Russia), Elizabeth J. Invited speakers: Anton Alekseev (Geneva), Information: website http://www.risc.uni-linz. Billington (Australia), Rachel Camina (UK), Melanie Bertelson (Brussels), Alberto ac.at/conferences/adg2002 Daniela Nikolova (Bulgaria), Stefka Cattaneo (Zürich), Marius Crainic (Utrecht), [For details, see EMS Newsletter 43] Bouyuklieva (Bulgaria), Svetlana Topalova Jean-Paul Dufour (Montpellier), Ezra Getzler (Bulgaria) (Northwestern), Viktor Ginzburg (Santa 4-6: 3rd International Conference on Call for papers: each contributed short talk Cruz), Victor Guillemin (MIT), Johannes Mathematical and Computational should contain original unpublished results, Huebschmann (Lille), Boris Khesin Applications, Konya, Turkey should not exceed four pages, and should be (Toronto), Yael Karshon (Jerusalem), Jiang- Information: submitted before 10 June as a LaTeX file Hua Lu (Arizona), Yoshiaki Maeda (Keio), website http://www.selcuk.edu.tr/icmca2002 ([10pt]{article}, \textwidth 11.5 cm, \tex- Eckhard Meinrenken (Toronto), Juan-Pablo [For details, see EMS Newsletter 43] theight 16.5cm, \normalsize), e-mailed to Ortega (Nice), Tudor Ratiu (Lausanne), [email protected]. Confirmation of Nicolai Reshetikhin (Berkeley), Dmitry 4-7: International Conference on receipt in 3 days, information about accep- Roytenberg (Penn State), Pavol Severa Dynamical Methods for Differential tance within a month after receipt (Bratislava), Alan Weinstein (Berkeley), Chris Equations, Valladolid, Spain Programme committee: Cheryl Praeger Woodward (Rutgers), Ping Xu (Penn State), Information: (president, Australia), Jennifer D. Key (USA), Nguyen Tien Zung (Montpellier) website http://wmatem.eis.uva.es/~dmde02/ Valerie Berthe (France), Sarah Rees (UK), Programme committee: Anton Alekseev [For details, see EMS Newsletter 41] Karin Gatermann (Germany) (Geneva), Yvette Kosmann-Schwarzbach Local organising committee: Daniela (Ecole Polytechnique), Yoshiaki Maeda 4-7: Perspectives in Mathematical Physics, Nikolova (president, Bulgaria), Svetlana (Keio), Alan Weinstein (Berkeley) Rome, Italy Topalova (Bulgaria), Milena Dobreva Organising committee: Miguel Abreu, Ana [in honour of the 60th birthday of Prof. (Bulgaria), Blajka Radeva (Bulgaria) Cannas da Silva, Rui L. Fernandes (Instituto Giovanni Gallavotti] Proceedings: a volume of the workshop pro- Superior Tecnico) Information: ceedings will be issued and ready at the Sponsors: Center for Mathematical Analysis, website http://www.mat.uniroma2.it/pmp2002 beginning of the workshop Geometry and Dynamical Systems, European [For details, see EMS Newsletter 43] Location: Bulgaria, on the Black Sea, inter- Union, Portuguese Science Foundation national home of scientists ‘F. Joliot-Curie’, 8 Proceedings: will not be published 8-13: ALGORITMY 2002, Conference on km from the town of Varna Location: Department of Mathematics, Scientific Computing, High Tatra Deadline: 10 June for submission of talks Instituto Superior Tecnico, Lisbon Mountains, Podbanske, Slovakia Information: e-mail: Grants: some funds will be available for Information: [email protected], graduate and postdoctoral students, as well website http://www.math.sk/alg2002 website: www.moi.math.bas.bg/EWM02 as participants from countries in a difficult [For details, see EMS Newsletter 42] economic situation September 2002 Deadlines: 1 July for registration 9-12 : Conference on Harmonic Analysis, Information: e-mail [email protected], Luxembourg-Metz (Luxembourg-France) website www.math.ist.utl.pt/Poisson2002 Information: e-mail 1-5: 3rd WSEAS Int. MultiConference on [email protected], Applied and Theoretical Mathematics, 3-7: 8th International Conference on website http://www.cu.lu/harmonic_analysis Miedzyzdroje, Poland Stability, Control and Rigid Bodies [For details, see EMS Newsletter 43] Information: e-mail [email protected], Dynamics, Donetsk, Ukraine website http://www.wseas.org/conferences/ Information: 9-20: Siberian School on Geometry and 2002/poland website http://www.iamm.ac.donetsk.ua/ Analysis, Novosibirsk, Russia conf2002.html [dedicated to the memory of A. D. 1-9: 8th AHA 2002, International Congress [For details, see EMS Newsletter 42] Alexandrov (1912-99)] on Algebraic Hyperstructures and Programme: the main part consists of sever- Applications, Samothraki Island, Greece 4-6: Brno CDDE 2002 - Colloquium on al mini-courses in geometry and geometric Information: e-mail [email protected], Differential and Difference Equations, analysis [email protected], Brno, Czech Republic Programme committee: Yu. G. Reshetnyak [email protected] [dedicated to Prof. Frantisek Neuman on the (Chairman), V. A. Sharafutdinov, V. A. [For details, see EMS Newsletter 43] occasion of his 65th birthday, continuation of Toponogov, S. K. Vodop’yanov the Brno CDDE 2000 conference ] Main speakers (preliminary list): V. N. 2-7: Poisson 2002, Conference on Poisson Topics: qualitative theory of differential and Berestovskii (Omsk), V. N. Dubinin Geometry, Lisbon, Portugal difference equations and their applications (Vladivostok), S. V. Gol’din (Novosibirsk), V. [The third in a series of conferences on Main speakers: P. Drabek (Czech Rep.), J. K. Ionin (Tver’), V. V. Ivanov (Novosibirsk), Poisson geometry and related fields] R. Graef (USA), I. Kiguradze (Georgia), J. S. V. Matveev (Chelyabinsk), A. D. Mednykh Aim: Poisson geometry has developed rapid- Mawhin (Belgium), F. Neuman (Czech Rep.), (Novosibirsk), I. G. Nikolaev (Urbana- ly due to new and exciting results related to M. Pituk (Hungary), F. Zanolin (Italy) Champaign), Yu. G. Reshetnyk classification of Poisson brackets, deforma- Format: invited plenary lectures, short com- (Novosibirsk), E. D. Rodionov (Barnaul), I. tion quantisation, topological invariants and munications and posters Kh. Sabitov (Moscow), V. A. Sharafutdinov differential equations occurring in mathe- Abstracts: please send an electronic version (Novosibirsk), I. A. Taimanov (Novosibirsk) matical physics. This conference aims to by e-mail; see the website for the required Organising committee: S. K. Vodop’yanov bring together leading experts in Poisson format (Chairman), A. S. Romanov (Secretary), V. A. geometry and related fields, as well as young Organising committee: O. Dosly (chairman), Alexandrov, A. A. Egorov researchers who have made promising con- M. Bartusek, Z. Dosla, J. Vosmansky Location: Sobolev Institute of Mathematics, tributions, and so will be a forum to cover Proceedings: to be published in the series of Novosibirsk, Russia recent progress and to stimulate exchanges Monographs of Folia Facultatis Scientiarium Deadline: 15 July for submission of abstracts among active researchers Naturalium Universitas Masarykinae Information: e-mail [email protected], Topics: local properties (singularities of Brunensis website http://www.math.nsc.ru/conference/ Poisson structures, linear approximations), Location: Hotel Santon in the area of Brno wwwga/ Hamiltonian systems (moment maps), global dam lake geometry (Poisson-Lie groups, Poisson G- Deadlines: 31 May for registration (for later 9-27: School and Conference on spaces, Poisson supergeometry, quasi-Poisson registration, accommodation in the Intersection Theory and Moduli, Trieste, manifolds) and Poisson topology (modular Colloquium Hotel Santon is not guaranteed), Italy class, characteristic classes and other invari- 15 June for abstracts Theme: algebraic geometry: intersection the- ants, K-theory, integrability of Poisson mani- Information: e-mail [email protected], ory and moduli spaces folds). Related fields that will also be website http://www.math.muni.cz/cdde Topics: algebraic stacks, Gromov-Witten touched upon include: symplectic and relat- invariants and quantum cohomology, invari- ed geometries, integrable systems, deforma- 4-6: Fourth International Workshop on ants of singular varieties, complex symplectic tion and geometric quantisation, Lie alge- Automated Deduction in Geometry, RISC- moduli spaces, vertex operators EMS June 2002 25 CONFERENCES Main speakers: D. Abramovich (USA), K. 2002), Bari, Italy try; Lie groups and homogeneous spaces; Behrend (Canada), A. Bertram (USA), E. Topics: Feller semigroups and Markov geometry and integrable systems Frenkel (USA), D. Huybrechts (Germany), M. processes, positive operators and approxima- Main speakers: D. Alekseevsky (UK), M. Lehn (Germany), J. Li (USA), F. Loeser tion of functions, positive operators and Guest (Japan), M. Micallef (UK) (France), A. Vistoli (Italy) approximation for evolution equations, semi- Format: three courses each consisting of five Format: a two-week school followed by a groups of operators and evolution equations, lectures and several tutorials one-week conference cosine families of operators and evolution Organising Committee: J. Berndt (UK), J. Programme committee: E. Arbarello (Italy), equations Bolton (UK) G. Ellingsrud (Norway), L. Goettsche (Italy) Aim: the School is especially addressed to Sponsors: Engineering and Physical Science Sponsors: International Centre for Ph.D. students and young researchers, who Research Council (UK), London Theoretical Physics are already active in, or want to improve Mathematical Society Proceedings: we plan to publish a volume of their knowledge of, the above topics. Location: University of Durham (UK) lecture notes relating to the school Format: the main part comprises five short Grants: full-board accommodation for UK- Location: International Centre for courses (each five hours) and some invited based students, four bursaries for non-UK- Theoretical Physics (ICTP), Strada Costiera lectures. There will also be informal discus- based students 11, Trieste sions and a poster session in which newer Deadline: 5 July for registration Grants: limited funds are available for par- researchers can outline their research work Information: e-mail [email protected], ticipants from, and working in, developing and interests website http://www.hull.ac.uk/LMS-DG countries; grants from the European Invited speakers of the courses: Jan van Commission for young participants from Casteren (Univ. of Antwerp), Heinz H. 20-25: International Conference on Europe may also be available Gonska (Univ. of Duisburg), Jan Prüss (Univ. Computational Methods in Science and Deadline: already passed of Halle-Wittenberg), Ioan Raºa (Techn. Engineering (CMMSE-2002), Alicante, Information: e-mail [email protected], Univ. of Cluj-Napoca), Sen-Yen Shaw (Nat. Spain website http://www.ictp.trieste.it/www_users/ Central Univ. of Chung-li) Information: website www.ua.es/cmmse2002/ math/maths2002.html Invited lecturers: José Antonio Adell (Univ. [For details, see EMS Newsletter 42] of Zaragoza), Detlef-Hauke Mache (Univ. of 10-20: Advanced Course on Geometric 3- Dortmund), Giuseppe Mastroianni (Univ. of 23-27: Calculus of Variations in Nonlinear Manifolds, Bellaterra, Barcelona, Spain Basilicata), Abdelaziz Rhandi (Univ. of Phenomena, Martina Franca (Ta), Italy Information: Marrakech), Vincenzo Vespri (Univ. of Theme: non-linear analysis website http://www.crm.es/geom-mani Firenze) Topics: calculus of variations, variational Executive organizing committee: F. methods, non-linear differential equations 11-13: EACA-2002, 8th Meeting on Altomare ([email protected]), A. Main speakers: T. Aubin, H. Berestycki, F. Computer Algebra