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. 40 Building 303 DK-2800 Kgs. Lyngby, Denmark June 2001 e-mail: [email protected] KRZYSZTOF CIESIELSKI EMS Agenda ...... 2 Mathematics Institute Jagiellonian University Editorial - David Salinger ...... 3 Reymonta 4 30-059 Kraków, Poland SIAM-EMS Conference ...... 4 e-mail: [email protected] KATHLEEN QUINN Executive Committee Meeting ...... 6 The Open University [address as above] e-mail: [email protected] The Institute for Industrial Mathematics ...... 8 SPECIALIST EDITORS Workshop on Applied Mathematics in Europe ...... 9 INTERVIEWS Steen Markvorsen [address as above] GAMM Annual Scientific Conference 2001 ...... 11 SOCIETIES Krzysztof Ciesielski [address as above] The Methodology of Mathematics ...... 12 EDUCATION Tony Gardiner Interview with Björn Engquist ...... 15 University of Birmingham Birmingham B15 2TT, UK Interview with Manuel Valdivia ...... 16 e-mail: [email protected] MATHEMATICAL PROBLEMS Mathematical Societies: France ...... 18 Paul Jainta Werkvolkstr. 10 Mathematical Societies: Romania ...... 20 D-91126 Schwabach, Germany e-mail: [email protected] Personal Column ...... 23 ANNIVERSARIES Forthcoming Conferences ...... 25 June Barrow-Green and Jeremy Gray Open University [address as above] Recent Books ...... 30 e-mail: [email protected] and [email protected] and CONFERENCES Designed and printed by Armstrong Press Limited Kathleen Quinn [address as above] Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK RECENT BOOKS telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134 Ivan Netuka and Vladimir Sou³ek Published by European Mathematical Society Mathematical Institute ISSN 1027 - 488X Charles University Sokolovská 83 The views expressed in this Newsletter are those of the authors and do not necessarily 18600 Prague, Czech Republic represent those of the EMS or the Editorial team. e-mail: [email protected] and [email protected] ADVERTISING OFFICER NOTICE FOR MATHEMATICAL SOCIETIES Vivette Girault Labels for the next issue will be prepared during the second half of August 2001. Laboratoire d’Analyse Numérique Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: Boite Courrier 187, Université Pierre [email protected] et Marie Curie, 4 Place Jussieu 75252 Paris Cedex 05, France INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER e-mail: [email protected] Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, OPEN UNIVERSITY Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e- PRODUCTION TEAM mail: ([email protected]). Please include the name and full address (with postal code), tele- Liz Scarna, Kathleen Quinn phone and fax number (with country code) and e-mail address. The annual subscription fee (including mailing) is 60 euros; an invoice will be sent with a sample copy of the Newsletter.

EMS June 2001 1 EMS NEWS EMS Committee EMS Agenda EXECUTIVE COMMITTEE PRESIDENT (1999–2002) 2001 Prof. ROLF JELTSCH 19-21 June Seminar for Applied Mathematics EMS lectures at the University of Heraklion, Crete (Greece) ETH, CH-8092 Zürich, Switzerland Lecturer: Prof. George Papanicolaou (Stanford, USA) e-mail: [email protected] Title: Time Reversed Acoustics VICE-PRESIDENTS Contact: David Brannan, e-mail: [email protected] Prof. LUC LEMAIRE (1999–2002) 9-25 July Department of Mathematics EMS Summer School at St Petersburg (Russia) Université Libre de Bruxelles Title: Asymptotic combinatorics with applications to mathematical physics C.P. 218 – Campus Plaine Organiser: Anatoly Vershik, e-mail: [email protected] Bld du Triomphe B-1050 Bruxelles, Belgium 15 August e-mail: [email protected] Deadline for proposals for 2003, 2004 and 2005 EMS Summer Schools Prof. BODIL BRANNER (2001–2004) Contact: Renzo Piccinini, e-mail: [email protected] Department of Mathematics Deadline for submission of material for the September issue of the EMS Newsletter Technical University of Denmark Contact: Robin Wilson, e-mail: [email protected] Building 303 19-31 August DK-2800 Kgs. Lyngby, Denmark EMS Summer School at Prague (Czech Republic) e-mail: [email protected] Title: Simulation of fluid and structure interaction SECRETARY (1999–2002) Organiser: Miloslav Feistauer, e-mail: [email protected] Prof. DAVID BRANNAN Department of Pure Mathematics 24-30 August The Open University EMS lectures in Malta, as part of the 10th International Meeting of European Women in Walton Hall Mathematics Milton Keynes MK7 6AA, UK Lecturer: Michèle Vergne (Ecole Polytechnique, Palaiseau, France) e-mail: [email protected] Title: Convex polytopes TREASURER (1999–2002) Contact: Dr. Tsou Sheung Tsun, e-mail: [email protected] Prof. OLLI MARTIO 1-2 September Department of Mathematics EMS Executive Committee meeting, Berlin (Germany) P.O. Box 4 3-6 September FIN-00014 University of Helsinki Finland 1st EMS-SIAM conference, Berlin (Germany) e-mail: [email protected] Organiser: Peter Deuflhard, e-mail: [email protected] ORDINARY MEMBERS 15 November Prof. VICTOR BUCHSTABER (2001–2004) Deadline for submission of material for the December issue of the EMS Newsletter Department of Mathematics and Mechanics Contact: Robin Wilson, e-mail: [email protected] Moscow State University 19-21 November 119899 Moscow, Russia EMS lectures at Università degli Studi, Tor Vergata, Rome (Italy) e-mail: [email protected] Lecturer: Michèle Vergne (Ecole Polytechnique, Palaiseau, France) Prof. DOINA CIORANESCU (1999–2002) Laboratoire d’Analyse Numérique Title: Convex Polytopes Université Paris VI Contact: Prof. Maria Welleda Baldoni, e-mail:[email protected] 4 Place Jussieu 22-23 November 75252 Paris Cedex 05, France Fifth Diderot Mathematical Forum e-mail: [email protected] Title: Mathematics and Telecommunications Prof. RENZO PICCININI (1999–2002) Venues: Eindhoven (Netherlands) Helsinki (Finland) and Lausanne (Switzerland) Dipartimento di Matematica e Applicazioni Contact: Jean-Pierre Bourgignon, e-mail: [email protected] Università di Milano-Bicocca Via Bicocca degli Arcimboldi, 8 20126 Milano, Italy 2002 e-mail: [email protected] 9-10 February Prof. MARTA SANZ-SOLÉ (1997–2000) Executive Committee Meeting in Brussels, at the invitation of the Belgian Facultat de Matematiques Mathematical Society and the Université Libre de Bruxelles Universitat de Barcelona 24 February-1 March Gran Via 585 EMS Summer School in Eilat (Israel) E-08007 Barcelona, Spain Title: Algebraic Geometry, Computations and Applications e-mail: [email protected] Contact: Mina Teicher, e-mail: [email protected] Prof. MINA TEICHER (2001–2004) 1 March Department of Mathematics and Computer Deadline for Proposals for 2003 EMS Lectures. Science Bar-Ilan University Contact: David Brannan, e-mail: [email protected] Ramat-Gan 52900, Israel 31 May e-mail: [email protected] Executive Committee meeting in Oslo (Norway) EMS SECRETARIAT 1-2 June Ms. T. MÄKELÄINEN EMS Council Meeting, Oslo Department of Mathematics 3-8 June P.O. Box 4 Abel Bicentennial Conference, Oslo. FIN-00014 University of Helsinki Finland tel: (+358)-9-1912-2883 2004 fax: (+358)-9-1912-3213 25-27 June telex: 124690 EMS Council Meeting, Stockholm (Sweden) e-mail: [email protected] 27 June - 2 July website: http://www.emis.de 4th European Congress of Mathematicians (4ecm), Stockholm (Sweden) 2 EMS June 2001 EDITORIAL possible outcome of a reform that has been imposed from above without consultation with the academic disciplines. Indeed, the picture could be even bleaker: the ominous EditorialEditorial phrase ‘a European dimension to quality assurance’ conjures up a vision of philistine David Salinger bureaucratic control, and maybe the impo- sition of a common curriculum. The Bologna Declaration: a Bachelor’s degree for all To be fair, the Bologna Declaration declares specifically that it is aiming for convergence, not uniformity, and the evi- On 19 June 1999, 29 European Education dence so far is that each country is inter- Ministers signed a document that has preting the Declaration in its own way. become known as the Bologna Declaration. One of the strengths of European Higher Education is its diversity and its ability to What did they sign up to? generate and inspire outstanding teachers, The Declaration envisages the creation of a students and researchers. It would be fool- ‘European Higher Education Zone’, in ish to throw that away. order to improve the employability and Without falling into the trap of impos- mobility of European citizens and to ing its own uniformity, the European increase the international competitiveness Mathematical Society would like to know of Higher Education in Europe. This is to whether sufficient consensus exists within be achieved by: the mathematical community for the • the adoption of a common framework Society to draw up a position paper on the for comparable degrees, and the pre- basis of which to try to influence the way scribing of a transcript known as the thing develop. ‘Diploma Supplement’; Obvious questions are: • a measure of standardisation of degree • 3 or 4 years for a Bachelor degree? lengths: a first degree should be no • is a degree in mathematics already suf- shorter than 3 years and ‘relevant to the introducing the new system while continu- ficiently ‘relevant to the labour market’? European labour market as an appro- ing with the old pattern, and several coun- • should there be an informal common priate qualification’; tries have essentially repackaged the old idea of what is done in the first year, or • this first degree should be the passport system as a ‘Bachelor + Master’ degree. two, of a mathematics degree? to any higher degree (Masters or The majority view seems to be that a Doctorate), which would last from two to Bachelor degree should normally take 3 I hope that you think this issue is suffi- five years; years (or 180 ECTS credits); however, ciently important to contribute to a debate • a credit system, such as European there is allowance for Bachelor degrees in the EMS Newsletter, in your National Credit Transfer System (ECTS), also taking 4 years (or 240 credits), as is the Society, or within the EMS itself. covering lifelong learning; case in Scotland and Ireland: it is possible The text of the Bologna Declaration is • a European dimension in quality assur- that the 4-year course known as the MMath available at www.qaa.ac.uk/crntwork/nqf/bmb/ ance; in England and Wales would also come bologna%2Dtextonly.htm and a report on • the elimination of any remaining obsta- into this category. progress in implementing the Declaration cles to the mobility of students and may be found at www.oph.fi/publications/ teachers. What are the implications for mathematics trends2 The countries involved should introduce degrees? the necessary changes by 2010. Certainly, less can be done in a shorter David Salinger teaches in the School of Many of the signatories have now time-frame. If this is coupled with the Mathematics, University of Leeds, UK, and is brought forward proposals to bring their requirement to make degrees more rele- the Publicity Officer of the EMS. systems of Higher Education in line with vant to the labour market, a very bleak pic- the Declaration. In several countries ture could be painted: a downgraded first where the first degree has usually taken degree, in which applications are taught more than four years to complete (for without their theoretical underpinnings; CALL FOR example, in Germany, Spain, the comparatively few students continuing to PROPOSALS: Netherlands and Denmark), this could higher degrees; a decrease in mathematics mean a drastic change. However, positions in universities. SUMMER SCHOOLS Germany has taken the unusual step of To my mind this is one (but only one) The European Mathematical Society intends to make an application to the European Union with the aim of financ- ing nine Summer Schools for the years JEMS 2003, 2004 and 2005. The topics must Canadian be of interest to a relatively large audi- (Journal ence of young Ph.D. students in Pure Mathematical of the and Applied Mathematics. Please send European Mathematical Society) your proposal to the Chairman of the EMS Summer School Committee: Prof. Society The latest issue of JEMS (Vol. 3, No. Renzo Piccinini, Dipartimento di 2) contains: Matematica e Applicazioni, Università A reciprocity agreement has been N. Gamara, The CR Yamabe conjec- di Milano-Bicocca, Via Bicocca degli signed between EMS and the Canadian ture: the case n = 1 Arcimboldi, 8, 20126 Milano, ITALY Mathematical Society (Société mathé- G. Bouchitté and G. Buttazzo, Deadline for submitting proposals: matique du Canada). This continues a Characterization of the optimal shapes 15 August 2001. growing list of such reciprocal agree- and masses through Monge-Kontorovich For more information, please con- ments, which already includes the equation tact the EMS office (c/o Tuulikki American Mathematical Society and the T. Fisher, Some examples of 5 and 7 Makelainen, at [email protected]. Australian Mathematical Society. descent for elliptic curves over Q fi). EMS June 2001 3 EMS NEWS AppliedApplied MathematicsMathematics inin ourour ChangingChanging WWorldorld September 2-6, 2001 Berlin, Germany First SIAM-EMS Conference

ORGANIZED BY: EMS, SIAM and ZIB

CHAIRS: R. Jeltsch, G. Strang and P. Deuflhard

INTERNET: http://www.zib.de/amcw01 E-MAIL: [email protected]

PROGRAMME COMMITTEE Vincenzo Capasso, Milano, Italy Peter Deuflhard, Berlin (chair) Heinz Engl, Linz, Austria Björn Engquist, Stockholm, Sweden David Levermore, Maryland, USA It is a pleasure to write about the Volker Mehrmann, Berlin cooperation between SIAM and the Bill Morton, Oxford, UK European Mathematical Society. A Stefan Müller, Leipzig, Germany special (and very substantial) joint conference comes this year to Berlin: INVITED PLENARY SPEAKERS September 2-6 at the ZIB Institute Medicine: Alfio Quarteroni, I / CH (Konrad-Zuse-Zentrum). The list of invited speakers – on a really wide Biotechnology: Michael Waterman, USA range of applied mathematics – is Materials Science: Jon Chapman, UK really impressive. Environmental Science: Andrew Majda, USA May I ask you to look at Nanoscale Technology: Michael Griebel, D www.zib.de/amcw01 for the details of Communication: Martin Grötschel, D the conference. The date for submis- Traffic: Kai Nagel, CH sion of abstracts and posters (30 Market and Finance: Benoit Mandelbrot, June) is still ahead. The title of the USA conference is also the title of this Speech / Image Recognition: Pietro Perona, note to you – this is not a conference USA to miss. Engineering Design: Thomas Y. Hou, USA Just a word about the genesis of the Peter Deuflhard conference. I very much want SIAM CONFERENCE OFFICE to help applied mathematicians There will be invited talks, minisymposia, con- world-wide. It is not an American SIAM/EMS Conference 2001 Erlinda C. Körnig Sigrid Wacker tributed talks and posters. Please consult our society (the ‘A’ in SIAM is for website for registration, accommodation infor- Konrad-Zuse-Zentrum Berlin (ZIB) Applied!) and nearly 40% of our mation and submission guidelines. The confer- members live and work outside the Takustr. 7 ence office prefers on-line registration and on- US. I think an important feature is D-14195 Berlin-Dahlem line submission of abstracts. its non-exclusiveness, mathematically Germany and in every way. Activity Groups INTERNET: http://www.zib.de/amcw01 were recently established in E-MAIL: [email protected] TOPICS Computational Science and 1. Medicine Engineering, Mathematics of the Life DEADLINES medical imaging methods; Sciences, and Imaging Science. The computational assistence of surgery, whole society welcomed our efforts to June 30 Deadline for submission of abstracts and posters therapy planning; serve our members and all of applied hospital information systems; July 30 Programme and collected mathematics in Europe, and this pharmacokinetics, tumor growth model- abstracts Berlin conference is a major step. ling; The conference began from conver- artificial organs, immune system model- sations with Peter Deuflhard, who ling; offered the excellent facilities of ZIB REGISTRATION FEES infectuous disease control, in Berlin. Peter has chaired the SIAM / EMS Non- epidemic spreading; whole effort admirably. Rolf Jeltsch Members Members physiology (e.g. dynamics of cardiovascu- picked up the idea and proposed a Early Registration (prior to 04/01/01) lar or of respiratory system). joint conference with the EMS – bril- US$150,— US$200,— liant! Our scientific committee and 2. Biotechnology all our plans have been the result of DM300,— DM400,— EUR150,— EUR200,— biomolecular structural storage schemes, excellent collaboration, and we all patent recognition and circumvention; Full Registration (after 03/31/01) want to continue. conformational molecular dynamics, drug This is something good for our sub- US$210,— US$260,— design, cell factory; ject and also for our own research. I DM420,— DM520,— mathematical modelling in biopolymer- am very happy to have the chance to EUR210,— EUR260,— ization; write about it, and to attend it! sequence alignment, fuzzy reasoning; Meals and accommodation expenses are density functional theory, ab-initio com- Gilbert Strang [[email protected]] is not covered. putation. Professor of Mathematics at MIT 4 EMS June 2001 EMS NEWS

3. Materials science 7. Traffic multiscale analysis and algorithms, realistic modelling and simulation of optimal periodic train scheduling, net- multigrid and domain decomposition, composite materials, magnetic mate- work planning; wavelets, rial, polymers, glass, and paper; schedule synchronization; turbulence modelling. crack propagation and further failure discrete and continuous traffic flow mechanisms; models; Applicants for financial support to attend the 1st phase transitions, crystal growth, traffic on-line simulation and control, EMS-SIAM Conference, Applied Mathematics in superconductivity, and hysteresis; route guidance and planning; our Changing World control of phase transitions and solidi- traffic assignment EU will support the 1st EMS-SIAM conference fication, modelling of ironmaking with 44,000 euro to give grants to young process; 8. Market and finance researchers from EU and associated states. EMS coupling of atomistic and continuum financial mathematics and statistics; is paying 3000 euro for those from Eastern models, quantum-classical approxi- option pricing; Europe who do not belong to associated states. mation and calculation. derivative trading, risk management; Please distribute this information as widely as pos- economic time series. sible. 4. Environmental science Complete information on the conference is given climate and climate impact research, 9. Speech and image recognition on the website stochastic climate modelling, interme- signal analysis; http://www.zib.de/amcw01/ diate complexity modelling; pattern recognition. Here are the requirements a young researcher has short and medium range meteorology to submit to be considered. and oceanography; 10. Engineering design pollution transport in air, water, and transport systems in air, in water, or As mentioned in our website, we need the follow- soil; on land; ing requirements in order to process your appli- atmospheric chemistry, ozone hole; energy conversion, distribution and cation for financial support: computational hydrology. conservation; 1. Short curriculum vitae smart design of consumer products. 2. Letter/s of recommendation from Dean or 5. Nanoscale technology department head integrated optics, optical networks; MATHEMATICAL SUBJECTS 3. List of publications quantum electronics and optics, gen- PDE analysis and modelling, 4. Letter of application stating the reasons for eral microwave technology; complex coupled PDE systems, attending the conference, with reference to study nanoscale techniques in medicine, optimal control of PDEs and heteroge- and research fields porous materials. nous systems, 5. Type and title of conference contribution, with variational principles, an abstract not exceeding 75 words. 6. Communication inverse problems, Applications will be reviewed by the Organising telecommunication and optical net- stability and bifurcation analysis, Committee. Funds may then be available from works: analysis, simulation, opti- PDE computational finite element the German Scientific Foundation, from the mization; methods, European Commission and from the European transmission rate optimization; spatial and temporal homogenization, Mathematical Society. However, full financial survivable networks, network design; spatial statistics, support cannot be guaranteed. frequency assignment, channel alloca- stochastic geometry, You can send the above requirements to the tion, load balancing. interacting particle systems, Conference Office: fax: +49 (30) 841 85-107. stochastic analysis, Deadline for submission is 30 June 2001.

EMS June 2001 5 EMS NEWS ExecutiveExecutive CommitteeCommittee meetingmeeting Kaiserslautern (Germany), 10-11 March 2001 David Brannan

The agenda of the EC meeting had been separate the way that corporate and indi- e-mailed in advance to the chairs of the vidual members are expelled. For exam- EMS committees, seeking their comments ple, would it be possible to consider a non- and input; this will be standard practice in paying individual member as having future. resigned? Two years’ non-payment was suggested as being the maximum allow- Present: Rolf Jeltsch (President, in the able. Article 7.2 states that members of the Chair), David Brannan, Bodil Branner, Executive Committee shall be elected for a Doina Cioranescu, Luc Lemaire, Olli period of 4 years, but that consecutive ser- Martio, Renzo Piccinini, Marta Sanz-Sole vice shall not exceed 8 years. This was dis- and Mina Teicher; (by invitation) Carles cussed, together with the question of the Casacuberta, Tuulikki Makelainen and period of service of a President, whether David Salinger; and (by invitation to a the Society should have a President Elect, portion of the meeting) Ari Laptev and and whether there should be slots on the Bernd Wegner. Apologies were received EC for a President Elect and Past from Victor Buchstaber and Robin Wilson. President. Rules 15 and 16 in the By-Laws The President thanked the Institute for concerning the President were discussed. Industrial Mathematics (ITWM = Institut It was agreed that the rule that the für Techno- und Wirtschafts Mathematik) President must be a delegate should be in Kaiserslautern for its hospitality. Ari Laptev and Tuulikki Mäkeläinen deleted. In Rule 27, it was agreed that the fee of a reciprocity member’s individual Officers’ Reports Membership membership should be 2y. The President reported that he had recent- Based on the editorial of Anatoly Vershik The composition of the next Executive ly sent letters to committee members in the December 2000 issue of the EMS Committee was discussed. It was thought whose terms of office had come to an end, Newsletter, the committee discussed ways to that the President needs to be someone to the Newsletter team, and to all EMS indi- improve cooperation with corporate mem- with considerable time and energy, the vidual and corporate members. He had bers from Central and Eastern Europe. ability and funds to travel widely, the sup- also been informed of a new publisher, The EC also discussed ways to promote port of their own institution, and funds for European Science Publisher, with R. individual membership: it wished it to be various expenses; and that the President Stumpe and H. Schwer in charge. He and made easy to join the EMS. It decided to and Secretary should normally come from about 800 others had attended the GAMM ask its corporate member societies to give different countries. Annual Meeting in Zürich on 12-15 appropriate information on the EMS to February. The President had received an their members, especially to young per- 4th European Congress of invitation to attend the Jürgen Moser sons; to encourage their members to sub- Mathematicians, 4ecm memorial conference in Leipzig on 30 scribe to both the national society and the The dates 27 June-2 July 2004 were fixed. May-3 June. EMS at the same time; to encourage mem- The associated Council meeting will be The Treasurer reported briefly on the ber societies and individual members to held from Friday 25 June to Saturday 26 Society’s financial statement for the year pay the EMS dues of some young mathe- June. 2000. He noted that the variation in the maticians; and to encourage member soci- It was agreed to draft a Letter of income from dues is mostly due to fluctu- eties to mention that they are members of Understanding between the EMS and the ations in the patterns in which the corpo- the EMS on their home pages and newslet- 4ecm organisers. The EC was assured of rate members send the fees they have col- ters. the safe financing of the Congress, and a lected; that individual membership of the Although the EMS has a membership draft budget would be prepared for the Society is slowly rising; that various insti- application form on the EMIS web site, the Berlin EMS EC meeting. tutions help out the EMS by subsidising EMS prefers that individual members The EMS EC congratulated Ari Laptev the travel costs of attendance at EC meet- should join the EMS via their national for the financial contributions acquired, ings; that the annual cost to individual mathematical society; this avoids any and for a very innovative outline pro- members of an EMS subscription is potential clash of interest with a national gramme. Selection of the speakers would approximately equal to the annual cost of society, and avoids the need for the EMS to take place in Spring or Autumn 2002, or producing and mailing the four issues of pay prohibitive bank charges. The Spring 2003; the early selection of plenary the Newsletter to that member; and that Administrator pointed out that EMS mem- speakers was considered important; pro- income from advertising in the Newsletter bers can now pay by credit card. posals will be asked for suggestions for had risen considerably. The year 2000 speakers from corporate members. The was the first year the Society had made a Council Meeting in 2002 4ecm organisers had suggested that some deficit, mostly due to costs related to the The Council meeting will be held on 1-2 network meetings could be held in Council meeting and the Congress 3ecm in June 2002 in Oslo, with the first session Stockholm in 2004, and that other groups Barcelona. starting at 10 a.m. on 1 June 2002. An should be able to be invited as mini-sym- announcement would be made in the posia. Having poster sessions was recom- Electronic Votes March 2001 Newsletter. mended to the organisers, because fund- Since the previous EC meeting in London, The Working Group formed to suggest ing for attendance often requires partici- the following decisions had been taken by changes needed to the Statutes (David pants to present a poster as a minimum electronic voting: to approve the proposed Brannan, Olli Martio, Andrzej Pelczar and requirement. Statutes for the European Mathematics Mina Teicher) presented its draft, and sev- The composition of the Prize Committee Foundation [EMF]; and to add the Institut eral items were discussed. Among them: for 4ecm was discussed, and also rules for Henri Poincaré (IHP), Centre Emil Borel, Article 3.4 states that the expulsion of a the operation, conduct and operational and the Emmy Noether Research Institute member shall be by a decision of the timing of the Prize Committee. It was for Mathematics to the membership of Council; the item is formulated in more recalled that the Felix Klein Prize is paid ERCOM. detail in By-Law I.6. The EC wished to by the IUTWM Frauenhofer Institute and 6 EMS June 2001 EMS NEWS has its own rules of conduct for its prize other applied societies. Mathematics in Malta. committee. The objective was to find out what is There was a discussion of possible names expected from the EMS, how to make for the EMS Lecturer in 2002. The EU applied mathematicians feel more at home There was a lengthy discussion of the EU’s in the EMS, how best to represent the Publications Sixth Framework Programme, which starts applied field in Brussels, and the role of Carles Casacuberta was re-elected in 2003. (Further information about the applied mathematics in curricula. Publications officer for the years 2001- Framework can be found on the website Mark Roberts was elected chair of the 2002, and Chair of the Publications http://www.cordis.lu/improving/call/acm_2000 Committee for Developing Countries for the Committee. The membership of the 02.htm). The EC felt that the present draft years 2001-2004. Publications Committee will thus com- of the Sixth Framework Programme On the recommendation of the chair of prise: Carles Casacuberta (Chair); Publicity seemed to favour big projects over a long the Education Committee, its membership officer, David Salinger; JEMS Editor-in- period of time, a scheme ill suited for was agreed as follows: Tony Gardiner Chief, Jürgen Jost; Newsletter Editor, Robin mathematics. The EMS suggestion of (University of Birmingham, UK) in the Wilson; Chair of Electronic Publishing ‘return home fellowships’ for Marie Curie chair, Willi Dörfler (University of Committee, Bernd Wegner; Managing Fellows was included in the present draft; Klagenfurt, Austria), Sava Grozdev Director of EMSPh, Thomas Hintermann. also, there is a possibility of inviting (Bulgarian Academy of Sciences), Rudolf It was reported that four books are in Fellows from ‘other countries’, meaning Straesser (University of Bielefeld, preparation in the EMS Springer series, apparently any country, which is what EMS Germany), Eva Vasahelyi (Eötvös-Lorand one coming out this year. An advertise- had always asked for. The old ‘Networks’ University, Hungary), Abraham Arcavi ment for JEMS had been e-mailed to all and all forms of ‘Euroconferences’ appear (Weizmann Institute, Israel), Gerd EMS corporate members. to have vanished from funding opportuni- Brandell (Univiversity of Lulea, Sweden) There was an interesting discussion ties. and Olli Martio (Helsinki). Vinicio Villani about a possible recommendation of infor- The EC decided to send in the EMS (University of Pisa, Italy) had agreed to mation on the first page of papers in math- comments again, and to try to influence a remain a member in the short term to give ematical journals. A proposal considered change in EU policy through the organisa- advice, etc. The TOME contract had been suggested that journals should present on tion ‘Euroscience’. The Executive signed, and a Group of Experts would now the first page of each article: title of jour- Committee thanked Luc Lemaire for the be appointed by the Education nal (and/or common abbreviation); vol- valuable work he had done for the EMS in Committee. ume/issue number; ISSN; URL/DOI/other this area There was an interesting discussion con- identifier of the journal; other common The EMS is a scientific advisor to the cerning a joint declaration of the bibliographic information specific to this extension of the EULER Project; more European Ministers of Education, who had journal/issue; publication year or other information on this can be found on the convened in Bologna on 19 June 1999; a date of publication; copyright date (if dif- EMIS/EULER web site. The Reference follow-up meeting will be held in Prague in ferent from above); URL/DOI/other iden- Levels project would hold a final meeting 2001. As a result of the ‘Bologna tifier of the article if available; author(s) on 11-12 May 2001 in Luxembourg. The Declaration’, Swiss universities have made names, spelled out full first name(s); affili- EMS is also a partner in the LIMES project guidelines to change their degrees to con- ation(s); title; page range; primary MSC (Large Infrastructure in Mathematics - form to the Bachelor’s and Master’s classification(s); secondary MSC classifica- Enhanced Services), where FIZ is the main degrees. It was felt that the EMS should tion(s); English keywords; abstract. The contractor; the EMS represents the users form a view on the Declaration. (Relevant EC supported concerted action on such of Zentralblatt; the next meeting of the information can be found on the web sites: uniformisation, and the matter was LIMES partners would be in April in www.qaa.ac.uk/crntwork/nqf/bmb referred to LIMES. Copenhagen. /bologna%2Dtextonly.htm and http://www. On the recommendation of the Raising unige.ch/cre/activities/) Public Awareness of Mathematics Committee, EMS Committees EC approved three prizes of 200, 150 and For readers’ information, the Chairs and Special Events 100 euros for an EMS-competition for the their terms of office are as follows: The Fifth Diderot Mathematical Forum, best article on mathematics for a general Applied Mathematics: H. Engl (1998-2001); on Telecommunications, will take place on audience. The RPA Committee will act as Database Committee: L. Guillopé (2001- 22-23 November 2001 in Eindhoven the jury for the competition. 2004); (Netherlands), Helsinki (Finland) and Developing Countries: C. Lobry (1999- Lausanne (Switzerland). European Mathematics Foundation 2002); [EMF] and EMS Publishing House Education: Tony Gardiner (2001-2004); Summer Schools [EMSph] Electronic Publishing: Bernd Wegner (2001- Impressive posters for the St Petersburg The final Statutes of EMF were approved 2004); Summer School have been prepared by by an e-mail vote of the EC. ERCOM: O. Barndorff-Nielsen (1999- David Salinger. The AMS and NSF have A further meeting of EMSPh had been 2002); given support to some US participants. held on 9 March; the Managing Director The Group on Relations with European The Prague Summer School had received would start work on 1 September 2001. Institutions: R. Jeltsch (1999-2002); financing from the European Science The logo for the EMF will be the EMS logo Publications: Carles Casacuberta (1998- Foundation as an AMIF grant; its web page with different letters. The EC extended its 2001); was ready, and the poster had been print- thanks to Rolf Jeltsch for his work for the Raising Public Awareness of Mathematics: ed. Foundation and Publishing House. Vagn Lunsgaard Hansen (2001-2004); A Summer School in Fluid Mechanics is Special Events: J.-P. Bourguignon (1999- planned to be held in Romania in July Zentralblatt für Mathematik 2002); 2002. The other Summer School for 2002 There was a discussion of the business of Summer Schools: R. Piccinini (2000-2003); will be held in Eilat (Israel) during the last Zbl, a venture jointly owned by the four Support of East European Mathematicians: H. week of February. bodies represented on the Consultative Zieschang (1998-2001); The deadline for submission applica- Committee: Springer-Verlag, the Women and Mathematics: E. Mezzetti (2000- tions for summer schools in 2003 was Heidelberg Academy, FIZ and EMS. 2003). moved to 15 August 2001. France supports Zbl via its editorial unit in The EMS would be holding a workshop The EC decided to grant up to 2000 France. on Applied Mathematics in Europe on 4-6 euro to enable Eastern European mathe- May 2001 in Berlingen, Switzerland. The maticians to attend the EMS lectures by Relations with Mathematical Institutions, President had sent out invitations to the Professor Michele Vergne during the 10th Organisations and Consortia EMS corporate members and to several Meeting of the European Women in The EULER (European Libraries and EMS June 2001 7 EMS NEWS Electronic Resources in Mathematical Sciences) project had finished in The Institute for Industrial Mathematics December 2000, and is being continued (Institut für Techno- und Wirtschaftsmathematik, ITWM) until December 2001; the EMS is a partner in this. A further continuation from The Institute for Industrial Mathematics ing to adapt theorems and algorithms to January 2002 is probable, and it was dis- (Institut für Techno- und practical models, and to find practicable cussed whether the EMS should be a part- Wirtschaftsmathematik, ITWM) was found- solutions which often differ from optimal ner in this further extension of the project. ed in 1995 by members of the research ones. Here, the classical disciplines of IWI (Institut für Wissenschaftliche groups on Technomathematics and applied mathematics, such as numerics, Information, Institute for Scientific Economathematics at the University of differential equations, stochastics and opti- Information) had a founding meeting on 13 Kaiserlautern (Germany). From the begin- misation, represent ITWM’s basic compe- November 2000 in Osnabrück, at which ning, it was managed by the Fraunhofer- tence. Also, there are other fields of theo- Rolf Jeltsch had represented the EMS; Gesellschaft, striving for integration. After ry that have turned out to be mostly math- MPRESS (Mathematical PREprint Server a successful evaluation in 1999, the ITWM ematically oriented domains between System) was defined as its main activity in became a member of the Fraunhofer- mathematics and technology, such as fluid the IWI statutes. MPRESS will be man- Gesellschaft from the beginning of 2001. dynamics, image processing, neural net- aged from Osnabrück by IWI; it was It is the first Fraunhofer institute with a works, inverse problems, SPH, system and agreed that the EMS should join IWI as a mathematical focus. control theory, queueing theory, fluid- member. The Fraunhofer-Gesellschaft is the structure interactions and facility location Olli Martio was elected to represent the leading organization for institutes of planning. Since its foundation, the ITWM EMS on the Committee for the Banach applied research in Germany, undertaking has carried out more than 200 different International Center in Warsaw for 2001- contract research on behalf of industry, the projects on the basis of these competences, 2004. service sector and the government. regarding its central departments: The theme of the First SIAM-EMS Commissioned by customers in industry, it • virtual material and product design; Conference on 2-6 September 2001 in provides rapid, economical and immedi- • simulation and optimisation of technical Berlin will be Applied Mathematics in our ately applicable solutions to technical and and logistics processes; Changing World. organisational problems. • systems of diagnosis in quality and It was reported that the agreement with Within the framework of the European process control and in medicine. the Canadian Mathematical Society had now Union’s technology programs, the The product range includes software been signed. Fraunhofer-Gesellschaft is actively developed on the basis of our know-how, The American Mathematical Society allows involved in industrial consortia that seek consulting, support, and system solutions. its reciprocity member societies to nomi- technical solutions to improve the compet- At the ITWM, simulation software is both nate four individuals for free membership, itiveness of European industry; the used and developed, often in cooperation three of whom must be students. It was Fraunhofer-Gesellschaft also assumes a with leading software enterprises. agreed that the President should select the major role in strategic research. The cooperation partners of the ITWM persons for free AMS membership. Commissioned and funded by Federal and are companies from very different branch- Länder ministries and governments, the es, such as the automobile and aeronauti- Relations with Funding Organisations organisation undertakes future-oriented cal industry, classical engineering, elec- and Political Bodies research projects that contribute to the tronics, and the whole range of textile A grant had been received from UNESCO- development of innovations in key tech- industry. Other partners are service Roste; this had been partly used to cover nologies and spheres of major public con- providers, such as the German Railway and some costs of the Alhambra 2000 meeting cern. The creation of images of the real Lufthansa, research institutes, and institu- and those of the St Flour EMS summer world in the virtual world of models and tions of the social system. school. software, and their application for the Today, the ITWM is the spearhead of The list of EURESCO Conferences in solution of problems, is of central impor- mathematics in industry, and it intends to 2001 in Mathematics was discussed; it was tance today and refers to all fields of indus- strengthen and enlarge this position. felt that it would be good to start a series in try, from space technology to textile indus- Currently, about 80 full-time scientists and biology or medicine if a suitable person to try. PhD students (mainly mathematicians and take responsibility for it could be identi- Mathematics is the technology required physicists) work at the ITWM, with 50 part- fied. for the creation of these images and their time employees. The annual income efficient implementation into software, (2000) amounted to almost 10 million DM Publicity and is the raw material for the models and (5.1M €). Nearly 75 per cent of the annual The Publicity Officer reported that an the basis of each computer simulation. In turnover results from projects placed by application form for EMS individual mem- this context, the main objective of the industry or public funding. The head of bership had been inserted in the ITWM is to develop real applications of the institute is Professor Dieter Prätzel- December issue of the Newsletter. Forms mathematics by using methods of mathe- Wolters, who in Summer 1999 replaced its were also available at the GAMM meeting matical modelling and scientific comput- founder, Prof. Helmut Neunzert. in Zürich; the EMS had shared a booth with Zentralblatt at the GAMM meeting. The EMS will have a booth at the EMS- SIAM meeting in Berlin in September 2001.

Future meetings There will be an EC meeting during the EMS-SIAM Conference in Berlin on 1-2 September. The Spring 2002 meeting will be held in Brussels on 9-10 February; and the Summer 2002 meeting will be in Oslo before the Council on Friday 31 May 2002.

And finally … The EC members expressed their appreci- ation to Rolf Jeltsch for his effective and cheerful management of the meeting. The Executive Committee meeting (Kaiserslautern) was held at the ITWM 8 EMS June 2001 WORKSHOP WWorkshoporkshop onon AppliedApplied MathematicsMathematics inin EurEuropeope Berlingen (Switzerland), 4-6 May 2001 Sebastià Xambó-Descamps

This workshop can be seen as the first major initiative by the European Mathematical Society (EMS) in addressing the problem of making sure that ‘applied mathematicians can feel that the Society is also their home’. The main result of the workshop was the Berlingen declaration, which was agreed upon and signed by all participants. It consists of the following nine points:

1. The presence of applied mathematics in EMS bodies and policy decision making should be significantly increased. 2. The applied mathematics committee must be kept an active body for the time being. Its mission statement should be adapted to the new role of the commit- tee. The chair should be invited to the Executive Committee meetings. 3. Pure and applied mathematics should be equitably represented in the publica- tions of the EMS. 4. Special interest groups should be creat- ed gradually. 5. EMS should consider increasing its Trevor Stuart, Mina Teicher, Jef Teugels, • five national societies: Belgian activities by collaborating with interna- Jean-Philippe Vial, Sebastià Xambo- Statistical Society, Danish Operations tional, national and regional societies in Descamps and Anatoly Yagola, at Research, Finnish Inverse Problems organising meetings. Berlingen, Sunday 6 May 2001. Society, Italian Association of 6. The EMS should further develop its Mathematics Applied to Economic and Summer School Programme. It is noted The workshop was meant to be a ‘brain- Social Sciencies, SIMAI (Society of with satisfaction that the existing pro- storming week-end’, which should ‘ini- Industrial and Applied Mathematics in gramme includes topics in both pure tialise a positive discussion’, hopefully to Italy); and applied mathematics. be ‘followed up during the EMS-SIAM • four applied mathematics members of 7. EMS should work towards the goals that meeting in Berlin’ (2-6 September 2001). the EMS: ECMI (European Consortium (a) the students majoring in mathemat- In the view of the reporter, the meeting on Mathematics in Industry), ESMTB ics should be exposed to applications of developed in a positive and constructive (European Society on Mathematics and mathematics in sciences or other areas; manner by all participants and altogether Theoretical Biology), GAMM (b) high school teachers have adequate it was a definite success. (Gesellschaft für Angewandte education in applied mathematics and On arrival at Berlingen it was a pleasant Mathematik und Mechanik), SMAI mathematical modelling. surprise to see that the EMS President, (Société de Mathématiques Appliquées 8. EMS should formulate a position with Rolf Jeltsch, was waiting in front of the et Industrielles); regard to the Bologna declaration of hotel to greet the participants: he had • other member societies: Catalan 1999. received back surgery the previous Friday, Mathematical Society, Hellenic 9. It is noted with satisfaction that the EMS recovery from which needs more than one Mathematical Society, Institute of established a committee to raise public week for most people. Actually he partici- Mathematics and Computer Science of awareness of mathematics. EMS should pated actively in most of the events (and Moldavia, János Bolyai Mathematical promote local initiatives, encourage col- everybody perceived that his back Society, London Mathematical Society, laboration with various organisations, improved steadily as a result of this Mathematical Institute SANU- and collect and disseminate information engagement!), but the person that actually Yugoslavia, Slovenian Mathematical, on initiatives of member societies in this chaired the joint discussions – with great Physical and Astronomical Society, area. skill, I should say – was EMS Vice-presi- Société Mathématique de France, Signed by Saul Abarbanel, Goetz Alefeld, dent Bodil Branner. Society of Romanian Mathematicians. Luis Bonilla, Bodil Branner, Franco Friday afternoon was devoted to short Brezzi, Vincenzo Capasso, Doina presentations of the societies that were After that, and before dinner, the EMS was Cioranescu, Svetlana Cojocaru, Georgias present at the meeting: presented (its structure, activities and self- Dassios, Emilia Di Lorenzo, Heinz Engl, • five international applied mathematics introductions of the members of the Bjorn Engquist, Andras Frank, Constantin societies: Bernoulli Society, ECCOMAS Executive Committee that were present) Gaindric, Mats Gyllenberg, Rolf Jeltsch, (European Community on and a preliminary list of topics to be dis- Allan Larsen, Zoran Markovic, Mireille Computational Methods in Applied cussed in the workshop was written down. Martin-Deschamps, Olavi Nevanlinna, Sciences), ICIAM (International After dinner the EMS presentation contin- Julia Norton, Mihael Perman, Colette Congress on Industrial and Applied ued (4ecm, EMS publishing house, EMS Picard, Renzo Piccinini, Olivier Pironneau, Mathematics), Institute of Mathematical activities at the European Union level), Franz Rendl, Marilena Sibillo, Léopold Statistics, Mathematical Programming and the list of topics was discussed and Simar, Erkki Somersalo, Silvana Stefani, Society; improved. The 4ecm outline, presented by EMS June 2001 9 WORKSHOP / OBITUARIES Björn Engquist, was found to be consistent were discussed on the Sunday morning matical methods. with the spirit of the workshop, and hence and were further modified until everybody The Committee, instead of competing, with the strategy of the EMS, particularly was happy with their phrasing. The long wants to cooperate with other, some- because it devotes an equal amount of time draft, and the previous documents that led times more specialised, societies on the to physics, chemistry and biology, and also to it, will be known and used by the European and international level and because it includes network lectures and Executive Committee, whereas the decla- with applications-oriented member soci- sections. ration was meant to be made public and to eties especially in further improving the On Saturday morning, five topics were be included in this report. public and political awareness about the chosen (structure, publications, scientific The reporter believes that the importance of mathematics to cultural, activities, education, awareness) and each Berlingen declaration will become an economic and social development. participant decided to which he/she would important step in the history of the EMS. like to belong. Since the groups on scien- Being a highly synthetic document, woven In any case, everybody felt that the success tific activities and on education had only on the basis of consensus, it cannot reflect of this committee will result in its becom- two members each, they were merged into the lively and witty discussions that led to ing unnecessary. a single group of four members, so that at it. Here are a few hints, however, on the Consensus on point 8 of the declaration the end only four working groups were spirit of the discussion of some of the key was not easy, for many participants formed. These groups, which worked issues. It was noted, for example, that the thought it should have been considerably independently for the rest of the morning, declaration fits well with the Statutes and tighter on what the EMS stance concerning presented their conclusions in a joint By-Laws of the EMS (cf. Article 2 of the the Bologna declaration should be. The meeting in the afternoon. Each group Statutes, on the purpose and nature of its main difficulty was that some key terms ended with a written statement that took activities). involved in the more comprehensive state- into account the discussion that followed When the ‘Applied Mathematics ments that were discussed did not mean the presentations. These statements were Committee’ was discussed, its present mis- the same in different European countries. combined into a single document draft by sion statement, as approved by the To mention one example: no agreement a subgroup consisting of one or two repre- Executive Committee, was taken into could be reached concerning the number sentatives of each of the four working account, and in particular the following of years that should be required to become groups, plus the members of the Executive points: a ‘professional mathematician’, although it Committee that were present, and finally a The Committee sees its role in promot- seemed to this reporter that a good num- short declaration draft of nine points was ing Applied Mathematics as a whole ber of participants thought that, whatever distilled from it late on Saturday evening. through and within EMS, since applica- its meaning, it should be greater than Both the declaration and the document tions cannot be separated from mathe- three years. OBITUARIES differential equations. In the early 1960s Jacques-Louis Lions he developed a school of numerical analy- John Fauvel (1928-2001) sis in PDEs, using a systematic and rigor- 1947-2001 Michel Bercovier ous variational approach. He also was at the origin of control theory in PDEs and Jacques-Louis Lions died during the night can be credited for the use of Sobolev of 16-17 May in Paris after a long illness. spaces in Engineering. He directed Born in 1928 he graduated from the dozens of ‘Doctorat’ students, who would Ecole Normale Supérieure, Paris, in 1950 also apply these ideas to an analysis of the and received his Doctorat d’Etat in 1954, finite element method. His numerous stu- with Laurent Schwartz as his advisor. He dents have taught around the world, keep- was successively professor at the Université ing in touch with him, giving rise to a new de Nancy, Université de Paris and Ecole French mathematical school headed by Polytechnique, and then held a chair at the him, and exerting a lasting and wide- Collège de France (Emeritus from 1998). spread influence on the international com- munity. He was a member of 20 academies in countries such as the former USSR, US, UK, EC, as well as in the Third World, and a Doctor Honoris Causa of nineteen univer- sities. He won many major prizes and awards, including the Von Neumann prize (1986), the Japan Prize for Science (1991), the Technion’s Harvey prize (1991) and We regret to announce the death of John the Reid’s SIAM prize (1998). Fauvel, Historian of Mathematics, at the His students mourn the passing of a age of 53. A distinguished scholar and pio- great man, a scientific father and friend. neer and promoter of the uses of the histo- He served as the secretary-general of For a short CV see: http://www.college- ry of mathematics in education at all levels, the IMU, and then as its president. He was de-france.fr/college/bibliographies/Lions. he was a man of wide interests, a book- a member of 1’Académie des Sciences, and html lover and collector, an inveterate enthusi- was its president for two years. While A register for condolences has been ast and facilitator, a source of encourage- teaching and carrying on his research he opened at http://acm.emath.fr/amm/cond ment and inspiration to so many, and a was Inria’s president (from 1980-84) and oleances.html (in French) and http://acm. much-loved friend to all. then president of the French space agency emath.fr/amm/condoleances-en.html (in He was a good friend of the EMS (CNES) from 1984-92. In his last years he English). Newsletter, having recently written articles was active in industry, being a board mem- on the Keele University Turner Collection ber or scientific adviser. Michel Bercovier was a doctoral student of (issue 31) and John Napier (issue 38) and His exceptionally prolific work covered Jacques-Louis Lions, and now teaches at the interviewed Jan van Maanen (issue 34) and both analysis and applications in partial Hebrew University of Jerusalem. Bernhard Neumann (issue 39).