and its Applications, Attalienti ([email protected]), M. Béthuel, N. Hirano, R. Kohn, C. S. Lin, F. Peñaranda de Duero, Spain Campiti ([email protected]), L. Murat, F. Pacard, T. Rivière, E. Séré, M. Aim: to provide a forum for researchers in D’Ambrosio ([email protected]), S. Struwe, C. Stuart computer algebra as well as for those who Diomede ([email protected]), G. Programme committee: A. Ambrosetti, L. use its techniques. There has been an EACA Metafune ([email protected]), D. Ambrosio, V. Benci, V. Coti Zelati, G. Dal meeting held in Spain every year since 1995; Pallara ([email protected]) Maso, D. Fortunato, A. Marino the 2001 meeting was attended by many Grants: the deadline for grants for young Organising committee: D. Fortunato, A. researchers from all over the world. The researchers has passed Masiello, A. Salvatore participation of young researchers is espe- Site: Hotel Villaggio Cala Corvino, on the Sponsors: M.I.U.R., Politecnico di Bari, cially encouraged Apulian coast near Monopoli, a town 35 kilo- Università degli Studi di Bari Topics: include, but are not restricted to, metres from Bari, Italy Location: Sala della Biblioteca Comunale, effective methods in algebra, analysis, geom- Deadline for registration: already passed Palazzo Ducale in the old town of Martina etry and topology; algorithmic complexity; Information: contact one of the executive Franca in southern Italy scientific computation via symbolic-numeri- organisers, Deadline: 14 September for registration cal methods; development of symbolic- website http://www.dm.uniba.it/documenti/ Information: numerical software; analysis, specification, formazione/SummerSchool-OMEEAP2002/ website www.dm.uniba.it/martina2002 design and implementation of symbolic com- index.htm putation systems; applications to science and 23-27: Ramification in Arithmetic and technology 16-17: Annual Francophone Meeting of Geometry, Paris, France Main speakers: C. Andradas (Univ. Classification, Toulouse, France Information: http://www-math.math. Complutense, Madrid, Spain), B. Buchberger Theme: classification topics, including neur- univ-paris 13.fr/~ramifica/ (RISC-Linz, Austria), J. Elias (Univ. al networks, graph theory, image processing, Barcelona, Spain), I. Emiris (INRIA, Sophia- remote sensing, multivariate modelling, pat- 23-4 October: The Calculemus Autumn Antipolis, France), A. Simis (UFPe, Recife, tern recognition, datamining School 2002, Pisa, Italy Brazil), U. Walther (Purdue Univ., USA) Main speakers: A. Appriou (ONERA), J-P. Theme: integration of computer algebra and Scientific committee: M.-E. Alonso (Univ. Barthelemy (ENSTB), A. Ciampi (Canada), deduction Complutense), I. Bermejo (Univ. La F. Critchley (England), A. Degenne (Caen), Aim: the School will bring together a large Laguna), J.-L. Bueso (Univ. Granada), F.-J. T. Denoeux (Compiegne), G. Govaert number of experts from the field of comput- Castro (Univ. Sevilla), J. Elias (Univ. (CNRS), S. Holmes (USA), D. Ladiray er algebra and deduction systems. The goal Barcelona), Ph. Gimenez (Univ. Valladolid), (Luxembourg), J-P. Rasson (Belgium), F. is to train young researchers, high school L. González-Vega (Univ. Cantabria), A. Rossi (LISE/CEREMADE), T. Snijders teachers and representatives from industry Montes (U.P. Cataluña), T. Recio (Univ. (Netherlands), J. Ten Berge (Netherlands), on the state-of-the-art research and current Cantabria), J. Rubio (Univ. La Rioja), J.-R. S. Thiria (LODYC), B. Victorri (ENSP) systems in this field. The school is a summit Sendra (Univ. Alcalá) Location: Université du Mirail of the activities of the EU training network Organiser: Ph. Gimenez (Dept. Algebra, Grants: for 3 participants with support of Calculemus and the broader Calculemus Univ. Valladolid) AUPELF interest group Host institution: University of Valladolid Deadlines: 1 September for registration, 15 Objectives: to give young researchers a per- (Spain) May for abstracts spective on state-of-the-art symbolic compu- Location: Palacio de Avellaneda, Peñaranda Information: e-mail [email protected], tation and symbolic reasoning; to dissemi- de Duero (Spain) web site http://www.irit.fr/SFC2002/ nate advanced scientific knowledge on the Deadlines: already passed for submission; 28 integration of computer algebra systems and June for early registration 16-20: LMS/EPSRC Short Course on deduction systems; to foster contacts between Information: e-mail [email protected], Differential Geometry, Lie Groups and the research communities of computer alge- website http://www.uva.es/eaca2002 Homogeneous Spaces, Durham, United bra, deduction, mathematics education, and Kingdom industry 15-22: International Summer School on Aim: to introduce research students to sever- Format: participants will be trained both the- Operator Methods for Evolution Equations al topics in differential geometry oretically and experimentally on selected and Approximation Problems (OMEEAP Topics: introduction to differential geome- topics and tools. They will have the oppor- 26 EMS June 2002 CONFERENCES tunity to experiment with the main tools of Video; Robotics, Distance Learning and Scope: A. N. Kolmogorov’s creative legacy, the area, and researchers developing the Intelligent Communication Systems, optimisation theory and its prospects, tools will receive valuable feedback. Ph.D. Skiathos, Greece approximation methods and stability in con- students, mathematics and computer science Information: website http://www.wseas.org/ trol, variation methods for non-linear sys- teachers, and personnel from industry are conferences/2002/skiathos/ tems investigating and their applications, expected to participate mathematical models of economic systems Topics: deduction systems, computer alge- October 2002 control, mathematical models of control bra, proof planning, group theory, formal technical, natural and humanities methods, model checking, systems of polyno- Languages: Russian, English mials, partiality, integration of decision pro- 9-11: 7th Conference on Shell Structures, Call for papers: authors are invited to sub- cedures, mathematical exploration, mathe- Theory and Applications (SSTA2002), mit abstracts. Contributions must be pre- matics databases, mathematical learning Gdañsk-Jurata, Poland pared in LaTeX environments, mathematical system net- Information: website Programme committee: V. M. Filippov, A. works, system support in mathematics educa- http://www.pg.gda.pl/ssta2002 B. Kurzhansky, Yu. S. Osipov, V. A. tion, and more [For details, see EMS Newsletter 42] Sadovnichy, V. M. Tikhomirov (chairs); A. I. System demos: Inka, Vse, Coq, Theorema, Bulgakov (deputy); A. P. Afanasiev, A. V. Omega, Mizar, Isabelle, Activemath, Mbase, February 2003 Arutyunov, N. A. Bobylev, A. G. Chentsov, V. MathWeb, NuPrl, Lambda-Clam, NuSMV, B. Demidovich, V. V. Dikusar, A. V. Dmitruk, Gap, Mathbook, RDL, LBA, and more I. V. Evstigneev, V. I. Levin, G. G. Magaril- Main speakers / lecturers Alessandro 5-7: 4th IMACS Symposium on Il’yaev, S. M. Nikol’sky, Yu. V. Pokorny, E. L. Armando (Italy), Christoph Benzmüller Mathematical Modelling, Vienna, Austria Tonkov, M. I. Zelikin; E. S. Zhukovsky (sci- (Germany), Bruno Buchberger (Austria), Information: website entific secretary) Alan Bundy (Scotland), Jacques Calmet http://simtech.tuwien.ac.at/MATHMOD Organisers: Moscow M. V. Lomonosov State (Germany), Arjeh Cohen (Netherlands), [For details, see EMS Newsletter 41] University, V. A. Steklov Institute of James Davenport (England), Herman Mathematics of the Russian Academy of Geuvers (Netherlands), Fausto Giunchiglia 5-7: 4th MATHMOD Vienna 4th IMACS Sciences, Ministry of Education of Russian (Italy), Dieter Hutter (Germany), Manfred Symposium on Mathematical Modelling, Federation, Ministry of Industry, Science, Kerber (England), Michael Kohlhase (USA), Vienna, Austria and Technologies of Russian Federation, Christoph Kreitz (USA), Ursula Martin Aim: scientists and engineers using or devel- Tambov Region Administration, Tambov G. (Scotland), Andreas Meier (Germany), Erica oping models or interested in the develop- R. Derzhavin State University Melis (Germany), Tobias Nipkow (Germany), ment or application of various modelling Proceedings: to be published Marco Pistore (Italy), Marco Roveri (Italy), tools can present ideas, methods and results Location: the buildings of Tambov G. R. Jörg Siekmann (Germany), Volker Sorge and discuss their experiences or problems Derzhavin State University (England), Werner Stephan (Germany), (Internatsional’naya st., 33, Tambov, Russia) Andrzej Trybulec (Poland), Wolfgang with experts of various areas of specialisation Deadlines: 1 March for registration, 1 Windsteiger (Austria), Tom Kelsey Scope: theoretical and applied aspects of the November for abstracts (Scotland), Olga Caprotti (Austria) various types of mathematical modelling Call for papers: students and participants (equations of various types, automata, Petri Information: e-mail [email protected], are invited to submit short papers (up to 5 nets, bond graphs, qualitative and fuzzy [email protected], pages) related to the objectives of the school models, etc.) for systems of dynamic nature website http://www.opu2003.narod.ru Programme and organising committee: (deterministic, stochastic, continuous, dis- 11-18: Conference on Topological Agebras, Christoph Benzmüller (Saarland University, crete or hybrid with respect to time, etc.); their Applications, and Related Topics, Chair), Regine Endsuleit/Clemens Ballarin comparison of modelling approaches, model Bedlewo, Poland (Univ. of Karlsruhe, Chair), Carlo Traverso simplification, modelling uncertainties, port- [in honour of Professor Wieslaw Zelazko] (Univ. of Pisa, Local Organiser), Jörg based modelling, and the impact of items Topics: general theory of Banach and topo- Siekmann (Saarland Univ., Calculemus such as these on problem solution, numerical logical algebras; connections with operator Network), Jacques Calmet (Univ. of techniques, validation, automation of model- theory, complex analysis, harmonic analysis, Karlsruhe, Calculemus Network), Corinna ling and software support for modelling, co- and homological methods; representations, Hahn (EPO/ Eurice GmbH, Calculemus simulation; applications of modelling in con- structure and classification of topological Management) trol, design or analysis of systems in engi- algebras Sponsors: Dipartimento di Matematica neering and other fields of application Main speakers: E. Albrecht (Germany), G. R. (Università di Pisa), Calculemus Network, Format: special sessions, presentations of Allan (England), H. Arizmendi-Peimbert German Research Centre for Artificial modelling and simulation software, book (Mexico), C. Badea (France), P. C. Curtis Intelligence (DFKI), Research Institute for exhibition (USA) H. G. Dales (England), M. Applications of Computer Algebra (RIACA), Organiser: Division for Mathematics of Fragoulopoulou (Greece), T. W. Gamelin City of Pisa, Saar Toto GmbH Control and Simulation (E114/3), Vienna (USA), B. Gramsch (Germany), A. Ya. Proceedings: course handouts will be distrib- University of Technology. Chair of IPC: Helemskii (Russia), A. Inoue (Japan), J.