10 EMS June 2001 GAMM GAMMGAMM AnnualAnnual ScientificScientific ConferConferenceence 20012001 Zürich (Switzerland), 12-15 February 2001 Rolf Jeltsch

The Gesellschaft für Angewandte Mathematik bilities cannot be avoided. und Mechanik (GAMM) usually holds its The scientific activities started with the annual meeting in a German speaking city. traditional Prandtl lecture, introduced by The previous two conferences took place at J. Szodruch, President of the DGLR Metz in the Alsace (France), and at (Deutsche Gesellschaft für Luft- und Göttingen (Germany). Raumfahrt), and delivered by P. G. Hamel, On 12-15 February 2001, more than Director since 1971 of the Institute of 800 participants accepted an invitation Flight Mechanics at the DLR in from colleagues at the Swiss Federal Braunschweig. He lectured on the model- Institute of Technology (ETH) to visit ling of flight dynamics, stability and con- Zürich. Researchers came from 34 differ- trol – a perfect mix of fluid dynamics, ent countries, including a large group mathematical control and engineering. from Central and Eastern Europe, and At this highly intensive meeting there ETH opened a shelter where participants were more than 600 contributed lectures could stay free of charge. In addition, the on mathematics and mechanics, arranged Swiss National Science Foundation and in 21 sections. There were fourteen ple- P G Hamel, Prandl lecturer ETH gave grants to support participants nary lectures and a dozen mini-symposia from Central and Eastern Europe. focused on new subject areas. As is The event started with a welcoming GAMM’s tradition, one of the plenary lec- party for those registering on Sunday. At tures was a public lecture. This year, the opening ceremony Rolf Jeltsch wel- Werner Stützle, from the University of comed the participants on behalf of the Washington in Seattle, gave an insight into local organising committee, and men- mathematical aspects of three-dimensional tioned that the last Zürich meeting had photography. The main goal is the been held in 1967, organised by the late ‘inverse’ of computer-aided manufactur- Professor Peter Henrici. As President of ing: given a physical object such as a the EMS he announced the forthcoming human body, a model of a car, a turbine 1st EMS-SIAM meeting in Berlin in blade, or a house, create a computer model September and the recent EMS workshop of the object that captures its shape and on Applied Mathematics in Europe in appearance. A special feature of the G Alefeld, GAMM President Berlingen, Switzerland (see report on page Zürich conference was a second public lec- 9). The Vice-President of Research at ture, presented by Marco Avellaneda of the ETH, Albert Waldvogel, welcomed the Courant Institute in New York. He lec- participants on behalf of ETH. In his pre- tured on Monte Carlo simulation in quan- sentation he presented a survey of ETH in titative finance, giving a very lively intro- Zürich, especially the gradually rising duction to this attractive and modern sub- number of students: it is interesting to note ject. that over 25% of the graduate students are Without doubt, the good weather foreign, with about 50% at faculty level. enabled participants to enjoy Zürich and He also discussed the emergence of com- its environs, as well as to experience good putational sciences and engineering and science. how ETH is making an effort to support The next annual GAMM meeting will be this new development. at Augsburg (Germany), from 25-29 March Göetz Alefeld, the President of GAMM, 2002. Herbert Steinrück, von Mises prizewinner opened the conference with remarks on the development of students and the importance of producing IT-educated spe- cialists who also have a background in clas- sical engineering. At its annual meeting, GAMM awards the Richard von Mises prize to a young scientist for exceptional research in applied mathematics and mechanics. This year’s winner was Herbert Steinrück of the Technical University of Vienna, who studied mathematics at the Institute of Technology in Vienna and received the prize for his work in several fields, especially in fluid mechanics where he intensively studied mixed convection on horizontal plates. In particular, he showed that the boundary layer at the upper side of a cooled horizontal plate can move against the flow direction; this implies that the boundary layer equations do not have a unique solution and that numerical insta- Opening ceremony, GAMM 2001 EMS June 2001 11 FEATURE ARTICLE TheThe MethodologyMethodology ofof MathematicsMathematics RONALD BROWN and TIMOTHY PORTER This article is in two parts; the second part will appear in the September 2001 issue.

This article is based on a talk given by the ence between human beings and other first author to students and staff of the animals, that humans have this ability to Departmento de Geometria e Topologia at the reflect on what they do, and that this abil- University of Seville in November 1993. ity affects beneficially a lot of human The issues presented there have been part activity. One aspect of this reflection is of a continued debate and discussion at that it leads to the notion of value judge- Bangor over many years, and this ment, again a faculty which humans have explains why this is a joint paper. which is not apparently shared by other Various versions of this article have been animals, or at least not in a way in which published. [1]. we can communicate, by and large. The aim of the talk, and the reason for Reflection on an activity is, generally, a discussing these topics, was to give stu- useful way of increasing its effectiveness, dents an understanding and a sense of as we are able to analyse what is essential, pride in the aims and achievements of what is important, and how the activity their subject, and so to help them explain can be done avoiding the easiest of mis- these aims and achievements to their takes in method. On these grounds it is friends and relatives. This pride in itself reasonable that we should reflect on the would be expected to contribute to their Ronald Brown activity of mathematics. In reflection, we enjoyment of the subject, whatever their also usually are aware of the value of the own level of achievement. Because of the case of many more of them that this is what activity. this, and because of its origin, the tone of they feel. Another reason for our considering the article is principally that of an address I cannot share this opinion. When I think these questions was through a comparison to students. of the ablest students whom I have encountered with aspects of education in art. We have We do not claim to be alone in address- in teaching – i.e., those who have distinguished heard it argued that education in art and ing these questions. For some years Dr themselves by their independence and judge- design is considerably ahead of science Allan Muir (City University, London) has ment and not only mere agility – I find that education in arousing the interest and organised a How Mathematics works group, they have a lively concern for the theory of independence of students, so it is worth and there is a similar group in the U.S.A. knowledge. They like to start discussions con- considering how these educators go about Many of these issues are discussed in the cerning the aims and methods of the sciences, things. Here are aims that have been books by Davis and Hersh [3, 4]. and showed unequivocally by the obstinacy with given for a course in design: which they defend their views that this subject Some basic issues for mathematicians seemed important to them. 1. To teach students the principles of good We start by seeking discussion by teachers This is not really astonishing. For when I design; of mathematics at all levels as to what turn to science not for some superficial reason 2. To encourage independence and creativity; extent the training of mathematicians such as money-making or ambition, and also 3. To give students a range of practical skills should involve professional discussion of, not (or at least exclusively) for the pleasure of so that they can apply the principles of good and assessment in, possible answers to the sport, the delights of brain-athletics, then design in employment. questions of the following type: the following questions must burningly interest me as a disciple of science: What goal will be Is there something here from which 1. Is mathematics important? If so, for what, reached by the science to which I am dedicating mathematics courses can learn? Is it rea- in what contexts, and why? myself? To what extent are its general results sonable aims for a mathematics course to 2. What is the nature of mathematics, in com- ‘true’? What is essential and what is based replace in the above the word ‘design’ by parison with other subjects? only on the accidents of development?. . . the word ‘mathematics’? If not, why not? 3. What are the objects of study of mathemat- Concepts which have proved useful for order- Here is another quotation, from the ics? ing things easily assume so great an authority book by T. Dantzig [2]: 4. What is the methodology of mathematics, over us, that we forget their terrestrial origin and what is the way it goes about its job? and accept them as unalterable facts. They then This is a book on mathematics: it deals with 5. Is there research going on in mathematics? become labelled as ‘conceptual necessities’, ‘a symbols and form and with the ideas which are If so, how much? What are its broad aims priori situations’, etc. The road of scientific back of the symbol or the form. The author or main aims? What are its most important progress is frequently blocked for long periods holds that our current school curricula, by achievements? How does one go about by such errors. It is therefore not just an idle stripping mathematics of its cultural content doing mathematical research? game to exercise our ability to analyse familiar and leaving a bare skeleton of technicalities, 6. What is good mathematics? concepts, and to demonstrate the conditions on have repelled many a fine mind. It is the aim which their justification and usefulness of this book to restore this cultural content and It may be thought by some that these depend, and the way in which these developed, present the evolution of mathematics as the questions are beside the point, a waste of little by little . . . profoundly human story it is. time, and not what a real mathematician There are a number of reasons, apart should be considering. Against this we from the authority of Einstein, to consid- Is there something in this from the point would like to give a quotation from Albert er the above questions. A professor of of view of a higher level of teaching of Einstein (1916) [5]: mathematics in the UK with whom we dis- mathematics? This book dates from the How does a normally talented research sci- cussed them suggested that the aim of 1930s. Have we made much progress entist come to concern himself with the theory of considering them was to get students to since then in dealing with the points he knowledge? Is there not more valuable work to reflect on the methods of mathematics. raises? be done in his field? I hear this from many of He remarked, as if seeing this for the first Now let us consider the questions (1)- my professional colleagues; or rather, I sense in time, that there was a well known differ- (6) in turn. 12 EMS June 2001 FEATURE ARTICLE What is the importance of mathematics? ing density from views through it of an X- beginnings of the universe, and the flow It is not generally recognised how much ray, where the only measurement is the of time over billions of years, as well as of a part mathematics plays in our daily change of intensity as the ray passes the furthest distances of space. What lives. Some of the mathematics is of through the body, for a large number of could be more enthralling? We have course quite old: every day we use num- varying positions of the ray. some money for this study, with various bers, graphs, addition and multiplication. telescopes over the world, but of course It is easy to forget that the invention of What is the nature of mathematics? not enough. these was at one time a great discovery. There is here a mystery. The Nobel The replacement of Roman numerals by prize-winner E. Wigner has written a The physicist: In physics, we study the fun- Arabic numerals, and so the possibility of famous essay ‘The unreasonable effective- damental constituents of matter. What a good bookkeeping system, is said to ness of mathematics in the natural sci- could be more fascinating? Without have led to the prosperity of Venice in the ences’ [8]. For us, the key word is ‘unrea- physics, there would be no astronomy, for 14th century. It is also of interest here to sonable’. example. Thus many more of the best note the importance of pedantry in math- He is talking about the surprise that students should study physics, and the ematics. A key aspect of the Arabic system the use of mathematics is able to give pre- Government should give us a lot of is its use of the number zero. At first it dictions that are in accord with experi- money. seems absurd to count the number of ment to the extent of nine significant fig- objects in an empty box. The surprise is ures. How is such astonishing accuracy The chemist: In chemistry, we make mole- how essential this is for an adequate possible? cules do things for us, so that chemistry is numeration system, in which the number It seems likely that a full ‘explanation’ part of our everyday lives. Without the 0 is used as a place marker. of the success of mathematics would need understanding found by chemistry, there The lack of this concept of zero held more understanding of language, of psy- would no study of the stars, and no up the progress of mathematics for cen- chology, of the structure of the brain and understanding of biology, of the forma- turies. its action, than is at present conceivable. tion of the planets. So, many of the On a higher level, without the mathe- Even worse, the development of such brightest students should study chemistry, matics of error correcting codes we would understanding might need, indeed must and the Government should give us a lot not have had the beautiful pictures of need, a new kind and type of mathemat- more money. Jupiter from Voyager II [9]. ics. It is still important to analyse the This mathematics is also essential in scope and limitations of mathematics. It The biologist: Biology is about life. What is many aspects of telecommunications and is also reasonable that such an analysis life? How did it come about? How does of computers, and in particular for CD should be a necessary part of the educa- it interact with us and the world? We are players. There is an amusing story about tion and assessment of a student of math- all concerned with life. So, many more this last application [7]. Negotiations ematics. Of what use is a student who students should study biology, and the were held by top management between does not know such things? Government should give us a lot more Sony and the Dutch company Philips Here then are some quotations from money. about the standards for CD. The this article: Japanese considered Philips’ proposal for . . . that the enormous usefulness of mathemat- The engineer: Engineering is about making error correction inferior to theirs, and in ics in the physical sciences is something border- things that control our environment and the end the Japanese proposal was ing on the mysterious, and that there is no do things for us. Without engineering, accepted. Back in Eindhoven, the embar- rational explanation for it. modern civilisation is inconceivable. rassed managers called in their science Mathematics is the science of skilful operations Many more students should study engi- directors to declare that the company did with concepts and rules invented just for this neering, and the Government should give not have sufficient expertise in this area purpose [this purpose being the skilful us a lot more money. called ‘coding theory’ and to find out operation . . . ]. where in Europe the real experts could be The principal emphasis is on the invention of Of course there are many more protago- found. To their dismay, the answer was concepts. nists in this story. Also, we have exagger- ‘in Eindhoven!’, in the person of the The depth of thought which goes into the for- ated the concern with finance. Yet, the Dutch number theorist Van Lint! mation of mathematical concepts is later justi- financing of an activity is one measure of Without the mathematics of cryptogra- fied by the skill with which these concepts are the importance attached to it. phy, there would not be possible the cur- used. Let us turn now to the mathematician, rent level of electronic financial transac- The statement that the laws of nature are writ- and ask for his/her story and justification tions crossing the world, and involving ten in the language of mathematics was prop- for existence in the hustle and struggle billions of dollars. Currently, the mathe- erly made three hundred years ago; [it is attrib- for a place in the scheme of things. It is matics of category theory, a theory of uted to Galileo] it is now more true than ever quite possible that from even a well- mathematical structures, is being used to before. known mathematician you will get no give new insights into future logics and The observation which comes closest to an clear answer. It might be claimed as an algebras for the design of the next gener- explanation for the mathematical concepts’ important achievement that, for example, ation of programs and software. cropping up in physics which I know is the solution has now been obtained of The enormous applications of mathe- Einstein’s statement that the only physical the- Fermat’s last theorem. Does such a solu- matics in engineering, in statistics, in ories which we are willing to accept are the tion, however, bring in the crowds or the physics, are common knowledge. The beautiful ones. It stands to argue that the con- cash? Why should it? Certainly, the solu- theories of the big bang, of fundamental cepts of mathematics, which invite the exercise tion is an achievement, but what is its gen- particles, would not be possible without of so much wit, have the quality of beauty. eral import? Why was so much effort mathematics. It is also imagined that the devoted to it? Is it merely comparable role of mathematics is being taken over by In order to discuss this, it is of interest to with breaking another record? There are the use of supercomputers. compare mathematics with other subjects, answers to these questions, but the ques- It is not so generally realised that these and to link this with the question of the tions seemed not to be asked in the glory supercomputers are the servants of math- objects of study of a subject, and of its of an apparent solution to a long-stand- ematical and conceptual formulations: importance. ing problem. the electronics is marvellous in that it Suppose we ask questions of a few of These questions are not idle. does the calculations so quickly and accu- our fellow scientists as to why one should Resources are limited. Any one person’s rately. For example, body scanners are study their subject. Their answers might interests are limited. We need a more an application, a realisation, of a piece of run as follows: convincing answer for the support of our 19th-century mathematics expressing subject, and to persuade people to study how to reconstruct a solid object of vary- The astronomer: In astronomy we study the it. Here is our try: EMS June 2001 13 FEATURE ARTICLE The mathematician: Mathematics is about and interaction with the world. In this References the study of pattern and structure, and the sense, mathematics has the form of a lan- 1. R. Brown and T. Porter, The Methodology logical analysis and calculation with pat- guage. It must be supposed that our abil- of Mathematics, I.C.M.I. Bulletin 37 terns and structures. In our search for ity to operate with concepts, with relation- (December 1994), and Math. Gazette 79, No. understanding of the world, driven by the ships, had and maybe continues to have an 485 (July 1995), 321-334. (Lithuanian ver- need for survival, and simply for the wish evolutionary value. sion: Matematikos metodologija, Alfa plius to know what is there, and to make sense It is also curious in this respect that the omega 98 Nr 1(5), 71-84), Cubo Matematica of it, we need a science of structure, in the achievements of mathematics are general- Educacional, 2 (2000), 85-100. abstract, and a method of knowing what is ly held by mathematicians to be the solu- 2. T. Dantzig, Number: the Language of Science, true, and what is interesting, for these tion of some famous problem. Certainly 1930, 2nd ed. 1954, Macmillan. structures. Thus mathematics in the end such a solution will bring to the solver 3. P. Davis and R. Hersh, The Mathematical underlies and is necessary for all these fame and fortune, or at any rate a certain Experience, Penguin, 1981. other subjects. This is part of our claim fame within the world of mathematicians. 4. P. Davis and R. Hersh, Descartes’ Dream, for your attention, and for the support for Yet the history of mathematics and its Penguin, 1988. our studies. applications shows that it is the language, 5. A. Einstein (1916), quoted in Math. methods and concepts of mathematics Intelligencer 12 (2) (1990), 31. Another part of this claim is the fascina- which bring its lasting value and everyday http://www-history.mcs.st-and.ac.uk/history/Math tion and wonder at the new patterns and use. We have earlier mentioned some ematicians/Einstein.html structures, the surprising relationships, examples of this. 6. A. Grothendieck (1985), private communica- which our study has found. Mathematics At a more advanced level, we can say tion. also brings humility. We know how hard it that without this language – for example, http://www-history.mcs.st-and.ac.uk/history/Math can be to decide the truth of but one that of groups and of Hilbert spaces – fun- ematicians/Grothendieck.html apparently simple and clear statement. damental particle physics would be incon- 7. J. van Lint (1994), private communication. We are aware of the limitations of mathe- ceivable. 8. E. P. Wigner, The unreasonable effective- matical truth, that not all that is true can Some of the great concepts that have ness of mathematics in the natural sciences, be proved, as shown by the undecidability been found important and have been Comm. Pure Appl. Math. (1960), reprinted in results of Gödel. You will not find a math- given rigorous treatments through this Symmetries and Reflections: Scientific Essays of ematician writing that the final solution, mathematicisation are: number, length, Eugene P. Wigner, Indiana University Press, the unified theory that will solve every- area, volume, rate of change, randomness, com- Bloomington, 1967. thing, is at hand. Rather, we are looking putation and computability, symmetry, motion, http://www-history.mcs.st-and.ac.uk/history/Math for the surprises that show us a new view of force, energy, curvature, space, continuity, ematicians/Wigner.html the world, and new riches to explore. infinity, deduction. 9. http://nssdc.gsfc.nasa.gov/image/planetary Experience leads us to expect these to Very often the problem to make some /jupiter/europa close.jpg appear. For the mathematician, the world mathematics is, in the words of a master of is not only stranger than you imagine, but new concepts, Alexander Grothendieck, School of Informatics, University of Wales, stranger than you can now imagine. It is ‘to bring new concepts out of the dark’ [6]. Dean St., Bangor, Gwynedd LL57 1UT, UK our job to investigate this strangeness. It is these new concepts that make the dif- ficult easy, which show us what has to be What are the objects of study of mathemat- done, which lead the way. Correction to ics? More important is the way mathematics This has already been answered to some deals with and defines concepts, by com- extent. Mathematics does not study bining them into mathematical structures. Problem Corner things, but the relations between things. A These structures, these patterns, show the In the Problem Corner in EMS description of such a relation is what we relations between concepts and their Newsletter 39, Problem 123 was incor- mean by a ‘concept’. Thus we talk about structural behaviour. As said before, the rectly printed. The correct version the distance between towns, and might objects of study of mathematics are pat- should be: feel this is less ‘real’ than the towns them- terns and structures. These patterns and selves. Nonetheless, relations between structures are abstract, a notion discussed 123. The sequence {xn} satisfies things, and our understanding of these in the sequel, where we also return to √(xn+2+ 2) ≤ xn ≤ 2, for all n ≥ 1. Find relations, is crucial for our operation in questions (4)-(6). all possible values of x1986.