-P. uted at the event. Short papers and poster Inge Troch Kahane (France), H. Koenig (Germany), K. contributions will be published in a technical Location: Vienna University of Technology B. Laursen (Denmark), M. Oudadess report Deadlines: already passed for submission of (Morocco), A. Yu. Pirkovskii (Russia), C. J. Location: conference at Dipartimento di abstracts, 1 December for submission of full Read (England), A. Rodrigues-Palacios Matematica, Università di Pisa; conference papers (Spain) accommodation at the 14th century monas- Information: contact Univ.Prof. Dr. Inge Programme committee: H. G. Dales (chair, try Santa Croce in Pisa Troch, Vienna University of Technology, England), G. R. Allan (England), A. Ya. Grants: the School is included in the EU Wiedner Hauptstrasse 8 - 10 A-1040 Wien, Helemskii (Russia), A. Rodrigues-Palacios Comenius Catalogue 2002 (grants for high Austria, tel. +431-58801-11451, fax. +431- (Spain) school teachers from the EU are available). 58801-11499, Local organising committee: A. Soltysiak Further grants for students will probably be e-mail [email protected], (Poland), K. Jarosz (USA) available website http://simtech.tuwien.ac.at/ Sponsors: Institute of Mathematics of the Deadlines: 1 July for registration, 1 August MATHMOD Polish Academy of Sciences, Adam for submission of papers Mickiewicz University, Poznan, Poland Information: May 2003 Proceedings: likely to be published in the e-mail [email protected], series ‘Banach Center Publications’ website http://www.eurice.de/calculemus/ Location: The Mathematical Conference autumn-school 11-16: International Conference on General Centre at Bedlewo, near Poznan, Poland Control Problems and Applications (GCP- Grants: probably support for participants 25-28: 2nd WSEAS International 2003), Tambov, Russia from countries in a difficult economic situa- Conferences on: Simulation, Modelling and [dedicated to the 100th anniversary of A. N. tion and young mathematicians Optimization; Signal, Speech and Image Kolmogorov] Information: e-mail [email protected], Processing; Multimedia, Internet and Theme: optimal control website http://main.amu.edu.pl/~ta2003 EMS June 2002 27 Zentralblatt MATH as a gateway to electronic and digitised articles in mathematics Bernd Wegner (Editor-in-Chief, Zentralblatt MATH)

With the growing availability of mathemat- ical articles in electronic form, Zentralblatt MATH was able to extend its services to an important new field of activities, the link- ing to offers of full texts. As a result, addi- tion to the traditional comprehensive sur- vey on the literature in mathematics pro- vided by Zentralblatt, the search facilities in the electronic version are combining the final information on a document of inter- est with an access to the document itself. This access may be activated with a sys- tematic literature retrieval in the Zentralblatt MATH database or just by using this database through the citation and ref- erence checker like a catalogue to find a location, where the document of interest is available. In both cases the user will find two buttons within the full display of the database entry, one linking to the com- plete electronic version of the document if available, and the other linking to a set of document delivery services. The link to the complete electronic ver- sion refers to the service of a publisher, a freely available offer of articles as in the ELibM of EMIS, or just to the installation of the journal on its own homepage. Links are updated when URLs of the offers change. Access to the complete version of the article depends on the regulations made by the provider. Hence, in order to get a copy of an article from a charged electronic version of a journal, a subscrip- tion to this journal will be requested from the user’s side. The link to the set of document delivery services at first gives a list of providers. For example, one of them is the State and University Library of Lower Saxony in Göttingen, which has one of the most com- prehensive collections of publications in mathematics. Having chosen a document delivery service of the user’s preference, the data of the corresponding publication will be exported to the provider’s OPAC, and if the document will be available there, an order form will appear automatically. The requested item will be sent to the user by e-mail, fax or postal mail, depending on how it is stored in the library’s holdings and in accordance with the regulations at the provider. The choice of the document delivery ser- vice by the user is mainly motivated by the delivery conditions, which strongly depend on the location of the user. The search software of Zentralblatt MATH allows for connecting a variety of such services. It is therefore easy to add further providers leading to a system of document delivery services that offers access to complete arti- cles at the most convenient conditions for the user. This development is in progress. 28 EMS June 2002 RECENT BOOKS many recent articles. Chapter 5 presents various results on the asymptotic behaviour of mild solutions of homogeneous and inho- RecentRecent booksbooks mogeneous Cauchy problems (relations between growth bounds and spectral bounds, edited by Ivan Netuka and Vladimír Sou³ek together with examples illustrating each one-sided inequality, splitting and non-reso- Books submitted for review should be sent to the which include conformal geometry of the nance theorems for orbits of bounded semi- following address: sphere, hyperbolic geometry, eight three- groups as an application of Chapter 4). Ivan Netuka, MÚUK, Sokolovská 83, 186 75 dimensional geometries, some four-dimen- Finally, three more concrete applications are Praha 8, Czech Republic. sional geometries and the geometry of orb- given. ifolds. In the second chapter, discrete Each chapter ends with reference notes S. Albeverio and P. Kurasov, Singular groups of homeomorphisms are studied. and the bibliography contains almost 400 Perturbations of Differential Operators, Chapter 3 is devoted to hyperbolic groups items. In short appendices vector-valued London Mathematical Society Lecture Note Series and manifolds and their invariants, and to a holomorphic functions, closed operators, 271, Cambridge University Press, Cambridge, description of arithmetic and non-arithmetic ordered Banach spaces and distributions are 2000, 429 pp., £29.95, ISBN 0-521-77912-X groups. Geometric finiteness as a central reviewed. The notation list (6 pages) and the This book is devoted to a study of spectral concept for geometric structures is presented index (7 pages) make the book more com- properties of self-adjoint operators inspired in the fourth chapter: the planar case is dis- fortable to use. This book may serve as an by equations arising in classical and quantum cussed first and basic ideas are introduced in up-to-date research monograph or a text- physics and in chemistry. A typical model of this setting, geometric finiteness in higher book for advanced graduate students. It is such an operator is a second order differen- dimensions is then explored from several clearly written with an emphasis on simple tial operator, together with its various per- points of view. Chapter 5 describes the proofs of (even well-known) theorems. (efa) turbations. geometry and topology of Kleinian mani- Rank one (and generalised rank one) per- folds and presents special features of low T. Aubin, A Course in Differential Geometry, turbations are studied first. Finite rank sin- dimensional cases. The concept of uniformi- Graduate Studies in Mathematics 27, American gular perturbations of a self-adjoint operator sation is introduced and developed in the Mathematical Society, Providence, 2001, 184 are then investigated, together with the cor- sixth chapter: starting from the classical two- pp., US$35, ISBN 0-8218-2709-X responding scattering theory. The Krein dimensional case, several modern concepts The book contains an introduction to differ- formula relating resolvents of two self- of uniformisations in higher dimensions are ential geometry on manifolds with an adjoint extensions of a given symmetric discussed. The last chapter presents the emphasis on Riemannian geometry. A operator, is extended to the case of infinite theory of deformations of geometric struc- knowledge of basic facts from topology, deficiency indices. Two-body and three- tures, and rigidity of hyperbolic structures, multi-linear algebra and the theory of func- body quantum-mechanical problems with quasi-Fuchsian structures, their bendings tions of several real variables is supposed, various interactions are discussed in the final and cone deformations are studied in detail, and a summary of necessary facts from these chapters. In the Appendix, the authors add ending with global properties of deforma- fields appears in the introductory chapter. 25 pages of historical remarks describing the tion spaces. There are many examples, The book begins with the definition of a main topics of the book in a historical per- notes and comments. differentiable manifold and a description of spective, including remarks on recent This book is a good source for readers some of its properties. Submanifolds are results. The book ends with an unusually interested in topics mentioned above. (jbu) then studied, including the Whitney embed- comprehensive bibliography consisting of ding theorem, the Sard theorem and a dis- almost a thousand items in more than 70 W. Arendt, C. J. K. Batty, M. Hieber and F. cussion of critical values of differentiable pages. Neubrander, Vector-valued Laplace maps. In Chapter 2, the tangent space of a The book offers a carefully and nicely writ- Transforms and Cauchy Problems, manifold, differential forms and their calcu- ten mathematical theory of the singular per- Monographs in Mathematics 96, Birkhäuser, lus, orientation on manifolds and manifolds turbations of self-adjoint operators. (vs) Basel, 2001, 523 pp., DM 196, ISBN 3-7643- with boundary are defined and Stokes’ theo- 6549-8 rem is proved. Integration of vector fields D. Alpay, The Schur Algorithm, Reproducing In this new monograph on Cauchy prob- and Pfaffian systems and their applications Kernel Spaces and System Theory, SMF/AMS lems, semigroups are treated from the point are described in the third chapter. Chapter Texts and Monographs 5, American of view of Laplace transform and harmonic 4 defines linear connections and parallel Mathematical Society, Providence, 2001, 150 analysis of Banach space-valued functions. transport on manifolds with a given connec- pp., US$49, ISBN 0-8218-2155-5 Approximately one third of the book tion. This is the English translation of a book (Chapters 1, 2, 4) is devoted to a compre- The main topic of this book is Riemannian which first appeared first in French in the hensive treatment of Laplace transform of manifolds. In addition to standard material, series Panoramas et Synthèses, published by functions with values in a Banach space. one can find here a discussion of invariant Société Mathématique de France in 1998. Classical results are formulated and proved operators on forms, the Hodge theorem, the The review of the French edition was pub- in this context (the Laplace integral, repre- spectrum of a Riemannian manifold, and the lished in Newsletter 34 (December 1999, p. sentation theorems, inversion formulas, Yamabe problem. More than half of the 36). (vs) holomorphic functions and asymptotic prop- book is devoted to exercises, problems at dif- erties). In Chapter 3, abstract Cauchy prob- ferent levels and solutions of exercises. The B. N. Apanasov, Conformal Geometry of lems are solved by means of Laplace trans- author’s aim was to facilitate the teaching of Discrete Groups and Manifolds, De Gruyter forms, and dissipative operators, holomor- differential geometry. The presentation is Expositions in Mathematics 32, Walter de phic semigroups, fractional powers of sector- very succesful, and I can strongly recom- Gruyter, Berlin, 2000, 523 pp., DM 298, ISBN ial operators and the role of UMD spaces are mend the book to anybody willing to learn 3-11-014404-2 discussed. Chapter 4 treats asymptotics of differential geometry, as well as to teachers This book presents a systematic study of con- vector-valued functions and their Laplace of the subject. (jbu) formal geometry of n-dimensional manifolds transforms, relating different limits at infini- and the related geometry of the correspond- ty (Abelian and Tauberian theorems) and S. Axler, P. Bourdon and W. Ramey, ing Riemannian spaces – in particular, discussing various notions of spectra of a Harmonic Function Theory, 2nd ed., hyperbolic geometry. Unified methods used function on R (Carleman, Beurling) and of a Graduate Texts in Mathematics 137, Springer, for the study involve the discrete holonomy vector with respect to a group (local spec- New York, 2001, 259 pp., DM 119, ISBN 0- groups of the corresponding geometrical trum). Using these concepts, results are for- 387-95218-7 structures. mulated about the asymptotic behaviour of A brief review of the first edition of this book Felix Klein’s approach to geometry given functions and of orbits of semigroups (con- appeared in Newsletter 10 (December 1993). by a couple (X, G), where X is a manifold and vergence, almost-periodicity, asymptotic There are several major changes in this sec- G is a group of homeomorphisms of X is pre- almost-periodicity). This chapter summaris- ond edition: a new and simplified treatment sented first, together with several examples, es in a systematic way the results scattered in of spherical harmonics, solvability of the EMS June 2002 29 RECENT BOOKS Dirichlet problem on the half-space with no 498 pp., £29.95, ISBN 0-521-80920-7 and 0- ters and Maillet’s determinant. growth conditions on boundary data, and a 521-79722-5 This book can be recommended to all new discussion of generalised versions of This book, written by one of the leaders in readers interested in theory of compact Liouville’s and Bôcher’s theorems. Many the field, has become the bible of random Riemann surfaces and their automorphism exercises have been added and several pho- graphs. This second edition contains two groups. (jbu) tographs of mathematicians related to har- new chapters, numerous new results and monic functions are included. The book is a over 150 additional references. Just as one E. Bujalance, A. F. Costa and E. Martínez nice introduction to the fundamental can compare a random graph with a living (eds.), Topics on Riemann Surfaces and notions of potential theory. (in) organism that evolves with time, so one Fuchsian Groups, London Mathematical Society could also compare this book with the life- Lecture Note Series 287, Cambridge University O. Biquard, Métriques d’Einstein asympto- story of this organism. Press, Cambridge, 2001, 177 pp., £24.95, ISBN tiquement symétriques, Astérisque 265, Société The long adventure starts in Chapter 2 by 0-521-00350-4 Mathématique de France, Paris, 2000, 109 pp., introducing the most frequently encoun- This book contains extended versions of lec- Ffrs 250, ISBN 2-85629-083-3 tered probability models of random graphs tures given at the conference ‘Topics on This book is devoted to asymptotically sym- and their basic properties. In Chapter 3, Riemann Surfaces and Fuchsian Groups’, metric Einstein metrics: this property means one learns about the distribution of degree held in Madrid in 1998. that its curvature at infinity approaches sequences and how to deal quickly with the There are two main themes. The first is asymptotically the curvature of a rank 1 sym- graph isomorphism problem in these mod- unification of two concepts underlying two metric space of non-compact type (hyperbol- els. Chapter 4 gives the probability that a different definitions of Riemann surfaces – ic spaces). In cases that correspond to random graph contains a given fixed graph one geometrical, where Riemann surfaces Einstein deformations of complex, quater- as a subgraph. The next two chapters are are defined as one-dimensonal complex nionic or octonionic symmetric spaces, some devoted to the components of a random manifolds, and the other analytic, based on Carnot-Carathéodory metrics appear on the graph with special emphasis on the largest analytic continuations and analytic functions boundary at infinity. In the last two cases, one – the so-called giant component. Chapters in function theory. The second theme is the the author obtains new structures at infinity 7-11 consider connectivity, matching, study of Riemann surfaces as a topological called contact structures (quaternionic or octo- Hamiltonicity, asymmetry and the diameter quotient of certain covering spaces with nionic). of random graphs. A special chapter is ded- respect to the action of a group: apart from After a short summary of the history of the icated to clique number, independence num- the plane C, the twice-punctured sphere and problem, the author summarises the results ber and chromatic number. In the Ramsey the tori, Riemann surfaces can be studied as of the book. The theory of Einstein defor- theory chapter, dealing with extremal prob- quotients of the group of the hyperbolic mations of hyperbolic metric is described lems, the probabilistic approach overpowers plane by a discrete group called a Fuchsian and an overview of analysis on symmetric deterministic methods. The book concludes group. spaces and constructions of Einstein metrics with random cubes, random matrices, ran- There are nine contributions: the geome- is given. Contact structures of quaternionic dom mappings, and applications of random try of Riemann surfaces, by A. F. Beardon; type are studied in Chapter 2, together with graphs in sorting algorithms. introduction to arithmetic of Fuchsian related induced structures, such as partial This book is primarily for mathematicians groups, by C. Maclachlan; Riemann surfaces, connections and twistors. The final chapter interested in graph theory and combina- Belya functions and hypermaps, by D. is devoted to constructions of quaternionic torics with probability and computing, but it Singerman; compact Riemann surfaces and Kähler metrics and twistor spaces. could also be of interest to computer scien- algebraic function fields, by P. Turbek; sym- The book is nicely written and can be rec- tists. It is self-contained and lists numerous metries of Riemann surfaces from a combi- ommended to anybody interested in the sub- exercises in each chapter. As such, it is an natorial point of view, by G. Gromadzki; ject. (jbu) excellent textbook for advanced courses or compact Klein surfaces and real algebraic for self-study. (rskr) curves, by F. J. Cirre and J. M. Gamboa; J.-C. Birget, S. Margolis, J. Meakin and M. moduli spaces of real algebraic curves, by M. Sapir (eds.), Algorithmic Problems in Groups T. Breuer, Characters and Automorphism Seppälä; periodic matrices and the Schottky and Semigroups, Trends in Mathematics, Groups of Compact Riemann Surfaces, problem, by R. Silhol and Hurwitz spaces by Birkhäuser, Boston, 2000, 307 pp., DM 148, London Mathematical Society Lecture Note Series S. M. Natanzon. Beardon’s paper is a nice ISBN 0-8176-4130-0 and 3-7643-4130-0 280, Cambridge University Press, Cambridge, overview of problems in the geometry of This volume contains sixteen papers based 2000, 199 pp., GBP 24,95, ISBN 0-521- Riemann surfaces, and can be used as a on talks at an international conference at the 79809-4 source for a series of lectures on this topic. University of Nebraska-Lincoln in May 1998 These notes describe some recent results on Real algebraic curves are well discussed in that brought together researchers in algo- automorphism groups of compact Riemann the papers by Cirre and Gamboa, and by rithmic problems in group theory, semi- surfaces. The author is interested in the clas- Seppälä. (jbu) group theory and computer science. sifications of (i) groups of automorphisms of Among the papers are two survey articles compact surfaces X of a fixed genus g ³ 2, up R. Cori and D. Lascar, Mathematical Logic. on the algorithmic theory of free groups, one to equivalence given by the natural action on A Course with Exercises. Part I, Oxford by Baumslag, Myasnikov and Remeslenikov, H1(X); (ii) all characters of a given finite University Press, Oxford, 2000, 338 pp., £25, and the other by Bencsath, Fine, Gaglione, group G arising from the natural action of ISBN 0-19-850049-1 and 0-19-850048-3 Myasnikov, Roehl, Rosenberger and groups of automorphisms of compact The first part of this course of mathematical Spellman. Another survey paper by Riemann surfaces X on H1(X). logic is based on the notion of truth, rather Kublanovskii is on the decidability of Rhodes The first two chapters present basic than on the notion of derivation from of a finite semigroup. Connections between notions and facts from the theory of axioms. This conception leads rather quick- the algebraic theory of finite monoids and Riemann surfaces, Fuchsian groups and ly to the problematics of computer process- the theory of communication complexity are characters, and introduces the module ing, especially to the resolution method surveyed in the paper by Raymond, Theson H1(X). Chapters 3 and 4 treat the structure described in the final chapter. and Therien. of groups of automorphisms of compact The topic is divided into four chapters – The volume also contains research articles Riemann surfaces and the description of sets propositional calculus, boolean algebras, on various aspects and interconnections of their generators and their properties. predicate calculus, and completeness theo- between the topics of the conference. It can The problem of determining all characters rems. Unlike most courses on mathematical be used both as an introduction to the sub- and groups of automorphisms for small logic, the second chapter deals with boolean ject of algoritmic problems in groups and genus g, with 2 £ g £ 48 is solved in Chapter algebras: this is also suitable for students of semigroups, and as a reflection of the cur- 5. The last two chapters give classifications computer science to whom the course is rent state of the subject. (jtu) of characters for a fixed group, first for a real addressed. For students interested in ‘more character, then for the case where non-real classical’ mathematical logic (such as model B. Bollobás, Random Graphs (2nd ed.), irrationalities appear in the character table theory, modal or many-valued logic), we rec- Cambridge Studies in Advanced Mathematics 73, of G. There are three appendices, dealing ommend Mathematical Logic by Ebbinghaus, Cambridge University Press, Cambridge, 2001, with abelian invariants, irreducible charac- Flum and Thomas.