14 EMS June 2001 INTERVIEW InterviewInterview withwith BjörnBjörn EngquistEngquist (NADA, KTH, Stockholm, and UCLA, Los Angeles)

interviewer: Olavi Nevanlinna, Helsinki University of Technology

Last weekend we met in Berlingen, between pure and applied maths. Some Another thing you started at the Royal Switzerland, and now you are here in organisations should contain both: I hope Institute is PSCI, a very nice and func- Princeton. Where would I find you next the EMS will be one of them. tioning concept. Could you say a few week? words about it? I will go on to a meeting on electromag- PSCI stands for Parallel and Scientific netic theory in Victoria, Canada, and then Computing Institute, and is a centre for Zürich, Stockholm and Moscow. This peri- university cooperation with industry. od is unusually hectic, but some people The centre is sponsored by industry and close to me think it’s always like that and government and supports over twenty claim that I get jetlag when I don’t travel. graduate students. The industries take an active part in the research and the So let us travel both in space and time, to mentoring. We work mainly in a pre- Sweden in the 60’s: why Uppsala, why competitive phase in which several indus- mathematics and why numerical analysis? tries can join in a common project. The Uppsala was by default. In those days, in aim is to include the full scientific com- Sweden, we were not sophisticated enough puting process in the projects – from to choose the best place depending on our modelling and analysis, via algorithms, to goals. You went to the closest university if software. you planned to continue your education, and in my case that was in Uppsala. I was I am interested in time-scales related to interested in physics and had to start with science and education. Earlier we talked a full year of mathematics. I loved it and about typical time-scales for mathematical was hooked. When Lennart Carleson left schools: they may last for 100 years or Uppsala for the Mittag-Leffler Institute, I You are involved in the planning of 4ecm, more and shift focus in 20 years. In mod- switched to numerical analysis with Heinz- which will be in Stockholm in 2004. What ern high-tech industry 20 years is already Otto Kreiss as professor; both were very will you do differently from earlier con- a very long time. Does that create a diffi- charismatic teachers. I was fortunate to be gresses? culty for education? one of his students when the Kreiss school I hope we will re-emphasise the theme of I do think we need to adjust to the faster of numerical analysis was formed. The unity in mathematics from the Budapest pace of changes in the technology of school lasted for at least 25 years – maybe congress, and will have a healthy mix from today. Students are not competitive if it’s still there. Even if many of us have core areas and from fields with closer ties they only know yesterday’s technology. changed focus, you might say we often to other sciences and to the rest of society. In the future we cannot expect an appli- function as a homogeneous group. We will make room for some European cation to be as central as fluid mechanics research programmes and maybe add a has been in applied mathematics during What is needed for a school or a tradition in Swedish touch with a Nobel symposium. the last fifty years. The computational mathematics to be established and to last? Even if there is no Nobel Prize in mathe- tools also change rapidly. In other fields a big laboratory gives the matics, it is clear that mathematics and It is, however, important to realise that focus and continuity, whereas a group of computation play an increasing role in the this fast pace affects only a fraction of mathematicians can just pack their suitcas- research behind the science and economics education. The major part (at least two- es and move. prizes. thirds) of the education in mathematics The leading person behind the school and its applications deals with fundamen- obviously means the most, but there are In Stockholm, at the Royal Institute of tal principles, and should be roughly the also the right time and the right place. Technology, you have started a program in same today as when I started over thirty After the Second World War, analysis was CSE – computational science and engineer- years ago. We should also remember that very strong in the Nordic countries. This ing. For how long do you expect CSE to fly? the university provides only the founda- was fertile ground for the new ideas in CSE may not live more than 10 years as a tion and that education will continue in numerical analysis from the US. Kreiss label, but I see it as a link in the funda- the industry. had close links to the Courant Institute and mental and very powerful development of I later spent a post-doc year there. From computational techniques applied to sci- A final question. How do you find energy the 1960s to the 1980s we had very little ence and engineering that we have had for all your work? Have you any hobbies? interaction with other European mathe- during the last fifty years. We have used The brief moment when you realise that a maticians. It is much better now. the labels ‘numerical analysis’ and ‘scientif- proof works or an algorithm and code ic computing’ in earlier stages of this does what you hoped for, that’s the This brings us to the meeting in Berlingen development. A new label both stimulates reward. These days the rewards often on the role of applied mathematics in the and indicates a change of focus, but not a come from seeing students develop and EMS. Why do we need affirmative action change of the overall direction. finding those moments of joy. with respect to applied maths in the EMS? Unfortunately most hobbies are crowded Pure mathematics dominates many of the What can we expect next – computational out of my schedule, but I enjoy skiing as national organisations in the EMS, and this bio-informatics? long as my children let me join them. In was carried over. It is natural for a society Bio-informatics will be very important for the summers I enjoy setting the spin- to focus on core areas. This is what hap- society, and computation will be very naker to reach one of my favourite islands pened with the IMU, and then ICIAM was important for bio-informatics. Whether it in the Stockholm archipelago, and then I created as a forum for applied mathemat- will also be a driving force for develop- am certainly not thinking of the existence ics. I believe it is essential for the health of ments in computational science is not yet of classical solutions to the Navier-Stokes mathematics to have good relationship clear. equations EMS June 2001 15 INTERVIEW

LookingLooking back:back: ManuelManuel VValdiviaaldivia (V(Valencia)alencia) interviewer: Joan Cerdà (Barcelona)

Initially you were oriented towards other ed me to attend it. There I met Yosida, fields. How were you attracted by mathe- Schwartz, Garnir and Köthe. Since then I matics, and what were your first experi- have been several times to Germany, invit- ences in the subject? ed by Professor Köthe. Fortunately I have I began my contact with mathematics a lot of friends in the mathematical com- research very late: I was over thirty years munity around the world. But I would like old. At that time, I was working in Madrid to single out my friend Professor Klaus as an agricultural engineer at the National Floret and the wonderful meetings he has Institute for Agronomic Research, and to organised over the years in the beautiful make some extra money I was teaching location of Spiekeroog and Vangerooge, mathematics at the School of Agriculture two German Frisian Islands in the North Engineers. Sea. I have always felt very attracted to mathematics, even when I was a child From your current position as Emeritus attending primary school in the village Professor in the Universitat de Valencia, where I was born – Martos, in the how do you regard the changes that the Andalusian province of Jaén. After some Spanish community experienced during the years I arrived in Madrid to study at the second half of the 20th century? University, where I enrolled in Law stud- When I arrived in Valencia, I found a des- ies; afterwards, in the 1950s, under the olate landscape. The full professorship influence of some friends, I chose to follow position I got did not have even a single Agriculture Engineer studies. Engineer book of mathematics. I went to Madrid, to studies in Spain were designed in such a the Education Ministry, and mentioned way that there was an entrance examina- the problem to the under-secretary; they tion, the ‘Ingreso’, held at certain private gave me 100,000 pesetas to buy some schools during June and September. Only books. Those were very difficult times. We when you had passed the Ingreso were you Which of your teachers, colleagues and stu- had no subscriptions to mathematics jour- allowed to enrol in that School to follow dents do you remember most? nals. We were isolated. There was no your studies. Usually, people had to As I mentioned earlier, I was quite old mathematical community: only some iso- spend three to five years passing that when I made my initiation into mathemat- lated individuals doing mathematics. examination, and five more years to finish ical research. It was my friend Dario It is always possible to find competent their studies at the School. Maravall Casesnoves, PhD in mathematics people who can do research, but it is nec- To prepare for the Ingreso, one had to and an agricultural engineer, who put me essary to put them on the right track. study several subjects, split in parts. The in contact with Professor Ricardo San Juan Fortunately, it was possible to do some exams of three of those parts were very Llosá, full professor of mathematical positive work during these years: contacts difficult to pass: biology, the first part of analysis at the Complutense University. with foreign mathematicians increased mathematics, and the second part of San Juan was the one that introduced me and also attendance at conferences. mathematics. In the first part of mathe- to research in mathematics. I learnt a lot Young mathematicians of great strength matics we studied algebraic analysis (fol- from him: he was my PhD advisor. In appeared, and there was a radical change lowing a book by Rey Pastor), trigonome- spite of our age difference, we were very in the position of mathematics in Spain. try and metric geometry; in the second good friends. San Juan, who had been a You only have to see now how many pub- part of mathematics, we studied calculus, student of Professor Julio Rey Pastor, was lications were produced by Spanish math- classical algebra and analytic geometry. I a very deep person. I consider myself very ematicians to realise the progress attained very much enjoyed studying that kind of fortunate for having met him and for the at that time. I believe that we should be mathematics at that time. long relationship I maintained with him. happy with the positive achievements that In 1966, when I had already become were made in Spain. Do you think that you entered mathematics full professor of mathematical analysis at at a difficult time? Valencia University, I developed a keen Have your scientific activities been mainly For me, the 1950s was a very difficult peri- interest in functional analysis. with pure mathematics? What is your opin- od. I did not have financial means to sup- Before I began working with San Juan, ion about the duality between pure and port my studies, so I had to study and Professor J. Horváth visited Madrid, invit- applied mathematics? work simultaneously. During my years ed by Professor San Juan, and gave a My scientific activity has mostly focused on preparing the Ingreso, I gave private course on quasi-analytic classes at what one may call pure mathematics. high-school lessons, and afterwards, when Complutense University. After that, both However, I do not believe that there is a I was a student at the Agriculture professors maintained a very good rela- duality between pure and applied mathe- Engineer School, I taught mathematics tionship. It was San Juan who wrote to matics. The choice of the term ‘applied’, privately to prepare the Ingreso in that Horváth about me and my interest in as it is commonly used, has not been very school. functional analysis. The answer was fortunate, since it causes much confusion. In 1960 I enrolled to study mathemat- prompt and Professor Horváth intro- If one wants to classify mathematics, it ics at the Complutense University. I was a duced me to M. De Wilde, who had great should be done in terms of quality, a much ‘libre’ (free) student, which required me to success with his thesis on the closed graph clearer and more important concept. prepare the subjects by myself without theorem. De Wilde was a student of Fortunately, applied mathematics of great attending the lectures. I went to the Garnir. In 1970, Professor Garnir organ- quality is done here in Spain, but honestly University for the exams only, and so I ised an important functional analysis it is hard for me to differentiate between it had very little contact with professors. meeting in Liège (Belgium), and he invit- and pure mathematics. 16 EMS June 2001 INTERVIEW In your field, what will the future develop- departments? ed. On the other hand, there is also a cer- ments be? Do you think that functional Although the mathematical level of Spain tain pressure to publish in particular jour- analysis, and mathematical analysis in gen- has clearly been raised during the 20th nals, since in the evaluation, done in the eral, should borrow ideas from other fields, century, providing a good basis in order to Ministry of Education, the Citation Index such as physics, biology or economics? form good professionals and researchers, is the reference used. This may simplify Should students be oriented towards some we have a hard time when trying to take things, especially if the papers are some- specific topics? profit from our intellectual resources. The how identified with the journals in which It is quite difficult to predict the future of problem of recruiting the best qualified they appear, since journals are already functional analysis, but I believe that it will mathematicians for our departments is classified in a given order. Personally, I continue to be applied quite a lot, since it clearly attached to the existence of good think they give the Citation Index more appears in a natural way in many prob- expectations for the future, and this is not credit than it really deserves from a scien- lems. I am also certain that mathematical so at the moment. I believe that our uni- tific point if view. To evaluate papers by analysis will take ideas from other fields, versities urgently need to make changes in their contents seems to me much more jus- such as physics, biology or economical sci- certain aspects. tified, although, obviously, it is longer and ences. Concerning the orientation of stu- harder to do. I believe that the evaluation dents towards certain fields of research I What should be the role of institutions and method they use in our country should be believe that we have not taken much time societies in the world of mathematics? modified. here in Spain to study the real application This question is much too wide for me but, of mathematics to other scientific fields, speaking about Spain, I believe there are Which parts of your professional life do you and there is in my opinion a great amount lots of things to be done. To acquire some remember with most pleasure? of interest and future in this type of ideas, it may suffice to take a look at what Personally, I have taken great pleasure in research. is being done by other more advanced teaching. I have dedicated many hours of countries with a longer mathematical tra- my life to the teaching of mathematics, and How do you view the near future? What dition. It is really astonishing for me that this has always been done following my can be done to attract new young students in Spain the C.S.I.C does not have an vocational trends. In particular, I remem- into mathematics? Institute for Mathematical Research. The ber with great pleasure when I had my first I am very much concerned about the existence of such an institute, in which one group of research students in Valencia and future of mathematics in Spain. It is quite could do basic mathematics of quality when I began to be a PhD advisor. This hard to convince young students to do among other things, would be good not was an unforgettable experience, since it research in mathematics when so little can only for Spanish mathematics but also for was the first time that I experienced such be offered by our universities. I fear that if the C.S.I.C. itself, since it would gain more activity and I felt very happy to find myself the administration does not take appropri- prestige. with these vocational and capable students. ate steps, the level that Spain has achieved in mathematical research, with so much Do you think that there is too strong (or Does mathematics share your time with effort and sacrifice, will undoubtedly weak) a pressure to publish? other hobbies? decrease. The pressure on publishing comes, in our I enjoy music quite a lot. Also different universities, from its economical reward, aspects of literature, novels, essays and … and about attracting good scientists, do since one’s salary is increased by a comple- poetry, and history too. I frequently spend you think that it is difficult to recruit the mentary amount after six years of publish- time reading and listening to classical best qualified mathematicians for our ing papers, if these are positively evaluat- music.

(Spezialforschungsbereich, coordinated research programs with yearly funding of Applied Mathematics in Austria close to 1 million euro each): There are mathematical SFBs in Graz (Optimisation Significantly Strengthened and Control) and in Linz (Numerical and Heinz W. Engl (Linz) and Norbert Mauser (Vienna) Symbolic Scientific Computing) and a similar large-scale project including four universi- ties and the Austrian Academy of Sciences In Austria, applied mathematics have been (G. Gottlob). on Number Theoretic Algorithms, another strongly fostered by recent joint activities The WPI is an open structure, open SFB on Quantitative Methods in Economics of scientists from the University and both for other projects that have passed a has a large mathematical core. Technical University (TU) Vienna: the new very selective international evaluation, and Recognising the increasingly strong Wolfgang Pauli Institute (WPI), founded by open for a development of the WPI position of applied mathematics in several START and Wittgenstein prizewin- towards an Austrian variant of a Max Austrian science, the Academy of Sciences ners (comparable to the Hess and Leibniz- Planck Institute, including places outside is currently discussing the possible found- prize in Germany) has the mission to pro- Vienna. ing of an Institute in that field. vide an excellent infrastructure for such The WPI also hosts the new interdisci- Finally, also on the ‘extreme’ applied ‘high end’ projects of the Austrian plinary Wissenschaftskolleg (doctoral school) end – for example, in Industrial National Science Foundation (FWF) and to on Modelling with Differential Equations Mathematics, new ‘Competence Centres’ create a ‘centre of excellence’ in mathe- where TU engineers like A. Kluwick and (co-funded by industry and government) matics, informatics and their application in H. Troger participate as well as the strong are emerging. the sciences. Austrian school in biomathematics (K. With all these initiatives, especially if Since applied mathematics is more and Sigmund) and the differential geometric properly linked, Austria can become a more transcending national boundaries, approach of P. Michor, which provided a global player in selected areas of applied the WPI is also particularly designed to link to the Erwin Schrödinger Institute mathematics. It goes without saying that host European projects like Marie Curie (Vienna). this strength in applied mathematics is Training sites or networks. In general, Austrian applied mathemat- deeply rooted in traditional Austrian The founding members of the WPI are ics has been quite successful in recent strengths in pure mathematics; for a pro- working in PDEs and ODEs – for example, years: The percentage of research funding ject like Number Theoretic Algorithms which in mathematical physics and semiconduc- going from FWF to mathematics has dou- has a span from very ‘pure’ topics to time- tor modelling (P. A. Markowich, N. J. bled, and especially applied mathematics ly applications in finance, even the ques- Mauser, C. Schmeiser and P. Szmolyan) or has been over-proportionally represented tion if this is to be considered ‘pure’ or financial mathematics (W. Schachermayer) in the high-end programs of FWF: ‘applied’ mathematics does not make and mathematically oriented informatics Wittgenstein prizes, START prizes, SFBs sense. EMS June 2001 17 SOCIETIES equipped with audio-visual facilities. Société Mathématique de France (SMF) Relationships between the SMF and SMAI Colette Picard and Mireille Martin-Deschamps The SMF and the SMAI try to work together whenever possible. Here are some recent examples of joint action: The SMF is an association, created in Concerning communication inside the • in collaboration with the Ecole 1872, whose purposes are ‘defending and French mathematical community, two of Polytechnique, an international confer- promoting mathematics and mathemati- our publications, the Officiel and the Gazette ence on Mathematics in Industry and the cians’. It currently has around 2000 mem- des Mathématiciens, announce main events services (16-17 November 2000); bers, mainly researchers and university (seminars and conferences), give informa- • a conference in honour of the French teachers, and also institutions, such as tion on open faculty positions, and convey prize winners of the 3rd European libraries and mathematics departments. members’ opinions on various issues. Mathematical Congress at Barcelona (9 The head office is located in Paris, at the Our server (http://smf.emath.fr) gathers November 2000); Institut Henri Poincaré, but there is also an useful information for mathematicians, a • establishment of a think-tank group on agency in Marseille, the SMF House, which directory of the members, a discussion the teaching of mathematics (commission is devoted to the distribution and storage platform, an on-line order form for books Kahane); of the publications. The SMF employs six and journals, information concerning past • publishing of a booklet promoting persons. and new publications, etc. mathematics to a large audience; • diffusion of information in real time Scientific publishing Scientific activities about the recruitment of teachers in the SMF is the main publisher in France for The annual meeting, open to a wide audi- French universities (opération Postes); mathematical books and journals at a high ence, offers lectures on a topic of current • an on-line information service for level, partly in French. interest. Bi-annual scientific sessions on young applicants for academic jobs (Livret Journals: The Bulletin, founded in 1873, the ‘state of the art’ aim at bringing togeth- du candidat); and its supplement, the Mémoires; er the most advanced researchers in a sub- • diffusion of information on seminars Astérisque, created in 1973, at the centenary ject as well as students and non-specialists. and conferences by setting up the database of the SMF; The Revue d’histoire des mathé- One-day meetings on a particular theme ACM (supported also by the EMS). matiques, created in 1994. are organised on a subject on the border Series: Panoramas et Synthèses, Cours between mathematics and other sciences. Special announcement Spécialisés, Séminaires et Congrès. In April 2001, the SMF published a special Thanks to grants from the French min- International relations issue of the Gazette, which contained a istries of education and research, and also The SMF has representatives in the IMU paper by Alessandra Carbone and Michael thanks to the work of many French mathe- and the EMS (it contributed to its creation) Gromov on mathematical slices of molecu- maticians, these journals and books, partly and has reciprocity agreements with many lar biology. in French, are distributed all over the foreign societies and exchange agreements world, and are internationally famous. with foreign journals. We have been taking care, for a few years, Since 1998, we have had a publishing of the distribution, as well as the scientific contract with the AMS, which translates and editorial work. some of our French books into English. SMAI (France) Today, one of our main concerns is the Colette Picard and transition to electronic publishing. The CIRM (Centre International de Mireille Martin-Deschamps Besides the paper version, we have set up Rencontres Mathématiques) an electronic version of the Bulletin for our The CIRM is a centre of research and subscribers. We are also planning the digi- training, which was created by the SMF in The Société de Mathématiques Appliquées et tisation of old issues. 1981, along the lines of the German Industrielles (SMAI) was founded in 1983 by We are also launching a reedition serie of Forschungsinstitut Oberwolfach. Its tasks a group of French applied mathematicians mathematical texts, or letters, which can are: who had become aware of the specific give a historical perspective on classical • the organisation of international meet- nature of their discipline and wanted to subjects. ings, bringing together mathematicians or work together for its continuing growth. researchers in related fields from France The SMAI now has about 1200 mem- An exchange and meeting place and abroad; bers from both the academic and the Created by, and for, the mathematical • the training of young researchers – in industrial communities. Members include community, SMF is a privileged go- particular, through intensive courses or experts in scientific computing, numerical between for mathematicians and those in summer schools. analysis, partial differential equations, politics and economics. Through joint The CIRM can accommodate around applied probability theory, statistics, con- actions, SMF keeps close ties with most 60 participants. It is located in the heart of trol, automatic control, optimisation, dis- academics or professional groups interest- an estate on the Luminy university campus crete mathematics, and so on. ed in the future of mathematics, and also near Marseille, and is housed in an entire- with the other sciences, through their ly renovated country house. These fea- Goals of the society organisations. We are especially con- tures enable the centre to offer special The main goal of the Society is to help cerned with questions of teaching at every facilities for scientific and research meet- develop applied mathematics through level. ings. Everything has been planned and research, industrial applications, teaching The SMF’s concern to inform a wider organised so that working and living con- and the training of researchers and engi- group about the actual mathematics led to ditions are of the highest standard. neers. the establishment in 1984 of the d’Alembert The mathematical library contains The SMAI strives to increase awareness Prize, which is awarded every two years for 35,000 books and the same number of of new developments in the use of applied a work that makes a piece of mathematics periodical journals, representing 375 dif- mathematics, and to encourage and facili- accessible to the public. Moreover, we cel- ferent titles, in addition to a bibliography tate them. The Society thus intends to be ebrated World Mathematical Year 2000 by research service. The database of the an organisation where all persons interest- awarding four special d’Alembert Prizes to library is accessible by computer networks. ed in applied mathematics and its uses can young students: these prizes were awarded The participants can use various comput- come together. In particular, it provides a for lectures presenting actual mathematics ers and connect with every place in the meeting ground for universities and indus- within the reach of young students. world, and two lecture rooms are entirely try. 18 EMS June 2001 SOCIETIES The Society also takes a strong interest prised some thirty-five titles, published by CIRM in Marseille, and start a research in the teaching of applied mathematics in Ellipses (Vols. 1 to 9) and by Springer- period of about one month on problems universities and engineering schools, as Verlag (starting with Vol. 10). defined in cooperation with industry. For well as in secondary education. In addi- Since 1995, the SMAI has assumed the the students, it is an opportunity to work tion, the SMAI works to encourage contin- scientific responsibility for the journal on really applied problems, and to develop uing education in the various fields of M2AN Mathematical Modeling and Numerical useful contacts. Each year, the topic of the applied mathematics. Analysis, which was founded by the AFCET school changes. This year, it is oriented with the publisher Gauthier-Villars. toward multi-scale problems. Structure Starting in 1998, an electronic version has The SMAI and GAMNI founded and The SMAI is a non-profit organisation cre- been available on the Web. Since 1999, the fund the Blaise Pascal Prize, which is ated under the French law of 1901. It con- publishing house EDP Sciences, as its new awarded every year by the French sists of individual and institutional mem- owner, has been in charge of the publica- Academy of Sciences for an outstanding bers (university or industrial laboratories). tion. contribution in applied mathematics and The Board of Directors, one third of Also in 1995, with the help of a grant numerical computation in the engineering which is renewed every year during the from the Ministry of Education, Research sciences. General Assembly, establishes the policy of and Technology, the SMAI launched a new the Society. It elects the President, European Series in Applied and Industrial Relations with other learned societies and Treasurer and Secretary from among its Mathematics, called ESAIM, a series of elec- international relations members. They, in turn, constitute an tronic publications consisting of three jour- The SMAI maintains and develops rela- Executive Board, which meets monthly to nals, with scientific criteria that are on a tions with French and foreign learned soci- implement the policy decisions of the par with those of the best paper journals eties. In France, the Society coordinates its Society, as defined by the Board of (editorial board, strict referee system). efforts with those of societies interested in Directors. These journals are ESAIM COCV (Control, related fields: the SMF (Société Within the Society, there are currently Optimisation & Calculus of Variations), Mathématique de France), the SFdS four special scientific interest groups: ESAIM P&S (Probability & Statistics) and (Société Française de Statistique), and is • the GAMNI (Groupe pour ESAIM Proc (Proceedings). Since 1998, actively involved in the GRIAM (Groupe l’Avancement des Méthodes Numériques the ESAIM series has been produced in de réflexion Inter-Associations pour les de l’Ingénieur), founded in 1973 as an cooperation with EDP Sciences. Since Mathématiques). independent organisation and integrated 1999, the series has included ESAIM Today, research, whether theoretical or within the SMAI at its creation, is con- M2AN. A full paper-version of the yearly applied, is international. Thus, the SMAI cerned with the development of numerical volumes is published at the end of each is itself an institutional member of the analysis in industry. year. EMS and of ECCOMAS. At the same time, • the MAS group (Modélisation Aléatoire the Society has formed ties throughout the et Statistique), founded in 1991, promotes Workshops, congresses, summer schools world with societies concerned with the statistical methods and applied probability Within France, the Society organises the development of applied mathematics, such theory in a wide range of technologies or yearly Congrès d’Analyse Numérique which as the AMS (American Mathematical applications. brings together more than 300 partici- Society) and SIAM (Society for Industrial • the MODE group (Mathématiques de pants to offers high level lectures. It also and Applied Mathematics) in the United l’Optimisation et de la Décision), also gives an opportunity to a large number of States, the IMA (Institute for Mathematics founded in 1991, is dedicated to the devel- young PhD students to present the results and its Applications) in the United opment of applied mathematics in such of their current research. Kingdom, in Germany the DMV (Deutsche domains as non-linear analysis, optimisa- The ‘Journées du groupe MODE’, also Mathematiker Vereinigung), which is a co- tion, discrete mathematics, operations organized yearly, provide the same type of editor of the journal ESAIM:P&S , the research, mathematical modelling in econ- format for its members and young PhD Gesellschaft für Angewandte Mathematik omy, finance and social sciences. students. Similarly, the MAS group organ- und Mechanik (GAMM) in Germany and • the AFA group (Association Française ises its ‘Journées du groupe MAS’ every surrounding countries, the Società Italiana d’Approximation) is issued from an associ- other year. di Matematica Applicata e Industriale ation created in 1989 and has been inte- The GAMNI, as co-founder of the (SIMAI) in Italy, and the Sociedad grated as a group of the SMAI in March ‘European Community on Computational Española de Matemática Aplicada (SEMA) 2000. Its goal is to promote the study and Methods in Applied Sciences’ (ECCO- in Spain. These collaborations have led to the use of functions approximation, mod- MAS), whose goal is to promote scientific reciprocity agreements and to the organi- elling and geometric design, multi-resolu- computing in industry at the European sation of joint conferences, as exemplified tion analysis, smoothing, signal analysis, level, takes part in the ECCOMAS by the active participation of the SMAI as a image analysis, tomography and scientific Conferences. The GAMNI itself organises member of CICIAM (Committee for visualisation. several workshops and congresses every International Conferences in Industrial year as well. and Applied Mathematics). The latter Activities of the society The SMAI also organizes a summer organises the International Congress for The SMAI engages in several publishing school of scientific computing, the CEM- Industrial and Applied Mathematics endeavours and organises meetings, work- RACS, ‘Centre d’été Mathématique de (ICIAM) every four years. The first ICIAM shops, congresses and summer schools. Recherche avancées en Calcul was organized by the SMAI in Paris in Scientifique’. 1987; ICIAM 1995, held in Hamburg, Publications This action is supported by the French drew close to 3000 participants. Three times a year the Society publishes its Department of Education, CNRS, Together with the SIMAI and the newsletter Matapli; it is sent to all mem- European funding, and is hosted by the SEMA, the SMAI has established the $3000 bers. This newsletter presents scientific CIRM, ‘Centre International de CICIAM Lagrange Prize, in recognition of articles, generally in the form of reviews, as Recherches Mathématiques’, SMF House. a life-time contribution to applied mathe- well as information on congresses, doctor- The training is both theoretical and matics. This prize, together with other al dissertations, recent publications and applied. First the participants attend a CICIAM prizes, was awarded for the first news of the applied mathematical commu- series of lectures at ASCI (Laboratoire de time at ICIAM in 1999 in Edinburgh to nity. calcul scientifique intensif du CNRS) in the Jacques Louis Lions. The SMAI’s monograph series, University of Paris-Sud in Orsay for about Mathématiques & Applications, publishes two weeks in July. The goal of these lec- For more information, use the website or write textbooks, mostly based on graduate cours- tures, delivered by well-known scientists, is to SMAI, Institut Henri Poincaré, 11 rue es (DEA) at universities and engineering to present the state of the art on the topic Pierre et Marie Curie, F-75231 Paris Cedex schools. By early 1998, the collection com- of interest. Then the students move to 05, FRANCE. EMS June 2001 19 SOCIETIES TheThe RRomanianomanian MathematicalMathematical SocietySociety Societatea de Stiinte Matematice din Romania Madalina and Vasile Berinde