30 EMS June 2002 RECENT BOOKS This book contains many stimulating exer- Dimensional Representation Theory, braic curves as cissoids, trocoids, epi- and cises, with solutions. In Corollary 4.19, an Monographs and Surveys in Pure and Applied hypocycloids, etc.). The curvature of curves explicit formulation of the assumption of the Mathematics 114, Chapman & Hall/CRC, Boca is introduced via moving frames, the inflex- closeness of the formula F would help the Raton, 2000, 428 pp., £53.99, ISBN 1-58488- ion points are discussed and their invariance reader: the assumption appears in the theo- 212-3 with respect to the isometries of the plane is rem used in the proof. The notation used in This book is an accessible and self-contained proved. Special problems, such as the con- the book sometimes differs from the stan- account of the central results of analytic tact of curves with lines and circles, evolutes, dard one (as used, for example, in the group representation theory and operator cusps and vertices, envelopes, orthonomics Handbook of Mathematical Logic). (kè) algebras. Starting from Borel spaces, the and caustics are studied and illustrated by exposition continues with fundamentals of examples. At the end of the book, planar R. Downey and D. Hirschfeldt (eds.), C*-algebras and the classical theory of von kinematics and its problems are described. Aspects of Complexity, de Gruyter Series in Neumann algebras. Since unitary represen- There are many examples and exercises. Logic and Its Applications 4, Walter de Gruyter, tations of groups correspond to *-represen- This is a nice textbook that can be recom- Berlin, 2001, 169 pp., DM 169, ISBN 3-11- tations of their group algebras, the exposi- mended to students of mathematics as well 016810-3 tion naturally continues with group actions as to students of physics or engineering. This book is based on lectures by the con- and the induced actions and representations. (jbu) tributors during the course ‘Computability, The final two chapters deal with operator Complexity and Computational Algebra’ algebras: the Hilbert algebras (including the J. Glaz, J. Naus and S. Wallenstein, Scan given in January 2000 in Kaikoura, New Tomita-Takesaki theory of the modular Statistics, Springer Series in Statistics, Springer, Zealand. It comprises notes for seven lec- ones) and the Fourier-Stieltjes algebra. New York, 2001, 370 pp., DM 192,49, ISBN 0- tures on different subjects, including basic This book will certainly be of interest to 387-98819-X complexity, computation with real numbers, specialists from a wide range of fields in The meaning of a scan statistic is clarified by parametrised complexity, Kolmogorov com- mathematics and physics – from algebra, via the following example. From 1991 to 1995 plexity, matrix groups computation, count- functional analysis and measure theory, to there were 19 cases of a particular type of ing complexity and aspects of continuum: quantum mechanics. (jtrl) cancer reported in a city. A 1-year period most of these are recently developed areas of (April 1993 to April 1994) contains eight computational complexity. S. D. Friedman, Fine Structure and Class cases. Is such a cluster statistically signifi- The contributions are intended neither as Forcing, de Gruyter Series in Logic and its cant? In general, N points are distributed surveys nor as introductions to the topics dis- Applications 3, Walter de Gruyter, Berlin, 2000, over (0, T). Let Sw be the largest number of cussed, but are (sometimes informal) 221 pp., DM 178, ISBN 3-11-016777-8 events in a window of length w. The maxi- overviews of concepts and key results. The In this book the class of constructible sets L mum cluster Sw is the scan statistic. material and level of presentation are acces- and generic extensions of L are investigated, This book is divided into two parts. The sible to those familiar with only the basics of with an emphasis on the method of class first part describes the use of scan statistics in computer science. Readers will not learn the forcing (and iterated class forcing), which applications: the main topics are retrospec- whole subject from any chapter of this book, appears to be a powerful means for solving tive and prospective scanning of events over but will find what the particular area of mod- mathematical problems. The class L was time, success scans in a sequence of trials, ern computational complexity is about; introduced by Gödel to prove the consisten- higher-dimensional scans, and scan statistics interested readers can find further details in cy of the continuum hypothesis and the in DNA sequences. The second part monographs or surveys referred to in each method of forcing was introduced by Cohen describes scan distribution theory and its chapter. The book should be valuable for to prove the independence of this hypothe- developments. The individual chapters are mathematicians who want to learn the basic sis. Since then, both methods have been sig- devoted to exact results, approximations, concepts of those areas of computational nificantly improved. and bounds for scan statistics. The case complexity covered by the book. (dkr) The book starts with an investigation of L when the size of the sliding window is and with a proof of some combinatorial prin- unknown or there is a need to detect clusters M. du Sautoy, D. Segal and A. Shalev (eds.), ciples (Diamond, Square and various ver- of events superimposed on trends, is also dis- New Horizons in pro-p Groups, Progress in sions of Morasses) that are used later for con- cussed. One of the interesting topics is clus- Mathematics 184, Birkhäuser, Boston, 2000, structions of various special partial orderings tering two types of letter pattern in a two- 423 pp., DM 178, ISBN 0-8176-4171-8 and (sets or classes of properties) used in the dimensional array, with an application to the 3-7643-4171-8 forcing method: some classical forcings are text of the Bible: the problem is to look at A pro-p group is the inverse limit of a system included, and many other techniques are words appearing as equally spaced letters in of finite p-groups – groups of prime-power used (such as indiscernibles) – for example, it a text. The words, whose letters’ positions in order where the prime p is fixed. The sys- is proved that such set-theoretical notions as the text form an arithmetic progression, are tematic study of pro-p groups in general is a large cardinals are closely related to special called equidistant letter sequences (ELS). It is recent development. This volume presents a properties of the reals. From many of the interesting to test whether such ELSs contain coherent account of recent achievments and hard problems solved in the book, let us hidden information. 1 points the way forward by bringing together mention the consistency of P 2 definable real The book contains a valuable bibliography articles by leading researchers in the field R (as a singleton) being constructible larger that includes over 600 references. It can be that develop various aspects of the theory in than 0 and strictly constructible less than 0- recommended to researchers working in twelve chapters. sharp. From the last chapter, we mention applications, as well as to specialists develop- The impetus for current research on pro-p some applications proving that some classi- ing methods for the scanning of events. The groups comes, broadly speaking, from four cal results of measurability, categoricity, and material is also suitable for graduate-level directions. The first is number theory: the perfectness of sets of projective hierarchy are courses. (ja) classical context is Galois cohomology, and best possible. The reader is supposed to be the modern one is the theory of p-adic Galois familiar with a standard course of set theory. R. E. Greene and S. G. Krantz, Function representations. The second source is the Refernces to the literature appear only in the Theory of One Complex Variable (2nd ed.), problem of classifying finite p-groups. The proofs in the last chapter. (kè) Graduate Studies in Mathematics 40, American third is the theory of infinite groups, and Mathematical Society, Providence, 2002, 502 finally there is the subject of ‘profinite group C. G. Gibson, Elementary Geometry of pp., US$69, ISBN 0-8218-2905-X theory’, of which the theory of pro-p groups Differentiable Curves: An Undergraduate This book was written for a first-year gradu- is only a well-developed part. A large num- Introduction, Cambridge University Press, ate course in complex analysis, and the first ber of open problems are presented Cambridge, 2001, 216 pp., £16.95, ISBN 0- edition has been revised and improved. The throughout the text and in the Appendix: 521-80453-1 and 0-521-01107-8 authors base their approach on ideas taken this makes the volume a rich source of This is an elementary introduction to the from multi-variable calculus already familiar promising directions for further research. geometry of curves in the Euclidean plane. to students, but they try to reduce the neces- (jtu) It contains standard material on the differ- sary topological material and concentrate on ential geometry of plane curves, and also of a straightforward approach to the analytical R. C. Fabec, Fundamentals of Infinite certain classical special curves (conics, alge- topics: the topological tools are concentrated

EMS June 2002 31 RECENT BOOKS in one (revised) Chapter 11. Cohen-Macaulay approximations due to students to count the number of heads or The book contains some advanced and Auslander-Buchweitz, as well as Ringel’s the- tails: it is not well known that K. Pearson was less traditional topics and includes, for ory of approximations for representations of offered an OBE (Officer of the Order of the example, theorems on rational approxima- algebraic groups. British Empire) and a knighthood, but he tion, Hardy spaces and the Bergman kernel. Unifying commutative noetherian rings refused both honours. It may be surprising One chapter is devoted to special functions with finite-dimensional algebras, the book to many readers that Borel was mayor of and the final one is on the prime number requires a large introductory Chapter I that Saint-Affrique and Minister for the Navy. theorem; its proof has also been rewritten. spans almost half of the text. The funda- The book is interesting reading and infor- The exposition is clear and written in an mentals of the highest weight theory are also mation from it can surely refresh lectures on accessible way for most students, who will presented in a self-contained way, in probability and mathematical statistics. (ja) also appreciate the exercises (555 of them!), Chapter III. Along with the general theory, both routine and ‘theoretical’ (with hints), several interesting applications are provid- K. Jänich, Vector Analysis, Undergraduate following each of the 16 chapters. Short ed: in Section II.2, the regularity (Cohen- Texts in Mathematics, Springer, New York, 2001, comments on the history and origins of Macaulay, Gorenstein, and local complete 281 pp., 108 fig., DM 69, ISBN 0-387-98649- notions and theorems are contained in the intersection) criteria for noetherian G-alge- 9 text. bras are proved. Section IV.2 deals with When and how to introduce students to sur- This book can be recommended as a text applications to the structure of equivariant face integration and ideas related to Stokes’ for a basic course (the first third of the text), resolutions of determinantal rings, and other theorem is a question that is difficult to as well as for an advanced course at graduate applications concern invariant theory. answer. The calculus books treat only the level. (jive) This monograph brings the reader to the simplest ideas related to the Gauss and bounds of knowledge in the subject. It will Stokes theorems, while a systematic treat- C. E. Gutiérrez, The Monge-Ampère be of interest to researchers and graduate ment of these questions in analysis courses Equation, Progress in Nonlinear Differential students, both in commutative ring theory for undergraduates is usually missing. This Equations and their Applications 44, Birkhäuser, and representation theory. (jtrl) book offers a very nice description of the Boston, 2001, 126 pp., DM 156, ISBN 0-8176- basic conceptual tools needed to explain 4177-7 and 3-7643-4177-7 S. Helgason, Differential Geometry, Lie these topics to mathematics students (the The Monge-Ampère equation det D2u = f is Groups, and Symmetric Spaces, Graduate concept of a manifold, Cartan calculus of dif- of great importance for its geometrical inter- Studies in Mathematics 34, American ferential forms, a general form of Stokes’ pretation and applications, and in recent Mathematical Society, Providence, 2001, 641 theorem), and includes some more advanced years, many remarkable advances have been pp., US$69, ISBN 0-8218-2848-7 (and very important) topics, such as the de achieved. This book develops the modern The first edition of Helgason’s classical book Rham complex, Hodge duality and Ricci cal- theory of the Monge-Ampère equation, appeared in 1962, and revised and substan- culus on Riemannian manifolds. including regularity results of L.A. Caffarelli. tially extended version was published in The book can be used for a course on With any convex function u, we can associate 1978 by Academic Press. The book under these topics, and only the rudiments of cal- a measure Mu by the formula Mu(E) = review is the third printing, published by the culus, linear algebra and a bit of topology are |¶u(E)|; here, ¶u is the normal mapping, or American Mathematical Society. A few inac- needed as prerequisites. A nice feature is subdifferential of u, and |...| is Lebesgue curacies have been corrected and some new that it contains many figures (making easier measure. For u smooth, the measure Mu has explanatory notes have been collected in a an intuitive understanding of the treated density det D2u, and it is thus natural to call dozen of pages at the end of the book. This topics), exercises with hints, and tests with a function u with Mu = f a generalised solution book has been famous for many years and answers. This book is a translation of the of the Monge-Ampère equation: this is com- used by several generations of readers. It is second German edition, so that it is now pared with the notion of viscosity solution. important that the book has again become accessible for a much broader audience. It is The Dirichlet problem for Mu = f is also available for a general audience. (vs) certainly one of the best books in the field solved, and various questions in regularity and can be strongly recommended for a gen- theory are studied. All C4-solutions of det C. C. Heyde and E. Seneta (eds.), eral mathematical audience. (vs) D2u = 1 satisfy a Hölder estimate for the sec- Statisticians of the Centuries, Springer, New ond derivative, which implies that entire York, 2001, 500 pp., DM 96,19, ISBN 0-387- K. Kaarli and A. F. Pixley, Polynomial solutions are quadratic polynomials. C1,a and 95238-7 and 0-387-95329-9 Completeness in Algebraic Systems, Chapman W2,p estimates are established for the solu- This book arose through the initiative of the & Hall/CRC, Boca Raton, 2001, 358 pp., tions where 0 < l< Mu < L< ¥. International Statistical Institute. It contains £56.99, ISBN 1-58488-203-4 This book is not restricted to presentation about 100 short biographies of selected sta- This book is on general algebraic systems – of the author’s results: the material is select- tisticians born prior to the 20th century, in particular, on affine completeness and ed according to its importance. The exposi- including biographies of persons who are polynomial completeness. After introducing tion is self contained, equipped with com- probabilists rather than statisticians. The necessary concepts on algebras, lattices and plete proofs and carefully arranged. The view of the authors is expressed on p.441: varieties in the first chapter, the authors pro- Monge-Ampère equation has many applica- ‘Probability’ is surely the life blood of ‘statis- ceed to lattices of equivalence relations, tions in differential geometry, the calculus of tics’ and any dividing line is impossible to including material on compatible function variations and optimisation, including the position. Many interesting facts are present- lifting. Chapter 3 introduces primal algebra Monge-Kantorovitch mass transfer problem. ed about scientists whose names are usually and systematically develops its natural gen- The methods, using some techniques of har- connected only with formulas and theorems. eralisations, including affine completeness: monic analysis, are beautiful and promising Let me introduce a few examples. De there are results on the important concepts extensions of other problems. This book is Morgan, when asked his age, declared: ‘I of congruence permutability, congruence one of the best sources for this purpose. was x years old in the year x2.’ (You can distributivity and near unanimity. The main (jama) check that he was born in 1806: find other results appear in Chapter 4 on affine com- statisticians who were not born in that year plete varieties. The final chapter describes M. Hashimoto, Auslander-Buchweitz and still can declare the same!) He also the affine complete members in several spe- Approximations of Equivariant Modules, refused to be proposed as a Fellow of the cial varieties, including the varieties of lat- London Mathematical Society Lecture Note Series Royal Society: ‘Whether I could have been a tices, modules, semi-lattices, etc. 282, Cambridge University Press, Cambridge, Fellow, I cannot know; as the gentleman said The book is clearly written and is accessi- 2000, 281 pp., £27.95, ISBN 0-521-79696-2 who was asked if he could play the violin, I ble to anyone with a basic knowledge of the In this monograph, the theory of Auslander- never tried.’ Further one reads that Boole methods and concepts of general algebraic Buchweitz approximations is developed for married Mary Everest, niece of Colonel systems. (jtu) the category of A-finite G-equivariant A- Everest after whom Mount Everest was modules, where G is a split reductive group named; that the Bonferroni inequality had M. Kerber and M. Kohlhase, Symbolic over a commutative noetherian ring R, and A already been derived by Boole; that Karl Computation and Automated Reasoning, The is a commutative noetherian G-algebra. This Pearson in one of his lectures scattered Calculemus-2000 Symposium, A. K. Peters, theory generalises and unifies the theory of 10000 pennies over room floor and asked his Natick, 2001, 270 pp., US$60, ISBN 1-56881-

32 EMS June 2001 RECENT BOOKS 145-4 applications are studied, including the poly- sample theory for statisticians. Although the The proceedings of CALCULEMUS 2000 splines on strips and on annuli in Rn: this more difficult results are stated without consists of fourteen full-length papers, short part is logically self contained and would proof, the conditions for their validity are description of two invited presentations, one meet the interests of a reader interested in given and the results are illustrated by inter- system description and twelve posters. The smoothing methods and computer-aided esting examples. For applied statisticians it selected papers were presented at the 8th geometric design, but not in wavelet analysis. is important to know relative efficiencies of CALCULEMUS Symposium, held on 6-7 Part II concentrates on the polysplines ana- frequently used tests (p. 176), robustness August 2000 in St. Andrews, Scotland. The logue of Schoenberg’s one-dimensional car- results concerning the t-test (p. 191), the per- Symposium was intended for researchers dinal splines. The author starts with the the- formance of two statistical tests applied to interested in both symbolic computation and ory of cardinal L-splines according to the data simultaneously (p. 376), and that mechanised reasoning. Micchelli, and then develops the theory of there exists a case when one can make a very The full-length papers cover a wide range cardinal interpolation polysplines on annuli: informative observation although its Fisher of topics in these fields and describe various the major result is a generalisation of the information is 0 (p. 462). The book also con- systems; they are self-contained and can be polynomial case considered by Chui. Part III tains a rich collection of problems and a use- divided into three groups. The first group is presents wavelet analysis using polysplines ful list of references, and can be warmly rec- about integration or standardisation of par- and provides a detailed study of one exam- ommended as a complementary text to lec- ticular systems (communication protocols for ple of spherical polyharmonic wavelet analy- tures on mathematical statistics, as well as a mathematical services based on KQML and sis. The author briefly recalls Chui’s results textbook for more advanced courses. It was OMRS; interfacing computer algebra and on cardinal spline wavelet analysis and originally used for a postgraduate statistics deduction systems via Logic Broker proves generalisations of all Chui’s basic course at Charles University, Prague, during Architecture based on Corba and results: the main conclusion is that the 2001/02. (ja) Openmath; Ù-ants, combining interactive attempt to make a reasonable multi-resolu- and automated theorem proving; and a tion analysis (MRA) by means of a refining A. Liu (ed.), Hungarian Problem Book III, progress report of the Theorema project). sequence of spaces of cardinal polysplines The Anneli Lax New Mathematical Library 42, The papers from the next group centre (on annuli or strips) leads to a considerable The Mathematical Association of America, around a particular problem, they describe a reconsideration of the whole store of basic Washington, 2001, 142 pp., £20.95, ISBN 0- new theory (integrated processing of self- notions of MRA. Part IV has a quite differ- 88385-644-1 contained mathematical text), new methods ent flavour: unlike the previous parts, it is This is a translation from Hungarian by for solving the problem (definite integration not concrete analysis. It considers the poly- Andy Liu. The Eõtvõs-Kirsch mathematical of parametric rational functions using splines for general interfaces. Even more competition for high-school students has DILTU method; learning methods in proof generally, the author introduces a very gen- been organised since 1894. The problems planning; meta-variables for natural deduc- eral class of polysplines, which are piecewise given in this contest from the periods 1894- tion in Theorema) or experiments and case solutions of a large class of higher-order 1905 and 1906-1928 were published in two studies (finding symmetries hidden in com- elliptic equations. A generalisation of the booklets of the ‘New Mathematical Library’ binatorial problems using Godzilla; formal Holladay extremal property and the exis- (Vols. 11, 12). This book contains the prob- and efficient proof of prime (2999) in COQ; tence of interpolation polysplines for the so- lems from the period 1929-43. exploring properties of residue classes of called ‘even-order polysplines’ are proved. The problems are divided into the follow- Zn). The last group describes extensions of This is a nicely written