‘Enthusiasm, harmony, unselfish work, the continuity of its ideas and traditions organisation, although it had existed de continuous sacrifice’ – these words have promoted by successive generations of facto since the first issue of Gazeta guided the journal Gazeta Matematica Romanian mathematicians. Matematica on 15 September 1895. Joining (Mathematical gazette) through the years, The forerunners of today’s Romanian the Romanian Society of Sciences in 1949 from its first issue in 1895. If the identity Mathematical Society were the Romanian to form the Society of Mathematical and of a society of any kind is given by its activ- Society of Sciences and the Society Gazeta Physical Sciences, with new statutes and ities, and if the activity of an academic soci- Matematica. under the presidency of a mathematician, ety is mainly expressed through its publi- The Romanian Society of Sciences was Grigore Moisil, the Society Gazeta cations, it is clear why the Romanian founded in 1897, when a society called The Mathematical Society has always been asso- Friends of Mathematical Sciences merged ciated with the monthly Gazeta Matematica with the Society of Physico-Chemical – its pennon publication – and with these Sciences; both of these had been founded words. However, this identity between the in 1894. The journal Bulletin de la Societe society and the journal is unofficial: the Roumaine de Sciences was born with the society publishes two other journals, both Society itself, but split later in 1922 into quarterly; but it is generally accepted that, the Bulletin Mathématique de la Société through its large audience, Gazeta Roumaine de Sciences and the Bulletin de Matematica has been, and still is, the soci- Physique de la Société Roumaine de Sciences. ety’s soul. In the first journal the papers focused Here we present some chronological mainly on higher mathematics, while landmarks in the history of the Romanian Gazeta Matematica published papers on ele- Mathematical Society, and focus on its mentary topics. The Romanian Society of activities, describing its role in high-level Sciences lasted until 1949 when, following mathematical education, and mentioning a the reform of the educational system, it few of its outstanding personalities. merged with the Society Gazeta Because the Society’s largest audience has Matematica. been for its journal on elementary mathe- The Society Gazeta Matematica was born matics, Gazeta Matematica, we focus on that in 1910, when the Romanian Parliament journal and on its spirit which has ensured approved a law concerning its statutes and C. Gogu - the first president of RSS Matematica continued its traditions and activities in the hybrid (mathematics and physics) society until 1964, when it split back into two societies, one of them being Societatea de Stiinte Matematice din Romania. Because of the role of the Society Gazeta Matematica in ensuring a large audience among mathematicians, teachers and students, the Romanian Mathematical Society is now officially con- sidered to have been founded in 1910, the same year as the Swiss Mathematical Society, but still rather late in the European mathematical scenery. As a result of the close links between the origins of the Romanian Mathematical Society and the journal Gazeta Matematica, the main characteristic of the society has always been its deep involvement in educa- tion, from the foundation of Gazeta Matematica to the famous International Olympiads. Unlike similar societies all over Europe, the first aims of Gazeta Matematica were to ‘improve the knowledge in mathematics of high school students’, rather than to pro- vide a forum for those occupied with high- er mathematics. It was an age of great need for engineering professionals, and the birth of Gazeta Matematica arose from such a cause: in 1894, correcting admission papers for the School of Bridges and Highways (now the Politechnica University in Bucharest) and noting the very poor level of mathematical knowledge of those who aimed at a career in the field, five

20 EMS June 2001 SOCIETIES method for attracting the most talented also been the organiser or co-organiser of youngsters was the introduction of con- several important international congress- tests, beginning with the annual Gazeta es. These include: Matematica contests (first organized in - the Congress of Mathematicians of 1902), continuing with the National Latin Expression (commemorating E. Olympiad from 1949, and initiating and Cartan), held in Brasov in September organising the International Mathematical 1969; among the participants were G. de Olympiad for the first time in 1959. Rham, J. Cerf and H. Cabannes (Articles have already appeared on this (France), P. Lelong (Switzerland), L. topic in Paul Jainta’s ‘Problem Corner’ in Gaudeaux (Belgium), P. Ribenboim EMS Newsletters 32, 34 and 36). The excel- (Canada), M. Piccone (Italy), O. Boruvka lent results of the Romanian team through (Czechoslovakia), D. Kurepa the years are just one example of the high (Yugoslavia), N. Kuhlmann (Germany) level of mathematical education, promoted and C. Foias (Romania). by the Romanian Mathematical Society - the 3rd Congress of the Inter-Balkan and the Gazeta Matematica, together with Mathematics Union, held in Bucharest other achievements of the representatives in 1966. of the Romanian Mathematical School. It - the annual conferences of the Romanian has become natural in Romania for gifted Mathematical Society, held since 1997 Gh. Titeica scholars in mathematics to work with (Bucharest 1997, Cluj-Napoca 1998, young engineers, Ion Ionescu, Victor Gazeta Matematica – generations of brilliant Craiova 1999, Constanta 2000, and Balaban (who gave the journal its name, mathematicians have been involved with Brasov 2001), where Romanian and for- but died just seven days after its first issue), this journal, that has appeared continuous- eign mathematicians report on their Vasile Cristescu, Mihail Roco and Ioan ly since its foundation, even in time of war, recent research results. Zottu, decided to issue a monthly journal and whose monthly audience increased to which could help scholars to solve prob- 100,000-120,000 copies in the period lems and study mathematics at a higher 1970-1989. level than they had done in school. Soon after, Andrei Ioachimescu and Gheorghe Titeica, the first pure mathematician, joined the Editorial Board. In the first issue, the board fixed their objectives: 1.to publish original papers in mathemat- ics; 2.to develop an appetite for the study of mathematics and doing original research.

Through the years, a special atmosphere formed around the Gazeta Matematica, a continual concern in developing a high mathematical culture, not only among its readers. Besides the high scientific quality of the published papers and problems, the first books of a series The Library of Gazeta Matematica appeared in 1901, a series that S. Haret I. Ionescu continued with translations of such classic Not only scholars, but also teachers are On five occasions the Romanian the objects of the activities of the Mathematical Society has organised the Romanian Mathematical Society and of International Mathematical Olympiad: the Gazeta Matematica: meetings, symposia, first one in 1959, then in 1960, 1969, 1978 congresses, summer schools and courses in and 1999 (for the 40th anniversary). The which university professors and school- Romanian Mathematical Society has also teachers meet to discuss the problems and partially supported its members to attend challenges of mathematical education. In the International Congresses of addition, a methodological series of Gazeta Mathematics in Moscow 1966, Nice 1970, Matematica has appeared since 1949 and Helsinki 1978, as well as other inter- (except for six years from 1974 to 1980), national congresses, by organising so- which publishes mainly didactical papers. called ‘scientific excursions’. So, every serious educational iniative in the Romanian mathematicians have also field of mathematics spins around the old been strongly involved in editing its third and ever young Romanian Mathematical publication: the Bulletin Mathématique de la Society, and around Gazeta Matematica. Société des Sciences Mathématiques de Other activities of the Romanian Roumanie, devoted to higher mathematics Mathematical Society have included the only. We mention, in particular, Ion Congresses of Romanian Mathematicians: four Ionescu, one of the founders of the Gazeta Gr. Moisil of these have been organised so far, in Matematica and called its spiritus rector, 1929, 1932, 1945 and 1956, and have Spiru Haret, who as Minister of Education books as Euclid’s Elements, with modern attracted Romanian mathematicians and introduced a new education law in 1898, papers of the time, and with original books outstanding foreign mathematicians, thereby establishing a modern mathemati- of Romanian mathematicians. The including H. Poincaré, P. Montel, V. cal educational system in Romania, Gh. Roumanian Mathematical Society was also Volterra, G. Darboux, H. Lebesgue, A. Titeica, T. Lalescu, A. Ioachimescu, D. involved in publishing school books. Denjoy, J. Hadamard. Pompeiu, P. Sergescu, Gr. Moisil But the most important and effective The Romanian Mathemaical Society has (President of the Romanian Mathematical EMS June 2001 21 SOCIETIES Society from 1949 to 1973), N. Teodorescu there is practically no-one under 50 left to such as Cuba, Vietnam and (eventually) (President of the Romanian Mathematical teach the younger generation.. North Korea. Society from 1973 to 1995 and Honorary Economically speaking, Romania is president from 1995 to 2000), T. uniquely disadvantaged among the candi- Scientific collaboration Popoviciu and C. Iacob. dates for EU membership. The salary of Finally, the importance of direct scientific Today’s objectives of the Romanian an established university lecturer is likely collaboration should not be overlooked: Mathematical Society include leading the to me no more than US$250 a month, at a inviting senior Romanians to Western con- educational and research activities, partici- time when the cost of living is rapidly con- ferences, and visiting them in return. For pating in the international scientific life, verging to Western levels. It is quite prob- those of us that have enjoyed the company, organising the Olympiads, discovering and able that the economy has finally bottomed and benefited from the scientific abilities encouraging talent, creating a proper cli- out, and is set to grow over the next 20 of Romanian graduate students and post- mate for communication and for develop- years (possibly somewhat unevenly); how- doctoral fellows, it seems particularly ing original mathematical values, and ever, this will certainly take a long time to appropriate to return the compliment to keeping the good tradition of a mathemat- feed through to basic science, and there is the schools that produced them. ical community around the old Gazeta a very real fear that by the time Romania is Matematica, a community capable of affirm- on its feet again, and (say) can satisfy the Note: Romanian scientists currently receive ing its values and contributing to the criteria for EU membership, its magnifi- grants from the West under a number of European and World scientific patrimony. cent scientific schools will have disap- projects, and they are very grateful for this For further information, see or the peared from the face of the earth. help. For example, Romania participates Romanian Mathematical Society’s home Quite apart from issues of morality or as an EU ‘associated state’ in EU page: human solidarity or fairness, there are at Framework 5 scientific networks and pro- least three imperative reasons of pure self- jects. On the positive side, this means that References interest for the West to support Romanian they already have some resources, such as 1. G. St Andonie, The History of Mathematics in science. First, to preserve what is unar- adequate computing facilities, and the Romania (3 vols. in Romanian), Editura guably an extraordinarily fruitful training experience of managing grants; they are Stientifica, Bucharest, 1965-1967. ground for young recruits into Western sci- thus in a good position to benefit from the 2. V. Berinde, Romania – the native country of ence. Second, to foster the eventual emer- kind of financial help advocated above. IMOs. A Brief History of the Romanian gence in Romania of a strong economic The problem with the present grants is Mathematical Society, Editura CUB PRESS 22, partner with its excellent scientific tradi- that they are always tied down by legal Baia Mare, 2000. tion still in place. Finally, preserving a restrictions, so that they cannot be used 3. F. Diac, The monograph of the Romanian solid educational system and intellectual where most needed, for example, to give Mathematical Society (in Romanian), Societatea tradition could provide an effective bul- their young people ‘Return home’ fellow- de Stiinte Matematice din Romania, wark against demagoguic and nationalistic ships. In addition, EU money (such as fel- Bucharest, 1999. politics of the extreme right or left that lowship and conference money) is in large could well emerge as a threat to peace in measure restricted to researchers under The authors of this article are Madalina the region; the pen, after all, is likely to be 35, with the unintended consequence that Berinde, ‘Babes-Bolyai’, University Cluj- considerably cheaper than the sword. essentially no resident Romanian scientist Napoca, and Vasile Berinde, North University can benefit. of Baia Mare. What can be done about it? ‘Return to Romania’ fellowships Historical and philosophical conclusion At present, one hears repeatedly from The Romanian intellectual tradition has many Romanian post-docs in Western uni- deep roots, going back into the 18th and Appeal for versities that they would like to return to early-19th century, when their students their country home, but that this is started travelling to France or Germany, to Romanian science absolutely impossible for financial reasons. be influenced by all the successive fashions In many such cases, a very modest stipend and revolutionary ideas of the West. The Miles Reid (Warwick) would make all the difference. (Estimated unification of the Romanian principalities price tag: US$1,000 a month in living in 1859 was an almost casual consequence The purpose of this appeal is to draw expenses, plus US$200 research expenses of manipulation by the Great Powers after attention to the devastating effect of the and a similar amount for the host institu- the Crimean War. From then on right current brain drain on Romanian science, tion: total US$16,800 per year, to last for 3 through to the Second World War, and to suggest ways in which Western sci- or 4 years per individual, possibly with Romanian social and economic thinkers entists and funding organisations could intermission to allow foreign travel.) Such dissected in extraordinary detail the prob- mitigate it with a relatively modest outlay a programme already exists: the United lems of a developing nation, including of effort and money. States Agency for International issues such as agrarian versus industrial, Development (USAID)’s scheme ‘Return state intervention versus laissez-faire, pro- The problem to Romania’: www.irex.org/programs/rtr, but tectionism versus free trade, foreign invest- Romania has almost unique strengths in much more is needed. ment versus self-reliance, etc. In short, several areas of intellectual activities, and how can a new nation such as theirs make supplies any number of top scientists to Small-scale financial help an honest living in the world? It would cer- Western universities. Its high school and Romanian scientific centres need small- tainly have astonished these thinkers to undergraduate programmes are still scale financial help from the West to devel- know that after the ravages of the Second among the strongest in the world, and its op bilateral partnerships with other former World War, and after the catastrophe graduates are eagerly sought after by US communist countries, such as their closest unleashed on the country by the vicious and European universities, and increasing- neighbours Hungary, Bulgaria, Czech and megalomaniac policies of Ceaucescu, ly also by computer and software compa- Republic, Poland, etc. There is tremen- one of their principal remaining com- nies. Of math students at Bucureshti dous scope here for mutual help in a con- modities – the brains of their young scien- alone, the top 20 students are offered text in which the brain-drain is not such a tists – is being systematically plundered for places abroad, in many cases even before serious issue. Since two countries stand to absolutely no return by Western universi- graduation; just imagine how Harvard or benefit, this would be a doubly effective use ties and companies. the Ecole Normale or Cambridge UK of Western money. As a somewhat longer would fare in such a regime. The shot, a very modest outlay would even Miles Reid is at the Mathematical Institute, Romanian academy and the faculties of allow Romanian universities to replace University of Warwick, UK their universities also feature high quality some of their own lost generation of grad- e-mail: [email protected] researchers, but the group is greying — uate students with recruits from countries web: www.maths.warwick.ac.uk/~miles 22 EMS June 2001 PERSONAL COLUMN PPersonalersonal ColumnColumn

Please continue to send the Editor information ed the 2000 George Dantzig Prize, for his Deaths on awards, appointments and deaths to this contributions to interior point methods for Column. The next Personal Column will convex programming. We regret to announce the deaths of: appear in issue 42 (December 2001). Sandu Popescu (Hewlett-Packard/Bristol) G. H. Bailey (17 November 2000) Awards has been awarded the Adams Prize of the University of Cambridge, for research in I. Noel Baker (20 May 2001) quantum information. Vladimir I. Arnold (Moscow/Paris) has Ernest-August Behrens (1 Dec 2000) been awarded a 2001 Wolf Prize for his Saharon Shelah (Jerusalem) has been Zygmunt Charzynski (29 January 2001) influential work in dynamical systems, dif- awarded a 2001 Wolf Prize for his funda- ferential equations and singularity theory. mental contributions to mathematical logic John G. Fauvel (12 May 2001) and set theory. Grzegorz Bobinski (Torun) and Andrzej Walter Felscher (9 December 2000) Komisarski (Warsaw) have received the Jozef Siciak (Krakow) has been awarded an two first Marcinkiewicz Prizes for students’ Honorary Doctorate by the University of F. G. Friedlander (20 May 2001) research papers. Uppsala. John Hawkes (11 April 2001) Carlo Cercignani (Milan) and Claudio Ian Stewart (Warwick) has been awarded Procesi (Rome) have been elected Fellows the 2001 Ferran Sunyer I Balaguer Prize, Michael R. Herman (2 November 2000) of the Accademia dei Lincei. with Martin Golubitsky (Houston), for their monograph: The symmetry perspective.. Roman Kaluza Kyzysztof Ciesielski and Zdzislaw Pogoda (Krakow) have received the Steinhaus Prize Jacek Tabor (Krakow) has received the Gottfried Meyer (13 September 2000) for the best Polish books popularising any Prize of the Polish Mathematical Society kind of science in the past four years. for young mathematicians. Crispin Nash-Williams (20 January 2001)