book of great value ing chapters: Combinatorics, Number particular systems (theory of continuous lat- for stimulating graduate students. It is Theory, Algebra, Geometry I (congruence, tices in Mizar; power series and polynomials aimed principally at specialists in approxi- similarity) and Geometry II (circles, vectors). in Mizar; logic and dependent types in mation and spline theory, wavelet analysis Each chapter contains problems (with one or Aldor). Many of the posters, as well as the and signal and image processing, and at more solutions) together with basic defini- description of CAS system Singular for poly- people using computer-aided geometric tions and various problem-solving tech- nomial computation, include URL for a design systems or smoothing and spline niques. The foreword is written by József more detailed description. methods in geophysics, geodesy, geology or Pelikán, well known as a member of the The volume covers selected topics and magnetism. It can be strongly recommend- Comittee of the International Mathematical describes new trends in the fields of deduc- ed as a comprehensive resource for self- Olympiads (IMO). One of the prizewinners tion systems, computer algebra systems and study. (knaj) of the Eõtvõs Competition was Miklos their integration. It is a valuable contribu- Császár (in 1942), chairman of the IMO in tion for researchers and postgraduate stu- E. L. Lehmann, Elements of Large-Sample 1982 in Budapest. dents in these fields. (jhr) Theory, Springer Texts in Statistics, Springer, The book will be very useful for students New York, 1999, 631 pp., 10 fig., DM 192,49, who participated, or will participate, in O. Kounchev, Multivariate Polysplines, ISBN 0-387-98595-6 mathematical competitions, as well as for Applications to Numerical and Wavelet This book consists of 7 chapters and an teachers and anybody interested in solving Analysis, Academic Press, San Diego, 2001, 498 appendix. Chapter 1 contains some mathe- mathematical problems. (lbo) pp., US$84.95, ISBN 0-12-422490-3 matical background, while Chapter 2 is This book introduces and develops a new devoted to convergence in probability and in L. Manivel, Symmetric Functions, Schubert type of multi-variate splines known as poly- law. The material of these chapters (132 Polynomials and Degeneracy Loci, SMF/AMS splines. The author studies cardinal poly- pages) has an introductory character and Texts and Monographs 6, American splines and polyharmonic wavelets in a com- many students of mathematical statistics will Mathematical Society, Providence, 2001, 167 plete analogy with the one-dimensional poly- know it from calculus or from courses in pp., US$44, ISBN 0-8216-2154-7 nomial cardinal splines and cardinal spline probability theory. Chapter 3 deals with per- The French edition of this book appeared in wavelets. Polysplines are piecewise polyhar- formance of statistical tests, with topics like 1998 in the series ‘Cours Spécialisés’, issued monic splines and provide a powerful means power and sample size, relative efficiency by the Société Mathématique de France; its of interpolating data: they also provide new and robustness, while Chapter 4 describes review appeared in EMS Newsletter 32 (June prespectives on wavelet theory, with applica- estimation problems: confidence intervals, 1999, p.34). The English translation was tions to signal and image processing. All accuracy of point estimators, comparing esti- issued in cooperation with the American these results may be considered as a step in mators, and sampling from a finite popula- Mathematical Society. (vs) the direction of the qualitative theory of par- tion; Chapter 5 extends these results to the tial differential equations. multi-variate case. In Chapter 6 we find J. C. McConnell and J. C. Robson, This book is in four parts. In Part I the non-parametric estimation (U-statistics, sta- Noncommutative Noetherian Rings, Graduate author provides a logical basis for the notion tistical functionals, density estimation, boot- Studies in Mathematics 30, American of polysplines and explains in detail the strapping), while Chapter 7 presents effi- Mathematical Society, Providence, 2001, 636 meaning of the data, smoothness and object cient estimators and test, mainly maximum pp., US$72, ISBN 0-8218-2169-5 concepts of the polyharmonic paradigm, and likelihood, Fisher information, and asymp- This is a revised and updated edition of a their implementation in spline analysis. totic normality. monograph first published under the same Polysplines on strips and annuli in R2 with This is a very nice introduction to large- title in 1987. Non-commutative noetherian

EMS June 2001 33 RECENT BOOKS rings have gained importance in the mean- in Lie groups of general type. The reader will find a basic mathematical time, with the appearance of quantum The second part (written by B. L. Feigin introduction to the theory of normed vector groups and related non-commutative struc- and D. B. Fuchs) is devoted to various coho- spaces and linear operators between them. tures. Starting (and ending) with the key mologies of Lie groups and Lie algebras. It The book has fifteen chapters, each end- motivating examples, the exposition pro- presents corresponding definitions (classical, ing with carefully selected problems to be ceeds to the classical Goldie theory and the van Est and Segal cohomologies of Lie solved. The first three chapters present the structure of the prime spectrum of the ring. groups; cohomology of Lie algebras), and basic principles of linear functional analysis: Part II deals with dimension theory: the some of their general properties and their the Riesz representation theorem, the Hahn- Krull, global, and Gelfand-Kirillov dimen- relations, as well as tools and methods for Banach theorem, the uniform boundedness sions are treated in detail. Part III deals with their calculations. The results of such com- principle and the open mapping theorem. extensions, starting with generic flatness and putations are presented in the last chapter Chapters 4 and 5 present the Riesz theory of the Nullstellensatz, and proceeding to stabil- for many important special cases (finite- compact operators and the general theory of ity and the Grothendieck group K0. dimensional Lie groups and Lie algebras, Fredholm and semi-Fredholm operators. The first edition of this book was the basic Lie algebras of vector fields and diffeomor- The introduction to spectral theory is con- reference in non-commutative ring theory, phisms, Lie groups and algebras of currents, tained in Chapter 6. Unbounded operators, stimulating research in the area since the Lie algebra of infinite matrices). One can unbounded Fredholm and semi-Fredholm late 1980s. Only a few changes were needed also find here useful interpretations of coho- operator are studied in Chapter 7. Chapter for the present edition, yet another sign of mology and homology in low dimensions, 8 deals with reflexive Banach space, and the quality of the monograph. (jtrl) and this part includes a very useful summary Chapters 11-13 cover Hilbert space. An of basic concepts and results in the field. introduction to Banach algebras is given in K. Nishiyama, H. Ochiai, K. Taniguchi, H. This book will be very useful as a reference Chapter 9, where the Fredholm and semi- Yamashita and S. Kato, Nilpotent Orbits, book and a source of information for stu- Fredholm perturbations are also presented. Associated Cycles and Whittaker Models for dents and researchers from both mathemat- Chapters 9 and 14 discuss special topics Highest Weight Representations, Astérisque ics and theoretical physics. (vs) from the theory of semigroups, measures of 273, Société Mathématique de France, Paris, operators and perturbation functions. The 2001, 163 pp., FRF 200, ISBN 2-85629-101- M. A. Picardello, Harmonic Analysis and last chapter contains important applications. 5 Integral Geometry, Research Notes in The book concludes with two appendices: This volume contains three papers, with an Mathematics 422, Chapman & Hall/CRC, Boca the first gives definitions of important introduction and concluding remarks Raton, 2001, 171 pp., £49.99,ISBN 1-58488- notions and symbols used throughout the (including some problems). In the three arti- 183-6 book, while the second contains a list of cles, the authors investigate irreducible uni- This volume contains the proceedings of the major theorems and indicates the pages tary highest-weight representations of reduc- first Summer University of Safi, Morocco, where they can be found. tive Lie groups of Hermitian type, not neces- and consists of sixteen contributions related This is a nicely written book of great value sary contained in the holomorphic discrete to real harmonic analysis and integral geom- for stimulating active work by students. It series. In particular, associated cycles, the etry. can be strongly recommended as an under- Bernstein degree and generalised Whittaker The proceedings include papers by T. graduate or graduate text, or as a compre- models for these representations are Nomura (invariant Berezin transforms), hensive book for self-study. (knaj) described. The Howe correspondence for where explicit spectral decomposition of this dual pairs, one of which is compact, is also important transform is described in several C. J. Scriba and P. Schreiber, 5000 Jahre explained, and the realisations of highest- cases, and A. Abouelaz (integral geometry in Geometrie. Geschichte Kulturen Menschen, weight representations in kernels of invari- the sphere Sd), where the geometric Springer, Berlin, 2001, 596 pp., DM 69, ISBN ant differential operators of gradient type approach based on the dual Radon trans- 3-540-67924-3 are presented. In the last paper, by S. Kato form for the sphere Sd is presented, includ- This book is an excellent and comprehensive and H. Ochiai, the degrees of orbits of mul- ing several explicit formulas and results. work on the history of geometry from pre- tiplicity-free actions of connected reductive Other contributions are concetrated on spe- historic times to the present time, written by algebraic group are computed. The subclass cific problems: F. Gonzales (John’s equation C. J. Scriba, professor of history of science at of orbits, consisting of holomorphic tangent and the plane-to-line transform on R3), T. Hamburg, and P. Schreiber, professor of bundles of Hermitian symmetric spaces, is Kakehi (Radon transforms on compact geometry at Greifswald. studied as a nice example. A complete list of Grassmann manifolds and invariant differ- The topics treated here contain the origins degrees of actions in hermitian and non-her- ential operators of determinantal type), S. of geometry and its history in Greece, the mitian cases is presented in the appendix of Gindikin (integral geometry on hyperbolic Orient, the European middle ages, the the last paper. spaces), M. A. Picardello (the geodesic renaissance and the last four centuries. In This book is an excellent source of infor- Radon transform on trees), E. C. Tarabusi, J. the last chapter is a discussion of the rela- mation for study and research in this field. M. Cohen and F. Colonna (the distribution- tionships between geometry and science, (jbu) valued horocyclic Radon transform on trees), technics or informatics: the last-but-one L. Atanasi (integral geometry on affine deals with descriptive, projective, synthetic A. L. Onischnik and E. B. Vinberg (eds.), buildings), A. d’Agnolo and C. Marastoni (a and non-Euclidean geometry and the origins Lie Groups and Lie Algebra II, Encyclopaedia topological obstruction for the real Radon of topology. We also find applications of of Mathematical Sciences 21, Springer, Berlin, transform), H. Dib and M. Mesk (on geometry in geodesy, cartography, astrono- 2000, 223 pp., DM 159, ISBN 3-540-50585-7 Laguerre polynomials of two variables), S. my and in art. Special attention is paid to This volume of the Encyclopaedia of Ibenmouloud and M. Sbai (Poisson trans- geometry in Islam countries, in India, Japan Mathematical Sciences treats two topics: dis- form on H3), H. Sami (transfer formula in and China. crete subgroups of Lie groups, and coho- the real hyperbolic space Bn), A. Essadiq (q- Each chapter begins with an overview of mologies of Lie groups and Lie algebras. analogue of Watanabe uniform transform the historical events and technical discover- The first part (written by E. B. Vinberg, V. associated to the q-continuous Gegenbauer ies of the corresponding period, including V. Gorbatsevich and O. V. Shvartsman) con- polynomials) and M. E. Beggar (realization very useful surveys on the progress in geom- tains a systematic treatment of all basic of a holomorphic discrete series of the Lie etry. In this way the book represents the results in theory of discrete subgroups of Lie group SU(1, 2) as star-representation). (jbu) valuable contributions of geometry to the groups. More complicated proofs of pre- cultural development of mankind. There sented results are usually omitted, and relat- M. Schechter, Principles of Functional are also some original short texts (in ed questions (discrete subgroups of motions Analysis (2nd ed.), Graduate Studies in German) from Plato, Archimedes and oth- in spaces of constant curvature) can also be Mathematics 36, American Mathematical Society, ers. Among the more than 200 pictures are found in Volume 19 of the Encyclopaedia. Providence, 2001, 425 pp., US$59, ISBN 0- reproductions of works by Dali and Escher The authors discuss in turn discrete sub- 8218-2895-9 and photographs of interesting surfaces. groups of locally compact topological This excellent book provides an elegant Each chapter also contains a number of groups, lattices in solvable Lie groups, lat- introduction to functional analysis, including problems, such as the proof of the Heron tices in semi-simple Lie groups and lattices related parts of theory of integral equations. formula, the construction of a quadrilateral

34 EMS June 2001 RECENT BOOKS inscribed in a circle, or calculating the Gauss is suitable as a reference book or as an tion, a construction of the multivariable curvature of the pseudosphere. At the end advanced textbook for PhD courses on infer- Conway polynomial of links in homology 3- of the book is a comprehensive list of more ence for stochastic processes. (ja) spheres is presented. At the end of the book than 350 references. the recent results of G. Meng, G. H. Taubes This book can be warmly recommended, H. C. Thode, Jr., Testing for normality, and the author on connections between the not only to historians of mathematics, but Statistics, Textbooks and Monographs 164, refined torsions and the Sileberg-Witten also to professional mathematicians, teach- Marcel Dekker, NewYork, 2002, 479 pp., invariant of 3-manifolds is briefly described. ers and students. (lboc) US$150, ISBN 0-8247-9613-6 The exposition is aimed at students, pro- The assumption that a sample comes from a fessional mathematicians and physicists S. Skiena, Calculated Bets: Computers, normal distribution is very frequent in math- interested in combinatorial aspects of topol- Gambling, and Mathematical Modeling to ematical statistics. Fortunately, in many ogy and/or in low-dimensional topology. Win, Cambridge University Press, 2001, 232 cases a central limit theorem helps a fast The necessary background for the reader pp., £12.95, ISBN 0-521-80426-4 convergence to normality of a test statistic, so includes a basic knowledge of topology and This interesting book is about a gambling that small or moderate departures from the homological algebra. (jtu) system that works. It tells how the author assumption about distribution of the popula- used computer simulations and mathemati- tion do not invalidate the results of the sta- A. van den Essen, Polynomial cal modelling techniques to predict the out- tistical analysis. In other cases, the assump- Automorphisms and the Jacobian Conjecture, come of jai alai (pelota) matches and bet on tion of normality is crucial – no wonder that Progress in Mathematics 190, Birkhäuser, Basel, them successfully. His method can work for the tests for normality have attracted statisti- 2000, 329 pp., DM 118, ISBN 3-7643-6350-9 anyone; at the end of the book the author cians for many years! One of the first was This book is divided into three main parts, describes the best way to bet on jai alai. With Karl Pearson, whose name is usually con- Methods, Applications and Appendices. humour and enthusiasm, Skiena discusses nected with the famous c2 goodness of fit The first part consists of seven chapters. other gambling systems, such as lotto, test. It is less well known that he also advo- The first one (Preliminaries) introduces the roulette, blackjack and the stock market: cated tests based on moments because they basic tools used throughout the book. The indeed, he shows how his jai alai system func- belong to the most powerful methods for next chapter (Derivations and polynomial tions like a miniature stock-trading system. detecting departures from normality. automorphisms) is devoted to the interplay The book will be surely of interest not only This book is a good reference text on test between polynomial automorphisms and for the fun of jai alai, but also for all those for univariate and multivariate normality. locally nilpotent derivations. In Chapter 3 who would like to learn about the program The first part concerns testing for univariate (Invertibility criteria and inversion formulae) trading systems, the future of internet gam- normality. The author describes plots, prob- various criteria for polynomial automor- bling, how mathematical models are used in ability plots, regression tests, tests using phisms are presented. Chapter 4 (Injective political polling, what is the difference moments, goodness-of-fit tests and other morphisms) investigates some conditions between the correlation and causality, and so tests for complete samples, tests for outliers, under which injective endomorphisms are on. If you are interested in gambling and power comparisons, and testing for normali- surjective, while the next chapter (The tame mathematics, the odds are that this is a book ty with censored data. The second part of automorphism group of a polynomial ring) for you! (jant) the book is devoted to tests for multivariate deals with polynomial rings with coefficients normality. Additional topics include testing in a commutative Q-algebra. In Chapter 6 M. Taniguchi and Y. Kakizawa, Asymptotic for normal mixtures, robust estimation of (Stabilization methods) the stabilization Theory of Statistical Inference for Time location and scale, and computational issues. principle is described and is applied to a series, Series in Statistics, Springer, New York, Three appendices contain data sets, parame- reduction of the Jacobian conjecture. In the 2000, 661 pp., DM 203,19, ISBN 0-387- ter and critical values, and a computer sub- last chapter of the first part (Polynomial 95039-7 routine for optimisation. Nowadays, it is maps with nilpotent Jacobian), a large class The first three chapters of this book serve as easy to use a computer and to calculate some of such mappings is investigated. an introduction to the asymptotic theory of statistics for testing normality. However, it is The second part consists of three chapters, statistical inference. This part is useful as a comfortable to have this book and to look in Application of polynomial mappings to review of modern probabilistic tools applica- it for whether the test is sufficiently powerful, dynamical systems, Group actions and The ble not only to stochastic processes but to the whether the sample is large enough, or Jacobian conjecture. whole of mathematical statistics, for exam- whether it is better to use another test. The last part consists of six appendices, ple, we find here Le Cam’s lemmas, results The book is clearly written with many the first five forming a sufficient background concerning local asymptotic normality, and interesting numerical examples and histori- for reading the text, while the last one pre- the asymptotic theory of estimation and test- cal remarks. The large bibliography will be sents special examples and counter-exam- ing for stochastic processes. There is an useful for readers who wish to obtain more ples to the whole text. (lbi) important section on criteria for the station- details about the methods described in the arity of non-linear processes, where several text. (ja) H. Walser, The Golden Section, Spectrum recent useful results are collected and dis- Series, The Mathematical Association of America, cussed. Since many estimators and tests have V. Turaev, Introduction to Combinatorial Washington, 2001, 142 pp., £17.95, ISBN 0- the same limiting behaviour, it is necessary Torsions, Lectures in Mathematics, Birkhäuser, 88385-534-8 to analyse their higher-order asymptotic Basel, 2001, 123 pp., DM 38, ISBN 3-7643- From antique times, the golden section has optimality. In Chapter 4, the concept of 6403-3 occurred frequently in geometry, architec- higher-order asymptotic efficiency of estima- This book is an extended version of the ture and art. We say that a line segment is tors is introduced, and a differential geomet- notes from the author’s lectures at ETH, divided in golden ratio if the larger subseg- rical framework of curved exponential fami- Zürich, in Spring 1999. It is an introduction ment is related to the smaller one as the lies is extended to a class of general stochas- to combinatorial torsions of cellular spaces whole segment is related to the larger sub- tic processes: it is shown that the maximum and manifolds, with special emphasis on tor- segment. The golden section plays an likelihood estimator is third-order asymptot- sions of 3-dimensional manifolds. important role not only in classical geome- ically optimal. The general approach is also The first two chapters cover the algebraic try, but also in fractals, in the study of applied to Fisher’s z-transformation, and foundations of the theory of torsions and Fibonacci sequences and in the theory of higher-order asymptotics of diffusion various topological constructions of torsions regular and quasi-regular solids. All of processes are investigated. The remaining due to K. Reidemeister, J. H. C. Whitehead, these connections are described in the book chapters deal with asymptotic theory for J. Milnor and the author. Connections under review. It contains a large collection long-memory processes, statistical analysis of between the torsions and the Alexander of pictures which help to understand the functionals of spectra, discriminant analysis polynomial of links and 3-manifolds are also content, and many of problems, whose solu- for stationary time series, and large devia- discussed. The third (and last) chapter of tions are given at the end. tion theory and saddle-point approximation the book deals with so-called refined torsions The book, a translation from the German for stochastic processes. and the related additional structures on original (B. C. Teubner, Leipzig, 1993) can This book contains a rich variety of mod- manifolds, specifically homological orienta- be recommended to students of high schools ern results scattered in papers and books. It tions and Euler structures. As an applica- and to their teachers. (lbo)

EMS June 2001 35