Alain Connes (Paris) is being awarded the Harold Thimbleby (London) has been Rogerio Silva Sousa Nunes (Feb 2000) 2001 Crafoord Prize in Mathematics by the appointed Gresham Professor of Robert A. Rankin (27 January 2001) Royal Swedish Academy of Sciences for his Geometry, in succession to Sir Roger work in the theory of operators and non- Penrose. J. J. Seidel (May 2001) commutative geometry. Robin Wilson (Milton Keynes/Oxford) has Claude Shannon (24 February 2001) Friedrich Hirzebruch (Bonn) has been been appointed Visiting Professor in the awarded the Banach Medal by the Banach History of Mathematics at Gresham Arthur Geoffrey Walker (31 March 2001) Mathematical Centre. College, London. J. A. Weightman (15 January 2001) Werner Hürlimann (Winterthur) has Günther Ziegler (Berlin) has been award- received the Gunnar Benktander Prize for ed a 2001 Gottfried Wilhelm Leibniz prize Helmut Wielandt (May 2001) work on financial data analysis. by the Deutsche Forschungsgemeinschaft (DFG) for his work in discrete geometry. Laurence Chisholm Young (24 Dec 2000) Marek Kaluszka (Lodz) has received the Great Prize of the Polish Mathematical Applications are invited for 2 Full Society for his research in statistics. Letter to the Editor Interview with Bernhard Neumann in EMS Professorships (C4) in Mathematics Newsletter 39 University of Bielefeld, Germany Stanislaw Kasjan (Torun) has received the I am writing about the publication in the Kuratowski Prize, awarded to Polish math- above article of remarks made by Bernhard For one of the positions the Department is ematicians aged 30 or less. Neumann about Professor George Steward, looking for either an algebraist or a number who was one of my predecessors as Head of theorist, and for the other either a topologist Francis Kirwan (Oxford), Adrian Smith Mathematics here at the University of Hull. or a geometer. Although I arrived here after he retired, I (London), Ian Stewart (Warwick) and Alex The person taking up the position is expect- came to know George Steward well through Wilkie (Oxford) have been elected Fellows ed to: of the Royal Society, London. visiting him and he was a considerable help to me in my early days as head of the Pure - participate fully in the teaching and Mathematics Department. Several of my col- research duties of the Department, Slawomir Kolodziej (Krakow) has received leagues in the Department here also know - become actively involved in the the Zaremba Great Prize of the Polish him – either because they were here before Department’s present and future research Mathematical Society for his research in he retired or came to know him later like me. projects, pluripotential theory. This letter is to express our view that publi- - have an interest in mathematics not cation of such remarks is unacceptable and restricted to their own field of expertise, offensive to the memory of Professor Steward Zbigniew Marciniak (Warsaw) has - be open to the possibilities of interdiscipli- received the Sierpinski Great Prize of the and to those of us who knew him either as friend or colleague. We would appreciate an nary cooperation. Polish Mathematical Society for his Applications received by 30 September 2001 research in algebra. appropriate acknowledgement and apology for this action, which does not fit at all well will be assured of consideration. with the mission of an organisation such as These should be sent to the Chairman of the Witold Marciszewski (Warsaw) has the EMS. Department of Mathematics, University of received the Mazurkiewicz Great Prize of Nigel Cutland Bielefeld, Box 100131, 33501 Bielefeld, the Polish Mathematical Society for his Germany. research in topology. Editor’s note. While the views expressed were entirely those of Professor Neumann, and not those The starting dates for these positions are of the EMS, we apologise for any offence that may provisionally set for 1 October 2002 and 1 Yurii Nesterov (Louvain) has been award- have been caused. April 2003, respectively. EMS June 2001 23 NEWS FFiveive YYearsears ofof DocumentaDocumenta HYKEHYKE MathematicaMathematica A Proposed Ulf Rehmann (Bielefeld) European Network

The fifth annual volume of Documenta Recently, Documenta Mathematica has in Applied Mathematica is currently being published in been selected by the SPARC initiative printed form, which seems to be a good (http://www.arl.org/sparc/) of scientific reason to look back on the journal’s histo- libraries in the USA as a journal in the Mathematics ry. Without any commercial assistance, ‘Leading edge’ category; Documenta con- more than 300 articles (covering 5000 siders this selection as a particular success. Norbert Mauser pages) have been published in most fields The SPARC initiative of more than 200 sci- of mathematics and including the three- entific institutions includes libraries from (WPI and University of Vienna) volume extra edition of the ICM’98 all the Ivy League universities in the US, Proceedings. and also from several leading European In the last call for Research Training The recent annual volume shows the universities. The goal of this initiative is to Networks of the 5th framework pro- liveliness and actuality of our discipline, in recommend high-level scientific journals gramme of the EU, the trend towards twenty-one interesting articles (covering that are produced and offered at a modest application-oriented training was 731 pages) from various branches of math- price, in order to compete with the price enhanced. ematics. A particular highlight in this vol- inflation of scientific journals. Usually, the The proposed IHP network Hyperbolic ume’s electronic version is the article recommended journals are produced by and Kinetic equations: asymptotics, numerics, Cross-over collision of scroll wave fila- universities or learned societies, which applications (HYKE), coordinated by N. J. ments by B. Fiedler and R. M. Mantel, operate the journals as a non-profit organ- Mauser (WPI Vienna) and B. Perthame which contains, together with exciting isation. (ENS Paris), includes 200 applied mathe- research results on parabolic differential Several well known, international com- maticians in 15 groups with satellites in 12 equations, extensive video-illustrations of mercial publishers have tried to take over countries, including Poland, Czechia and the most fascinating research aspects of the Documenta Mathematica, admitting that they Israel. article. This shows the superiority of the would not be able to keep the price of Created from the two successful TMR electronic way of journal production: such Documenta Mathematica as low as it is right networks Hyperbolic systems of conservation impressive visual presentation could never now. But it is unnecessary to raise the laws and Asymptotic methods in kinetic theory, be achieved by a book or by a convention- price of the journal. Documenta Mathematica and adding some key figures of the TMR ally produced journal. so far has been an economic success. (A network Viscosity solutions and applications During the last five years, Documenta management report on its first four years (including P. L. Lions), HYKE will attempt Mathematica has become a successful and was given by its managing editors in significantly to strengthen European internationally known journal. It is well September 1999: see http://www.mathe- applied mathematics. From the mathe- accepted by authors and by readers: its matik.uni-bielefeld.de/DMV/archiv/docu matical point of view, there is important usually quick decisions on publication and menta99.html). synergy between these three fields and the its author-friendly copyright regulations The journal has never taken financial new network is set to be a global player. attract many good manuscripts. The selec- support from any source, in spite of the At the core is a broad and complemen- tion of articles is careful and deliberate. fact that several offers have been made; tary international high level training pro- Positive publication decisions are made these were rejected in order to maintain gramme on ‘modelling-analysis-numerics’ on the basis of peer review and by the the financial independence of the journal. which intends to produce applied mathe- unanimous vote of the managing editors On the contrary, with its low-budget pro- maticians (in the sense of ‘pure mathemat- upon the suggestion of the communicating duction of the ICM’98 Proceedings, ics plus applications’) who can easily switch editor of each article. Everybody who is an Documenta Mathematica contributed to the between academia and industry. To this author of a Documenta article can be proud fact that the ICM ended up with a financial end, a link to ECMI is formed by includ- to be so. surplus, which was then used to establish a ing, for example, M. Anile, H. W. Engl, But an author can also be sure to find a big new scientific prize for mathematicians: and H. Neunzert. readership. Documenta Mathematica is see the author’s article ‘Efficient The network comprises a variety of sci- freely broadcasted on the world wide web Production of Mathematical Literature’ for entific expertise in the fields of differential by its two ‘native’ servers in Bielefeld and the workshop ‘Future of Mathematical equations, numerical analysis, scientific Urbana, and also by the more than forty Communication 1999’ at Berkeley, on computing, and also in various branches of mirror servers of the European http://www.mathematik.uni-bielefeld.de/ theoretical mechanics (continuum physics, Mathematical Society, and is therefore \char126rehmann/EP/. kinetic theory and quantum mechanics). world-wide accessible to everyone on the Using such a financial surplus from sci- As the focus of mechanics within the web. entific publication for the welfare and ben- applied mathematics community is shift- The access rates for the articles are sur- efit of our science, is something which ing, driven by the fact that modern appli- prisingly high: on average each article is many of us like to support, and Documenta cations often require modelling via micro- downloaded twice every three days, as a dvi Mathematica is proud for having already, as scopic physics, the proposed research on file, postscript file or pdf file (hence in its a relatively young journal, contributed to time-dependent PDEs seems very timely. full text); these numbers are from the such a desirable goal. These kinds of large networks should Bielefeld and Urbana servers, and do not also yield a positive impact on the include access by robots and automatic Editor’s note: In Ulf Rehmann’s article ‘The European Research Area, the new meta- search engines (which also contribute to Price Spiral of Mathematics Journals’ (EMS goal of the framework programmes. the distribution as they often serve local Newsletter 38), an incorrect web address was A similar large network in the field of mirrors). Many libraries in various coun- given; instead of http://www.mathematik.uni- algebraic geometry with an orientation tries subscribe to the printed version, bielefeld.de/\char126rehmann/BIB/ towards application (the EAGER network), which is currently always produced after it should read http://www.mathematik.uni-biele coordinated by A. Conte (Torino), was suc- each annual volume is complete. feld.de/~rehmann/BIB/ cessful in the previous call. 24 EMS June 2001 CONFERENCES Samoilenko (Co-Chairs, Ukraine), J. Beckers (Belgium), G. Bluman (Canada), P. Clarkson (UK), N. Debergh (Belgium), H.-D. Doebner FForthcomingorthcoming conferconferencesences (Germany), G. Goldin (USA), B. K. Harrison (USA), N. Ibragimov (Sweden), M. Lakshmanan (India), J. Niederle (Czech Republic), M. Tajiri Compiled by Kathleen Quinn (Japan), P. Winternitz (Canada), A. Klimyk, M. Shkil, I. Skrypnyk, I. Yehorchenko and R. Zhdanov (Ukraine) Please e-mail announcements of European conferences, Paolini (Brescia), D. Percivale (Genova), L. Site: Institute of Mathematics of National workshops and mathematical meetings of interest to Truskinowski (Minneapolis), J. Shah (Boston). Academy of Sciences of Ukraine and Ukrainian EMS members, to k.a.s.quinn @open.ac.uk. Organisers: G. Dal Maso (S.I.S.S.A.) and F. Pedagogical University Announcements should be written in a style similar to Tomarelli (Politecnico di Milano) Information: those here, and sent as Microsoft Word files or as text Location: Villa Erba, Cernobbio e-mail: [email protected] files (but not as TeX input files). Space permitting, each Information: Web site: http://www.imath.kiev.ua/~appmath/ announcement will appear in detail in the next issue of Web site: www.mate.polimi.it/villaerba2001 conf.html the Newsletter to go to press, and thereafter will be briefly noted in each new issue until the meeting takes 5-7: British Congress of Mathematics 9-22: European Summer School on Asymptotic place, with a reference to the issue in which the detailed Education, Keele, UK Combinatorics with Applications to announcement appeared Information: Mathematical Physics, St Petersburg, Russia Web site: http://www.bcme.org.uk Information: June 2001 e-mail: [email protected] 8-13: Second Workshop on Algebraic Graph Web site: www.pdmi.ras.ru/EIMI/2001/emschool/ Theory, Edinburgh, Scotland index.html 27-2 July: Midnight Sun Workshop on Information: [For details, see EMS Newsletter 38] Stochastic Analysis and Mathematical Finance, e-mail: [email protected] Kautokeino, Norway Web site: http://www.ma.hw.ac.uk/icms/current/ 10-15: Advanced Course on Symplectic Aim: to bring together researchers and students graph/index.html Geometry of Integrable Hamiltonian Systems, in stochastics and finance, and to discuss the lat- [For details, see EMS Newsletter 38] Bellaterra, Barcelona est developments in this exciting and rapidly Information: developing area of research under inspiration 8-14: Differential Geometry Valencia 2001, Web site: http://www.crm.es/sgihs from the midnight sun Spain [For details, see EMS Newsletter 39] Organising committee: Fred Espen Benth and [International Meeting on the Occasion of the Bernt Øksendal (University of Oslo, Norway) 60th Birthday of Professor A. M. Naveira] 11-16: Geometry, Symmetry and Mechanics I, Programme: presentations by invited speakers Main speakers: 50 minute talks: T. Aubin Lisbon, Portugal and workshop participants (París), M. Barros (Granada), J.-P. Bourguignon Scope: this meeting will focus on the geometry, Sponsor: NorFa via the network Stochastic (IHES), M. P. do Carmo (IMPA), K. Grove dynamics and numerics of mechanical systems Analysis and its Applications, led by Professor (Maryland). with symmetry and applications to areas such as Paavo Salminen, Aabo Academy, Finland 40 minute talks: L. Alias (Murcia), D. Blair atomic and molecular spectroscopy and contin- Deadline: for registration, already passed (Michigan), A. Borisenko (Kharkov), F. Brito uum mechanics. It is being organised under Information: contact Fred Espen Benth or (Sao Paulo), P. B. Gilkey (Oregon), O. Gil- the auspices of the EC Research Training Bernt Øksendal, Department of Mathematics, Medrano (Valencia), D. Johnson (Lehigh), S. Network ‘Mechanics and Symmetry in Europe’ University of Oslo, PO Box 1053 Blindern, N- Salamon (Oxford), L. Vanhecke (Leuven) (MASIE) and is sponsored by CAMGSD 0316 Oslo, Norway Organising committee: Manuel Barros (Lisbon), but is open to all scientists with inter- e-mail: [email protected] or (Granada), Francisco Carreras (Valencia), María ests in the relevant areas [email protected] Luisa Fernández (País Vasco), Àngel Ferrández Programme: several minisymposia on (tenta- (Murcia), Olga Gil-Medrano (Valencia), Ximo tively): Hamiltonian relative equilibria and peri- July 2001 Gual (Castellón), Luis Hervella (Santiago de odic orbits, singularities and perturbation of Compostela), Vicente Miquel (Valencia), integrable systems, non-holonomic systems, Salvador Segura (Aliacante) numerics of Hamiltonian systems, qualitative 1-6: Eighteenth British Combinatorial Sponsors (provisional): Ministerio de Ciencia y aspects of atomic and molecular systems, semi- Conference, Brighton, UK Tecnología, Generalitat Valenciana, Universitat classical methods, Hamiltonian PDEs and con- Information: de Valencia, Caja de Ahorros del Mediterráneo tinuum mechanics. Contributions to these are e-mail: [email protected] Information: particularly invited. Web sites: http://www.maths.susx.ac.uk/Staff/ e-mail: [email protected] Speakers: H. Broer, D. Chillingworth, P. JWPH/ Web site: http://radon.act.uji.es/~naveira/ Chossat, R. Cushman, G. Derks, F. Fasso, G. http://hnadel.maps.susx.ac.uk/TAGG/Confs/ Gottwald, A. Iserles, B. Leimkuhler, R. BCC/index.html 9-15: Symmetry in Nonlinear Mathematical Littlejohn, C.-M. Marle, J. Montaldi, R. [For details, see EMS Newsletter 36] Physics, Kiev, Ukraine Montgomery, J. Natario, San Vu Ngoc, W. Topics: classical, non-classical, conditional and Oliva, J.-P. Ortega, G. Patrick, T. Ratiu, S. 3-7: Barcelona 2001 EuroPhD Topology approximate symmetry, of equations of mathe- Reich, M. Roberts, D. Sadovskii, J. Scheurle, E. Conference, Bellaterra, Barcelona matical physics, symmetry in non-linear quan- Sousa Dias, G. Tanner, M. West, C. Wulff, B. Information: tum mechanics, quantum fields, gravity, fluid Zhilinskii, and other members of the MASIE Web site: http://www.crm.es/b2001etc mechanics, mathematical biology, mathematical Network [For details, see EMS Newsletter 39] economics, representation theory, q-algebras Organising committee: Mark Roberts and quantum groups, symbolic computations in (Warwick, UK), Esmeralda Sousa Dias (IST, 4-6: MathFIT workshop: The Representation symmetry analysis, dynamical systems, solitons Portugal) and Management of Uncertainty in Geometric and integrability, supersymmetry and parasu- Sponsors : MASIE-RTN contract number: Computations, Sheffield, UK persymmetry MASIE-HRPN-CT-2000-00113, CAMGSD- Information: Main speakers: J. Beckers (Belgium), O. Centro de Análise Matemática Geometria e Web site: http://www.shef.ac.uk/~geom2001/ Bogoyavlenskij (Canada), P. Clarkson (UK), Sistemas Dinamicos (IST, Lisboa) Edward Corrigan (UK), H.-D. Doebner Site: Instituto Superior Técnico, Lisboa 4-6: Variational Methods for Discontinuous (Germany), B. K. Harrison (USA), E. Ivanov Deadlines: for contributed talks and accommo- Structures, Applications to Image (Russia), M. Lakshmanan (India), J. Niederle dation, already passed Segmentation and Continuum Mechanics, (Czech Republic), A. Nikitin (Ukraine), Y. Information: International Workshop, Como, Italy Samoilenko (Ukraine), M. Tajiri (Japan), A. e-mail: [email protected] Speakers: E. Acerbi (Parma), J. M. Ball Klimyk (Ukraine), R. Zhdanov (Ukraine) Web site: http://www.math.ist.utl.pt/~edias/ (Oxford), G. Bouchitté (Toulon), G. Buttazzo Call for papers: those wishing to present an MASIE/GSMI (Pisa), G. Del Piero (Ferrara), I. Fonseca oral communication or a poster should send the (Pittsburgh), N. Fusco (Napoli), D. Kinderlehrer registration form (see the web-site) and abstract 15-20: Algorithms for Approximation IV (Pittsburgh), R. Kohn (New York), A. Leaci (plain ASCII or TeX) to International Symposium, Huddersfield, UK (Lecce), R. March (Roma), J. M. Morel (Paris), [email protected] Information: U. Mosco (Roma), D. Owen (Pittsburgh), M. Organising committee: A. Nikitin and A. e-mail: [email protected]

EMS June 2001 25 CONFERENCES Web-site: Http://Helios.Hud.Ac.Uk/A4a4/ Web site: http://www.karlin.mff.cuni.cz Abstracts: submission of abstracts through [For details, see EMS Newsletter 38] /~toposym/ http://at.yorku.ca/cgi-bin/amca/submit/cahk-01 e-mail: [email protected] Deadlines: for applications and suggestions for 17-23: Advanced Course on Global [For details, see EMS Newsletter 39] ISAAC awards, passed; for submission of Riemannian Geometry: Curvature and abstracts, 15 August Topology, Castelló de la Plana 20-24 Variational Sequences and Bicomplexes: Information: fax: +49-30-83875403 about Information: Advanced 5-day course, Opava, Czech ISAAC Web site: http://www.crm.es/geom2001 Republic e-mail: [email protected] [For details, see EMS Newsletter 39] Lectures: Group invariant solutions to differen- Web site: http://www.math.udel.edu/isaac tial equations and reduction of variational http://www.math.fu-berlin.de/rd/ag/isaac 18-28: Advanced Course on Modular Forms bicomplexes; introduction to variational and p-adic Hodge Theory, Bellaterra, sequences; geometric aspects of conservation 21-23: Ukrainian Congress of Mathematics Barcelona laws of non-linear differential equations (UCM-2001), Kiev, Ukraine Information: Lecturers: I. M. Anderson (Utah), D. Krupka Information: Web site: http://www.crm.es/tn2001 (Opava), A. Verbovetsky (Moscow) Web site: http://www.imath.kiev.ua/~congress/ [For details, see EMS Newsletter 39] Language: English Information: 24-30: 10th International Meeting of European 23-27: 20th IFIP TC 7 Conference on System Web site: http://www.math.slu.cz/levoca.html Women in Mathematics, Malta Modelling and Optimization, Trier, Germany Information: contact Dr. Tsou Sheung Tsun Information: 20-25: 3rd International ISAAC Congress, (EWM01), Mathematical Institute, 24-29 St e-mail: [email protected] Berlin, Germany Giles, Oxford OX1 3LB, UK, Web site: http://ifip2001.uni-trier.de Theme: Analysis fax: +44-1865-273583 [For details, see EMS Newsletter 38] Aim: to promote and advance analysis, its appli- Web site: http://www.maths.ox.ac.uk/~ewm01/ cations, and its interaction with computation August 2001 Scope: real, complex, hypercomplex analysis, 27-31: Equadiff 10, Czechoslovak International potential theory, differential geometry, differen- Conference on Differential Equations and their tial equations, operator theory, applied and Applications, Prague, Czech Republic 5-18: BALTICON 2001, Banach Algebra numerical analysis, computation Information: Theory in Context, Krogerup Hojskole, Main speakers: N. S. Bakhvalov and M. E. Eglit e-mail: [email protected] Humlebaek, Denmark (Moscow), A. D. Bruno (Moscow), M. Essén Web site: www.math.cas.cz/~equadiff/ Information: (Uppsala), P. Kuchment (Wichita), V. Maz’ya [For details, see EMS Newsletter 38] e-mail: [email protected] (Linkoeping), S. M. Nikol´skii (Moscow), T. Web site: http://www.math.ku.dk/conf/balticon Nishitani (Osaka), I. Prigogine and I. Antoniou September 2001 2001/ (Brussels), S. Saitoh (Kiryu), M. Singer (Raleigh), [For details, see EMS Newsletter 38] D. Tataru (Evanston) Sessions: function spaces and fractional calculus, 1-6: Number Theory and Arithmetical 5-18: Groups St Andrews 2001, Oxford, UK asymptotic decomposition (methods of small Geometry: Arithmetic Aspects of Fundamental Information: parameters, averaging theory), integral trans- Groups, Acquafredda di Maratea (near e-mail: [email protected] forms and applications, analytic functionals, Naples), Italy Web site: http://www.bath.ac.uk/~masgcs/gps01/ hyperfunctions, and generalised functions, geo- Topics: arithmetic aspects of Galois groups, [For details, see EMS Newsletter 36] metric function theory, complex function spaces, higher class field theory and generalisations, value distribution theory and complex dynamics; algebraic fundamental groups of schemes, 12-18: 39th International Symposium on Clifford analysis, octonions; non-linear potential motivic Galois groups, Galois action on funda- Functional Equations, Denmark theory, classical and fine potential theory, holo- mental groups, motivic structures on fundamen- Organising committee: Peter Friis and Henrik morphic and finely holomorphic functions; dif- tal groups, the anabelian programme Stetkaer (Aarhus University) ferential geometry and control theory for PDEs, Scope: recent progress in understanding arith- Information: differential geometry and quantum physics; sin- metic structures on algebraic fundamental e-mail: [email protected] gular boundary value problems for ODEs, groups of schemes and related topics – in partic- Web site: http://www.mi.aau.dk/isfe39/ dynamical systems, attractors for PDEs, spectral ular, number-theoretic aspects of the theory of theory of differential operators, pseudodifferen- algebraic fundamental groups of schemes, where 12-19: Summer School 2001 Homological tial operators, quantisation and signal analysis, much progress has been made in recent years Conjectures for Finite Dimensional Algebras, integral equations and pseudodifferential equa- Main speakers: Pierre Debes (France), Pierre Nordfjordeid, Norway tions, microlocal analysis, complex and function- Deligne (USA), Ido Efrat (Israel), Ivan Fesenko Information: contact Øyvind Solberg (oyvin- al analytic methods in PDEs, geometric proper- (UK), Jean-Marc Fontaine (France), Gerhard [email protected], NTNU, Trondheim) ties of solutions of PDEs, qualitative properties Frey (Germany), Sasha Goncharov (USA), Web sites: http://www.mathematik.uni- of solutions of hyperbolic and Schrödinger equa- Yasutaka Ihara (Japan), Uwe Jannsen bielefeld.de/~sek/summerseries.html tions; homogenisation, moving boundaries, and (Germany), Pierre Lochak (France), Makoto http://www.math.ntnu.no/~oyvinso/ porous media, constructive methods in applied Matsumoto (Japan), Hiroaki Nakamura (Japan), Nordfjordeid/ problems, hysteresis problems in applications, Michel Raynaud (France), Mohamed Saidi (UK), [For details, see EMS Newsletter 38] pattern formation, waves in complex media, Alexander Schmidt (Germany), Leila Schneps non-linear waves, mathematical analysis of prob- (France), Michael Spiess (UK), Akio Tamagawa 18-24: Convex Geometric Analysis, Anogia, lems in solid mechanics, direct and inverse scat- (Japan), Isabelle Vidal (France), Kay Wingberg Crete tering, inverse problems, inverse problems in (Germany), Zdzislaw Wojtkowiak (France), Main speakers: K. Ball (London), I. Barany medicine, mathematical methods in non- Leonardo Zapponi (Germany) (Hungarian Academy of Sciences), P. Gruber destructive evaluation and non-destructive test- Organising committee: Chair: Anthony J. Scholl (Vienna), A.Koldobsky (Missouri, U.S.A.), A. ing, stochastic processes, mathematical biology; (Durham, UK), Vice-Chair: Michael Spiess Pajor (Marne La Vallee, France), G. Schechtman numerical methods for PDEs, systems and opti- (Nottingham, UK) (Israel), S. Szarek (U.S.A.) misation, the analysis and computation of com- Grants: available for younger scientists – in par- Coorganiser: University of the Aegean plex systems, wavelets, computer algebra and ticular, those from less favoured regions in (Department of Mathematics) computer analysis Europe; limited funding for participants from Organisers: A. Giannopoulos (Crete), V.Milman Languages: for presentations, English, French, Central and Eastern Europe is also available (Tel Aviv), R.Schneider (Freiburg), S. Szarek German, or Russian; for Proceedings, English Notes: open to researchers world-wide, whether (U.S.A./Paris) Programme and organising committee: ISAAC from industry or academia. Participation is limit- Information: contact Susanna Papadopoulou, Board ed to 100. The emphasis will be on discussion Department of Mathematics, University of Crete, Grants: some ISAAC Awards are available for about new developments 71409 Heraklion, Crete, Greece, fax: 81-393881 younger scientists (below age 40) in analysis, its Deadline: for applications, already passed e-mail: [email protected] applications and computation Information: contact Dr. J. Hendekovic, Sponsors of the awards: Siemens, European Science Foundation, 1 quai Lezay- 19-25: 9th Prague Topological Symposium, DaimlerChrysler, Motorola, Berlin Mathematical Marnesia, 67080 Strasbourg Cedex, France, tel: International Conference on General Topology Society +33 388 76 71 35, fax: +33 388 36 69 87 and its Relations to Analysis and Algebra, Proceedings: contributions to proceedings not e-mail: [email protected] Prague, Czech Republic exceeding 10 pages should be sent before 1 Web site: http://www.esf.org/euresco/01/ Information: November to [email protected] pc01109a.htm

26 EMS June 2001 CONFERENCES 2-6: First SIAM-EMS Conference: Applied Function Spaces, Wroclaw, Poland [For details, see EMS Newsletter 39] Mathematics in our Changing World, Berlin, Information: Germany Web site: www.im.pwr.wroc.pl/~fsp/ 18-22: Euro Summer School on Proper Group Scope: the conference will not only have a sci- e-mail: [email protected] Actions, Bellaterra, Barcelona entific impact, but also an impact on the com- [For details, see EMS Newsletter 39] Information: munity of applied mathematicians in Europe Web site: http://www.crm.es/group-actions and North America. The major feature of the 5-7: LMS Workshop on Domain [For details, see EMS Newsletter 39] conference is to show that applied mathematics Decomposition Methods in Fluid Mechanics, is much more than just the classical application Greenwich, UK 19-22: International Conference on Algebraic towards classical engineering, like for example Information: Geometry and Singularities, Sevilla, Spain fluid dynamics or structural mechanics. Hence Web site: http://cms1.gre.ac.uk/conferences [in honour of Professor José Luis Vicente an emphasis will be on modern applications in [For details, see EMS Newsletter 39] Córdoba, on his 60th birthday] life sciences (medicine, biotechnology), materi- Main speakers: S. Abhyankar (USA), J. M. als sciences, nanoscale technology, and commu- 12-14: Seventh Meeting on Computer Algebra Aroca (Spain), J. Bueso (Spain), A. Campillo nication and Applications (EACA-2001) (Spain), E. Casas (Spain), A. Holme (Norway), Topics: medicine, biotechnology, materials sci- Information: S. González (Spain), J. Giraud (France), G-M. ence, environmental science, nanoscale tech- e-mail: [email protected] Greuel (Germany), K. Kiyek (Germany), Le nology, communication, traffic, market and Web site: Dung Trang (France), I. Luengo (Spain), O. A. finance, speech and image recognition, engi- http://www.unirioja.es/dptos/dmc/eaca2001/ Laudal (Norway), M. Lejeune-Jalabert (France), neering design. These include mathematical [For details, see EMS Newsletter 39] F. Loeser (France), Z. Mebkhout (France), T. T. subjects like PDE analysis and modelling, com- Moh (USA), V. Navarro (Spain), T. Recio plex coupled PDE systems, optimal control of 12-15: EuroConference on Combinatorics, (Spain), T. Sánchez (Spain), B. Teissier PDEs and heterogeneous systems, variational Graph Theory and Applications, Bellaterra, (France), A. Todorov (USA), F. Topsoe principles, inverse problems, stability and Barcelona (Denmark), O. Villamayor (Spain) bifurcation analysis, PDE computational finite Information: Programme committee: F. J. Castro Jiménez, element methods, spatial and temporal Web site: http://www.crm.es/comb01 L. Narváez Macarro, E. Briales Morales, P. homogenisation, spatial statistics, stochastic [For details, see EMS Newsletter 39] Pisón Casares geometry, interacting particle systems, stochas- Organising committee: F. J. Castro Jiménez, tic analysis, multiscale analysis and algorithms, 14-18: International Conference: Function L. Narváez Macarro, E. Briales Morales, F. J. multigrid and domain decomposition, wavelets, Spaces, Proximities and Quasi-uniformities, Herrera Govantes, R. Piedra Sánchez, P. Pisón turbulence modelling Italia, Caserta Casares Main speakers: medicine: Alfio Quarteroni [on the occasion of Som Naimpally’s 70 birth- Site: Facultad de Matemáticas. Avda. Reina (I/CH); biotechnology: Michael Waterman day] Mercedes, s/n. 41012 SEVILLA (USA); materials science: Jon Chapman (USA Information: Grants: probably support for young mathe- /UK); environmental science: Andrew Majda e-mail: [email protected] maticians (USA); nanoscale technology: Michael Griebel Web site: http://www.unina2.it/topological.sun/ Deadlines: registration by 20 July (D); communication: Martin Grötschel (D); homesun.html Information: traffic: Kai Nagel (CH); market and finance: e-mail: [email protected] Benoit Mandelbrot (USA); speech and image 16-22: Conference of the Austrian Web site: http://www.us.es/da/ recognition: Pietro Perona (USA); engineering Mathematical Society and the German design: Thomas Y. Hou (USA) Mathematical Society, Vienna, Austria 24-28: Fourth European Conference on Programme: 10 plenary lectures, about 20 Information: Elliptic and Parabolic Problems: minisymposia, contributed talks, poster ses- e-mail: [email protected] Applications, Gaeta, Italy sions, round table discussions, multimedia and Web site: http://www.mat.univie.ac.at/~oemg/ Information: software presentations, satellite activities Tagungen/2001/index.html e-mail: [email protected], Conference chairs: Gilbert Strang (MIT, [For details, see EMS Newsletter 39] [email protected] Cambridge), Rolf Jeltsch (ETH, Zürich), Peter Web site: http://www.math.unizh.ch/rolducgaeta Deuflhard (ZIB, Berlin) 17-21 Euroconference on Asymptotic [For details, see EMS Newsletter 38] Programme committee: Peter Deuflhard Methods and Applications in Kinetic and (Chair, Berlin), Heinz Engl (Austria), Björn Quantum-Kinetic Theory, Granada, Spain 24-28: III International Conference, Analytic Engquist (Stockholm), Stefan Müller Theme: partial differential equations and Probabilistic Methods in Number (Germany), David Levermore (USA), Volker Topics: kinetic and quantum-kinetic equations, Theory, Palanga, Lithuania Mehrmann (Germany), Bill Morton (Great nonlinear drift-diffusion models and entropy [in honour of J. Kubilius] Britain) methods, granular media flows, biology appli- Information: Organising committee: Eberhard Bänsch cations, non-linear dynamics in low-dimension- e-mail: [email protected] (WIAS), Peter Deuflhard (Chair), Herbert al semiconductors structures, quantum molecu- Web site: http://www.mif.vu.lt/ttsk/palanga.htm Gajewski (WIAS), Hans-Christian Hege (ZIB), lar chemistry, stochastic differential equations, [For details, see EMS Newsletter 39] Matthias Holschneider (Uni Potsdam), Peter astrophysics, cometary flows, combustion Imkeller (HU Berlin), Rupert Klein (PIK), Ralf Main speakers: A. Bobylev, J. Brey, E. Carlen, June 2002 Kornhuber (FU Berlin), Jens Lang (ZIB), C. Cercignani, L. Desvilletes, M. Fischetti, P. Roswitha März (HU Berlin), Volker Mehrmann Gerard, R. Glassey, F. Golse, K. P. Hadeler, A. (TU Berlin), Rolf H. Möhring (TU Berlin), P. Jauho, C. Joulin, A. Linan, A. Marquina, E. 10 - 16: Aarhus Topology 2002, University of Ulrich Nowak (ZIB), Konrad Polthier (TU Oran, G. Papanicolaou, F. Poupaud, M. Aarhus, Aarhus, Denmark Berlin), Werner Römisch (HU Berlin), Christof Pulvirenti, P. Souganidis, W. Strauss, L. Vega, Theme: algebraic topology Schütte (FUB), Jürgen Sprekels (WIAS), Fredi J. J. L. Velazquez, C. Villani, W. Zimmermann Main speakers: include Raoul Bott (USA), Tröltzsch (TU Berlin) Organising committee: J. Soler (Chair, Spain), Ralph Cohen (USA), Yakov Eliashberg ((USA), Site: the Free University of Berlin and the L. L. Bonilla (Spain), J. L. Vazquez (Spain) Jesper Grodal (USA), Karsten Grove (USA), Konrad-Zuse-Zentrum (ZIB) in Berlin-Dahlem Sponsors: European Commission, Spanish Lars Hesselholt (USA), Mike Hopkins (USA), Grants: some funding may be available from Government, Junta de Andalucia, Universidad Wolfgang Lück (Germany), Mike Mandell the German Scientific Foundation, the Carlos III de Madrid, Universidad Autonoma (USA), Fabien Morel (France), Bob Oliver European Commission, the EMS, and possibly de Madrid, Universidad de Granada (France), Erik K. Pedersen (USA), Zoltan Szabo UNESCO-ROSTE: see web site for how to Site: Palacio de Congresos (USA), Ulrike Tillmann (UK), Vladimir Turaev apply Deadlines: for abstracts, passed (France) Deadlines: for submission of abstracts and Information: Organising committee: Johan Dupont (Chair, posters, 30 June; for submission of applications e-mail: [email protected] University of Aarhus), Hans Jørgen Munkholm for financial support, already passed (for Web site: www.ugr.es/local/kinetic/eurokit (SDU, Odense University), Lars Hesselholt Eastern European countries), 30 June (for EU- (MIT, USA), Lisbeth Fajstrup (Aalborg Member states or EU-associated states) 17-26: Functional Analysis VII, Dubrovnik, University) Information: Croatia Deadline: for registration, to be announced at Web site: http://www.zib.de/amcw01 Information: the web site e-mail: [email protected] e-mail: [email protected] Information: Web page: Web site: http://www.math.auc.dk/~fajstrup/ 3-8: Sixth International Conference on http://www.math.hr/~congress/Dubrovnik01/ AT2002/

EMS June 2001 27 CONFERENCES OberwolfachOberwolfach PPrrogrammeogramme 20022002 Mathematisches Forschungsinstitut Oberwolfach Lorenzenhof, D-77709 Oberwolfach-Walke, Germany

Names of organisers are in square brackets. [Frank Allgöwer (Stuttgart), Huibert 9-15 June: Renormalization Group Participants at the Oberwolfach meetings are Kwakernaak (Twente)] [David Brydges (Virginia), Horst Knörrer invited personally by the director of the institute. 3-9 March: Miniworkshops (Zürich), Manfred Salmhofer (Leipzig)] Participation is subject to such an invitation. (Hints for applications: see above) 16-22 June: Geometric Convex Interested researchers, in particular young 10-16 March: Probability and Statistics Combinatorics mathematicians, can contact the administration of Random Algebraic Structures [Bert Gerards (Amsterdam), Andras Sebö of the institute. Since the number of participants [Jean-Dominique Deuschel (Berlin), Persi (Grenoble), Robert Weismantel is restricted, not all inquiries can be considered. Diaconis (Stanford), Friedrich Götze (Magdeburg)] Mini-Workshops offer to about 15 participants (Bielefeld)] 23-29 June: Miniworkshops the possibility to meet in Oberwolfach. The sup- 17-23 March: Reelle Algebraische und 30 June-6 July: Calculus of Variations port is the same as for the normal meetings: the Analytische Geometrie [Gianni Dal Maso (Trieste), Gero Institute covers all living expenses, but travel [Eberhard Becker (Dortmund), Ludwig Friesecke (Oxford), Tristan Riviere costs cannot be paid. The Mini-Workshops Bröcker (Münster), Michel Coste (Cachan/Paris)] should be research oriented. The aims could be (Rennes)] 7-13 July: Arithmetic and Differential to learn together an attractive new development 24-30 March: Nichtkommutative Galois Groups or to study a specific problem. The deadline for Geometrie [David Harbater (Philadelphia), B. applications is half a year before the date of the [Alain Connes (Paris), Joachim Cuntz Heinrich Matzat (Heidelberg), Marius van Mini-Workshop. Applications should contain a (Münster), Marc A. Rieffel (Berkeley)] der Put (Groningen)] description of the planned activity and the list of 31 March-6 April: Arbeitsgemeinschaft 14-20 July: Reelle Analysis participants. They can be sent at any time. mit aktuellem Thema [Detlef Müller (Kiel), Elias M. Stein Information is also available on the web site (wird in Heft 1/2002 der DMV- (Princeton), Hans Triebel (Jena)] http://www.mfo.de. Mitteilungen bekannt gegeben) 21-27 July: Nonlinear and Stochastic 7-13 April: Mathematische Logik Systems and Their Numerics Meetings [Yiannis N. Moschovakis (Los Angeles), [Michael Dellnitz (Paderborn), Wolfgang Helmut Schwichtenberg (München), Anne Kliemann (Ames), Edwin Kreuzer 6-12 January: Combinatorics S. Troelstra (Amsterdam)] (Hamburg-Harburg), Sri Namachchivaya [Laszló Lovász (New Haven), Hans Jürgen 14-20 April: Interactions between (Urbana)] Prömel (Berlin)] Algebraic Geometry and 28 July-3 August: Dynamical System 13-19 January: Optimization and Noncommutative Algebra Methods in Fluid Mechanics Applications [Dieter Happel (Chemnitz), Lance T. [Jerrold E. Marsden (Pasadena), Jürgen [Florian Jarre (Notre Dame), Claude Small (La Jolla), J. Toby Stafford (Ann Scheurle (München)] Lemarechal (Saint Ismier), Jochem Zowe Arbor), Michel Van den Bergh (Hasselt)] 4-10 August: Algebraische K-Theorie (Erlangen)] 21-27 April: Curvature and Dispersion [Dan Grayson (Urbana), Uwe Jannsen 20-26 January: Mengenlehre Effects in Nonlinear Partial Differential (Regensburg), Bruno Kahn (Paris)] Sy Friedman (Wien), Ronald Jensen Equations 11-17 August: Mathematical Methods in (Berlin), Menachem Magidor (Jerusalem), [Carlos E. Kenig (Chicago), Herbert Koch Tomography Hugh Woodin (Berkeley)] (Dortmund), Daniel Tataru (Evanston)] [F. Alberto Grünbaum (Berkeley), Alfred 27 January-2 February: Singularities and 21-27 April: Discontinuous Galerkin K. Louis (Saarbrücken), Frank Natterer Concentration Phenomena in Nonlinear Methods (Münster)] Elliptic and Parabolic PDEs [Dietmar Kröner (Freiburg), Christoph 18-24 August: Mathematical Theory and [Henri Berestycki (Paris), Bernhard Schwab (Zürich), Endre Süli (Oxford)] Modelling in Atmosphere-Ocean-Science Kawohl (Köln), Yanyan Li (Rutgers)] 28 April-4 May: Enveloping Algebras [Rupert Klein (Berlin), Andrew J. Majda 3-9 February: Orders in Arithmetic and and Algebraic Lie Representations (New York)] Geometry [Walter Borho (Wuppertal), Michel Duflo 25-31 August: Komplexe Analysis [Jürgen Ritter (Augsburg), Martin J. (Paris), Anthony Joseph (Paris/Revohot), [Jean-Pierre Demailly (Grenoble), Klaus Taylor (Manchester)] Rudolf Rentschler (Paris)] Hulek (Hannover), Thomas Peternell 3-9 February: The Arithmetic of Fields 5-11 May: Mechanics of Materials (Bayreuth)] [Wulf-Dieter Geyer (Erlangen), Moshe [Reinhold Kienzler (Bremen), David 1-7 September: Groups and Geometries Jarden (Tel Aviv)] McDowell (Atlanta), Ewald Werner [Michael Aschbacher (Pasadena), William 10-16 February: Stochastic Geometry, (München)] M. Kantor (Eugene), Franz-Georg Spatial Statistics and Statistical Physics 12-18 May: Quadratic and Hermitian Timmesfeld (Gießen)] [Adrian J. Baddeley (Nedlands), Dietrich Forms 8-14 September: Fundamental Groups in Stoyan (Freiberg), Wolfgang Weil [Detlev Hoffmann (Besancon), Alexandr Geometry (Karlsruhe)] Merkurjev (Los Angeles), Jean-Pierre [Fedor A. Bogomolov (New York), Jürgen 17-23 February: Positivität von Tignol (Louvain-la-Neuve)] Jost (Leipzig), Mina Teicher (Ramat-Gan), Polynomen 19-25 May: Oberwolfach-Seminars Michael Zaidenberg (Saint-Martin- [Eberhard Becker (Dortmund), Christian 26 May-1 June: Classical Algebraic d’Heres)] Berg (Kobenhavn), Alexander Prestel Geometry 15-21 September: Homotopietheorie (Konstanz)] [David Eisenbud (Berkeley), Joe Harris [Mike Hopkins (Cambridge), Karlheinz 17-23 February: Functional Analytic and (Cambridge), Frank-Olaf Schreyer Knapp (Wuppertal), Erich Ossa Complex Analytic Methods in the (Bayreuth)] (Wuppertal)] Theory of Linear PDEs 2-8 June: Geometric Analysis and 22-28 September: Topologie [Reinhold Meise (Düsseldorf), B. Alan Singular Spaces [Cameron Gordon (Austin), Wolfgang Taylor (Ann Arbor), Dietmar Vogt [Jean-Michel Bismut (Orsay), Jochen Lück (Münster), Bob Oliver (Paris)] (Wuppertal)] Brüning (Berlin), Richard B. Melrose 29 September-5 October: Geometrie 24 February-2 March: Regelungstheorie (Cambridge)] [Victor Bangert (Freiburg), Yuri Burago 28 EMS June 2001 CONFERENCES Mathematical Challenges of Molecular Biology Andreas Dress (Bielefeld), Peter Schuster (Wien) and Gönter Wagner (Yale) 11-17 November 2001, Deadline for application: 1 October Subjects: Molecular biology is currently undergoing a technological revolution. As more and more genomic and structural data become available, fundamental ques- tions about evolution, sequence-structure relations and functional genomics can be studied for the first time in a quantitative way, allowing for computer simulation and mathematical analysis. The new develop- ments involve many mathematical fields, including dynamical systems, combina- torics, random graph theory and evolution (St Petersburg), Ulrich Pinkall (Berlin)] Noncommutative Geometry in random media, topology and Fourier 6-12 October: Arbeitsgemeinschaft mit Alain Connes (Paris) analysis. Specific topics will include: old aktuellem Thema 14-20 October 2001, and new models of phylogenetic evolution (wird in Heft 3/2002 der DMV- Deadline for application: 1 September and their underlying mathematical struc- Mitteilungen bekannt gegeben) Subjects: We describe basic concepts of non- ture; sequence-structure relations of bio 13-19 October: Oberwolfach-Seminars commutative geometry and a general con- polymers, based on the concepts of combi- 20-26 October: Mathematische struction that extends the familiar duality natory maps and landscapes; analysis of Methoden der Geometrischen between ordinary spaces and commutative the genotype-phenotype map and model- Datenverarbeitung algebras to a duality between quotient ing of gene interaction (space configura- [Carl de Boor (Madison), Helmut spaces and noncommutative algebras. The tion topology and their Fourier decompo- Pottmann (Wien), Ulrich Reif basic tools of the theory, K-theory, cyclic sition; continuum effect models). (Darmstadt)] cohomology, Morita equivalence, opera- Prerequisites: This seminar is open to all 27 October-2 November: Stochastic tor-theoretic index theorems and Hopf mathematicians interested in questons Analysis algebra symmetry are reviewed. We dis- arising from molecular biology. Working [Gerard Ben Arous (Lausanne), Jean- cuss the foundational problem of ‘what is a knowledge of combinatorics and some Dominique Deuschel (Berlin), Ofer manifold in NCG?’ and explain the funda- basic ideas about combinatorial algorithms Zeitouni (Haifa)] mental role of Poincaré duality in K- and dynamical systems. References: A. 3-9 November: Miniworkshops homology which is the basic reason for the Dress, W. Terhalle, ICM 98, pp. 565-574 10-16 November: Oberwolfach-Seminars spectral point of view. http://www.mathematik.uni-bielefeld.de/docu 17-23 November: Lehrerfortbildung This leads us, when specializing to 4- menta/xvol-icm/16/16.html 24-30 November: Combinatorial geometries to a universal algebra called P. Schuster, Math Unlimited, Springer, Optimization the ‘Instanton algebra’ (joint work with G. 2001, pp. 1019-1038, and additional liter- [Thomas M. Liebling (Lausanne), Rolf Landi). We describe examples of noncom- ature available frpom http://www.tbi.univie. Hermann Möhring (Berlin), Uwe T. mutative manifolds and develop the basic ac.at/papers/ Zimmermann (Braunschweig)] notions of curvature and spectral action. 1-7 December: New Trends in Boundary We show that any compact Riemannian Front Propagation, Homogenization for Elements spin manifold whose isometry group has First- and Second-Order PDE and [Jean-Claude Nedelec (Palaiseau), rank r > 1 admits isospectral deformations Applications Christoph Schwab (Zürich), Ernst P. to noncommutative geometries. We give a Guy Barles (Tour) and Panagiotis Stephan (Hannover), Wolfgang L. survey of other recent developments, in Souganidis (Austin) Wendland (Stuttgart)] particular from joint work with H. 11-17 November 2001, 8-14 December: Algorithmische Moscovici and D. Kreimer. Deadline for application: 1 October Graphentheorie Subjects: Models in phase transitions and [Derek Corneil (Toronto), Klaus Jansen Numerical Methods for Free Boundary combustion give rise to interfaces moving (Kiel), Ingo Schiermeyer (Freiberg)] Problems with prescribed normal velocities. The 15-21 December: Thermodynamische Gerhard Dziuk (Freiburg) and Ricardo theory of viscosity solutions provides a very Materialtheorien Nochetto (Maryland) good framework for the rigorous analysis [Kolumban Hutter (Darmstadt), Ingo 14-20 October 2001, of such models. Asymptotic problems in Müller (Berlin)] Deadline for application: 1 September periodic and random environments are Subjects: Free boundary problems arise in a also related to homogenization questions Seminars variety of applications from phase transi- for first- and second order pde, as well as tions (crystal growth or continuous casting) to stochastic nonlinear pde. Topics to be OBERWOLFACH-SEMINARS 2001 to geometry (curvature-driven motion of covered in the course are: These seminars are a continuation of the DMV- surfaces or curves). This course will pro- (i) a theory for generalized front propaga- Seminars initiated by Deutsche Mathematiker vide an introduction to mathematical mod- tion and its applications to asymptotic Vereinigung. They address postdocs and PhD els for free boundary problems and to the problems, reaction diffusion equations students from all over Europe. The aim is to design and numerical analysis of algo- and particle systems, turbulent combus- introduce the participants to a particular new rithms. Topics will include numerical tion; development. The seminars take place at the methods for isotropic and anisotropic (ii) homogenization theory for Hamilton- Mathematisches Forschungsinstitut Oberwol- mean curvature flow (parametric model Jacobi equations and fully nonlinear sec- fach and the number of participants is restricted and level set model), as well as for varia- ond-order pde and its connections to to 25. Applications, including a short summa- tional inequalities and degenerate parabol- phase transitions and Hamiltonian ry of previous work and interest, should be sent ic equations (with emphasis on error con- dynamics; to Prof. Dr. Matthias Kreck, Universität trol and adaptivity). (iii) fully nonlinear stochastic pde. Heidelberg, Mathematisches Institut, Im Prerequisites: Basic knowledge of theory Prerequisites: A good background in pde; Neuenheimer Feld 288, 69120 Heidelberg, and numerics for partial differential equa- some probability knowledge will also be Germany. tions. useful, but is not required. EMS June 2001 29 RECENT BOOKS Edinburgh in July 1999. The Congress was jointly organised by the Institute of Mathematics and its Applications and the International Centre for Mathematical RecentRecent booksbooks Sciences, with involvement from the edited by Ivan Netuka and Vladimír Sou³ek Mathematics Departments at Edinburgh Univpersity and Heriot-Watt University. Over 1700 applied mathematicians from 66 Books submitted for review should be sent to the graduate lecture course. Part II shows how countries attended the Congress. The pro- following address: these results may be generalised to homeo- gramme for the half-day sessions normally Ivan Netuka, MÚUK, Sokolovská 83, 186 75 morphisms of a compact manifold that pre- consisted of two plenary lectures in parallel, Praha 8, Czech Republic. serve a certain finite measure. The second followed by two-hour parallel sessions of type of generalisation of the result of Oxtoby mini-symposia and contributed talks. In The reviews of the books by H. Krause and C. M. and Ulam, covered in Part III, concerns addition to the 31 plenary lectures, 250 Ringel, and J.-E. Rombaldi, appeared in EMS results without a compactness assumption mini-symposia, 400 contributed papers and Newsletter 39 with incorrect titles. The editor apol- for the underlying manifold, and the con- 60 poster presentations were given. ogises for this unfortunate mistake. comitant consideration of infinite preserved The proceedings includes texts of plenary measures. A fuller description of the lectures covering a wide range of topics in R. P. Agarwal, M. Meehan and D. O’Regan: authors’ work on non-compact manifolds applied and industrial mathematics, ranging Fixed Point Theory and Applications, appears in the Introduction to Part III. from the familiar areas of solid and fluid Cambridge Tracts in Mathematics 141, This monograph will be very valuable for mechanics and scientific computation to Cambridge University Press, Cambridge, 2001, anybody interested in ergodic or measure newer subjects such as financial mathematics 170 pp., £37.50, ISBN 0-521-80250-4 theory. (knaj) and the internet. Also included are sum- This excellent book provides a clear exposi- maries of the mini-symposia, details of prizes tion of the flourishing field of fixed point B. K. Bagchi, Supersymmetry in Quantum awarded, a list of participants, and texts of theory. The reader will find applications to and Classical Mechanics, Monographs and the addresses at the opening ceremony. many areas of current interest in analysis. Surveys in Pure and Applied Mathematics 116, This is an important summary of topical The book consists of 12 chapters, and prob- Chapman & Hall/CRC, Boca Raton, 2001, 222 and applicable mathematics from the lems of varying difficulty are given at the end pp., £49.99, ISBN 1-58488-197-6 world’s leading authorities in the subject. It of each chapter. The very extensive bibliog- The aim of this book is to describe the main will be an inspiration for graduate students raphy lists 191 items. lines of developments that have taken place and researchers. (knaj) The book starts from the basics of in super-symmetric quantum and classical Banach’s contraction theorem and mechanics (SUSYQM and SUSCM) in recent H. Bart, I. Gohberg and A. C. M. Ran Schauder’s theorem for non-expansive years. In Chapter 2, the basic principles of (eds.), Operator Theory and Analysis. The M. maps. Fixed point results are established for SUSYQM are outlined, starting with the har- A. Kaashoek Anniversary Volume, Operator several classes of maps: single-valued maps monic oscillator problem. A fairly complete Theory Advances and Applications 122, in finite- and infinite-dimensional Banach presentation of the mathematical tools asso- Birkhäuser, Basel, 2001, 433 pp., DM 238, spaces, non-self maps, multivalued map- ciated with SUSYQM are given, together ISBN 3-7643-6499-8 pings, and maps defined on Hausdorff local- with potential applications of the theory and This volume contains the proceedings of the ly convex linear topological spaces. The self-contained introduction to superspace international workshop at the Vrije three main approaches to establishing con- formalism. In Chapter 3, SUSYCM is con- Universiteit, Amsterdam, on the occasion of tinuation principles are also presented. A sidered and studied in the framework of the sixtieth birthday of M. A. Kaashoek, one chapter on degree theory concludes the vol- generalised Poisson brackets and quantisa- of the leading experts in operator theory ume. tion rules. The concept of SUSY breaking and its applications. The workshop focused This nicely written book presents an and the Witten index is developed in on areas in mathematical and functional extensive survey of the area and will Chapter 4, where the relevance of the analysis, where his ideas and results played undoubtedly be very valuable for researchers notions such as finite temperature SUSY, an important role. and graduate students in applicable analysis. regulated Witten index and quantum group The book starts with articles describing the (knaj) deformation of oscillator algebras is dis- life and mathematical achievements of cussed in more detail. Chapter 5 offers an Kaashoek and a list of his publications. The S. R. Alpern and V. S. Prasad, Typical elaborated treatment of factorisation meth- main part of the book consists of original Dynamics of Volume Preserving ods, shape invariance condition, and gener- research papers containing new and inter- Homeomorphisms, Cambridge Tracts in ation of solvable potentials. Chapter 6 deals esting results. The proceedings contains the Mathematics 139, Cambridge University Press, with the radial problem and spin-orbit cou- sixteen main contributions presented at the Cambridge, 2001, 216 pp., £30, ISBN 0-521- pling and in Chapter 7, applications of workshop. These papers cover a wide range 58287-3 SUSY to non-linear systems and a method of of topics centred around factorisation of This monograph covers the authors’ work constructing supersymmetric KdV equation matrix-valued functions, interpolation theo- over the past twenty-five years on generalisa- are discussed. Parasupersymmetry and ry and spectral theory. Other papers deal tions of classical results of John Oxtoby and some of its models are addressed in Chapter with canonical systems of differential equa- Stan Ulam on the typical dynamical behav- 8, including those obtained from truncated tions, operators in indefinite inner-product iour of manifold homeomorphisms preserv- oscillator algebra. Finally, in the Appendix, spaces, and the effect of small delays on sta- ing a fixed measure. Examples of properties a mathematical treatment of the derivation bility and control of partial differential equa- of homeomorphisms considered include of the form of the D-dimensional tions. The book will be a useful guide for a transitivity, chaos and ergodicity. A key idea Schrödinger equation is broadly outlined. wide range of readers in pure and applied here is the interrelation among typical prop- (pso) mathematics and engineering. (knaj) erties of volume-preserving bijections of the underlying measure space. J. M. Ball and J. C. R. Hunt (eds.), ICIAM R. Berndt, An Introduction to Symplectic The book is divided into three parts. The 99. Proceedings of the Fourth International Geometry, Graduate Studies in Mathematics 26, authors make the first part very concrete by Congress on Industrial and Applied American Mathematical Society, Providence, considering volume-preserving homeomor- Mathematics, Edinburgh, Oxford University 2001, 195 pp., US$36, ISBN 0-8218-2056-7 phisms of the unit n-dimensional cube. Press, Oxford, 2000, 336 pp., £65, ISBN 0-19- Symplectic geometry is a broad and well- They prove fixed point theorems of Conley- 850514-0 developed subject with numerous and strong Yehnder-Franks) in a number of short self- This volume presents the proceedings of the ties to other fields of mathematics. This contained chapters, which would be suitable Fourth International Congress on Industrial book offers a systematic exposition of sym- for an undergraduate analysis seminar or a and Applied Mathematics, held in plectic geometry for graduate students with 30 EMS June 2001 RECENT BOOKS a basic knowledge in algebra and analysis. It interpretation of the affine Toda field theo- Edinburgh in 1998. They consist mostly of is a translation of the book published (in ry as a 2+1-dimensional model with discrete surveys given by plenary speakers at this German) by the publishing house Vieweg in second space coordinate is described by R. meeting and cover various areas of the sub- 1998. M. Kashaev and N. Y. Reshetikhin. A paper ject. The proceedings of this conference In the introductory chapter, a mathemati- by R. M. Kashaev discusses quantum hyper- provide an excellent introduction to the cal formulation of classical theoretical bolic invariants of knots, and a short note by ideas and methods surrounding these excit- mechanics is summarised for readers with a T. Richter and R. Seiler shows possible ing theories. (ae) mathematical background: symplectic vector applications for the quantum Hall effect. spaces and the symplectic group are intro- The book gives many specific examples of B. Bruce and D. Mond (eds.), Singularity duced and studied from an algebraic point relations between discrete geometry and var- Theory, London Mathematical Society Lecture of view. Symplectic manifolds form the main ious types of (discrete) integrable models. It Note Series 263, Cambridge University Press, topic of the book, and are defined and stud- will be useful for interested readers, both Cambridge, 1999, 440 pp., £29.95, ISBN 0- ied in the second chapter, together with mathematicians and physicists. (vs) 521-65888-8 examples (cotangent bundles, complex pro- The meeting held in 1996 in Liverpool, on jective spaces, Kähler manifolds and coad- J. Boos, Classical and Modern Methods in the occasion of the sixtieth birthday of C. T. joint orbits). Hamiltonian vector fields and Summability, Oxford Mathematical C. Wall, covered a broad range of topics in the Poisson bracket are introduced in the Monographs, Oxford University Press, Oxford, singularity theory. The book contains 23 third chapter, followed by a treatment of 2000, 586 pp., £75, ISBN 0-19-850165-X contributions, many of them giving contact manifolds. The next two chapters This book is in three parts. The first two are overviews of specific subfields of the theory. contain an introduction to the moment map devoted to classical methods and functional- These papers are divided into five main top- and a study of the symplectic reduction; this analytic methods in summability, while the ics – complex singularities, stratifications has many applications and makes it possible last one contains material in which these and equisingularity theory, global singulari- to construct further interesting examples of methods are combined. The book seems to ty theory, singularities of maps, and applica- symplectic manifolds. The last chapter is be the most comprehensive monograph on tions of singularity theory. devoted to quantisation. There are four summability methods and so will be a very The first part contains reviews by K. appendices containing very short summaries valuable source for graduate students inter- Altmann (singularities of toric varieties), W. of facts from other mathematical disciplines ested in the field and for researchers in sum- Ebeling (on Arnold’s strange dualities), G.- needed in the book. Readers are expected mability or in topological sequence spaces. M. Greuel and E. Shustin (geometry of equi- to have a certain knowledge of the theory of As prerequisites, it requires a basic knowl- singular families of curves), E. Looijenga differential equations (the Frobenius theo- edge of linear algebra and function theory, (Knizhnik-Zamolodchikov equations and rem, in particular). combined with some parts of functional cohomology of local systems on the comple- This book is an excellent introduction to analysis. ments of hyperplane arrangements), A. symplectic geometry, carefully written and The book contains a brief self-contained Némethi (signatures of special types of 4- containing many interesting examples and exposition of infinite matrices (Chapter 2) or manifolds) and papers by J. Damon (a topo- comments. It can be recommended to any- required topological notions (Chapters 6 logical proof of a strengthened version of the body interested in this interesting and and 7). The first introductory chapter Varchenko conjecture), J. H. M. Steenbrink important field of mathematics. (jbu) explains the history of summability methods, (calculations of the spectra of isolated singu- and presents basic definitions and notions. larities of complete intersections of certain A. I. Bobenko and R. Seiler (eds.), Discrete Then classical methods are studied: results types) and T. Urabe (constellations of simple Integrable Geometry and Physics, Oxford include the classical Toeplitz-Silvermann singularities on fibres of a deformation of a Lecture Series in Mathematics and Its theorem (also proved later in Chapter 7 by a triangle singularity). In the second part, Applications 16, Clarendon Press, Oxford, 1999, functional analytic method) and other there is a paper by J. P. Brasselet and A. 370 pp., £45, ISBN 0-19-850160-9 results from the first decades and the end of Legrand (differential forms on singular vari- This book is an introduction to a new emerg- the twentieth century. The bibliography eties), two papers by A. A. du Plessis (related ing field of discrete geometry which has very includes 268 items: the list of symbols, sub- to the topological stability theorem), a survey strong ties to the theory of integrable sys- ject index and name index make searching by T. Gaffney and D. Massey (equisingulari- tems, both continuous and discrete, classical the book easy. The book can be recom- ty theory of complex analytic sets and map- and quantum. It is a collection of invited mended for all mathematical libraries, grad- pings) and a paper by M. Tibar (regularity at review papers, both by mathematicians and uate students and researchers in the field. infinity of polynomial functions). The third physicists who collaborated during the (jive) part includes three papers by V. V. Goryunov preparation of the publication. and J. W. Hill (Legendrean knots in R3), A. The book is divided into three parts. The H. W. Braden and I. M. Krichever (eds.), Libgober (Abelian branched covers of the first part concentrates on discrete analogues Integrability. The Seiberg-Witten and projective plane) and O. Saeki and K. of various classes of surfaces and their rela- Whitham Equations, Gordon and Breach Sakuma (elimination of singularities). tions to (smooth and discrete) integrable Publishers, 2000, 276 pp., £47, ISBN 90-5699- Singularities of mappings are represented by systems. It contains contributions written by 281-3 papers by K. Houston (an image-computing A. I. Bobenko, U. Pinkall, U. Hertrich- Integrable systems in mathematics have had spectral sequence), K. Houston and N. Kirk Jeromin, T. Hoffmann, W. K. Schief, A. a long history with ups and downs. The (a classification of germs of maps from Doliwa and P. M. Santini. The second part works of Jacobi, Abel, Riemann and dimension 3 to dimension 4) and two papers contains a discussion of discretisations of Weierstrass led to the solution of a number by W. L. Marar, J. A. Montaldi and M. A. S. classical integrable systems, based on the R- of important integrable problems from Ruas and by T. Fukui (zero-dimensional matrix approach or symmetry concepts for mechanics and physics. Following the invariants for certain types of maps). The difference equations. It consists of contribu- results of Poincaré and de Bruns, integrable part describing applications contains three tions by Y. B. Suris, F. W. Nijhoff and N. systems lacking any group symmetry were papers by P. S. Donelan and C. G. Gibson Kutz. The last part of the book is on quan- perceived as something exotic. This situa- (singular phenomena in kinematics), G. tum integrable systems and covers several tion changed drastically with the discovery of Ishikawa (singularities of developable sur- themes. A paper by J. Kellendonk, N. Kutz soliton theory, inverse scattering techniques faces), and S. Izumiya (singularities of first and R. Seiler contains a discussion of the and Seiberg-Witten theory. Yet, although order PDEs). spectral theory of Schrödinger operators many connections now exist between The book is a representative overview of describing electric particles moving in dis- Seiberg-Witten theory and integrable sys- research in the field. (vs) crete two-dimensional space under the influ- tems, the correspondence still remains poor- ence of a perpendicular magnetic field. A ly understood. E. Casas-Alvero, Singularities of Plane chapter by L. Fadeev and A. Y. Volkov dis- This volume includes contributions to a Curves, London Mathematical Society Lecture cusses quantum integrable models in 1+1- conference on Integrability: the Seiberg- Note Series 276, Cambridge University Press, dimensional discrete space-time. A possible Witten and Whitham equations, in Cambridge, 2000, 345 pp., £29.95, ISBN 0- EMS June 2001 31 RECENT BOOKS 521-78959-1 mathematical or computational exercises. Differential equations is a key subject in This book is devoted to the theory of alge- The third part of the book covers the mod- pure and applied mathematics, engineering, braic curves in the complex projective plane. elling of situations: cafeteria queues, fish biology, and physics. This book provides an Singularities of algebraic varieties form a growth, epidemics, etc. excellent combination of basic ODE theory very interesting and classical field of The book can be used as a course text, as and Maple. (pp) research that combines techniques and view- a source of examples for project work in var- points from different fields, such as algebra, ious mathematical courses, or as a book for M. Demuth, E. Schrohe, B.-W. Schulze and geometry, topology and analysis. The basic students who like to solve mathematical J. Sjöstrand (eds.), Evolution Equations, viewpoint in the book is geometrical, based problems. It is recommended to everybody Feschbach Resonances, Singular Hodge on the concept of infinitely near points on a interested in mathematics. (ml) Theory, Advances in Partial Differential curve. The idea of using such a tool to Equations, 16, Wiley-VCH, Berlin, 1999, 431 describe singularities comes from the work I. Chudinovich and C. Constanda, pp., DM198, ISBN 3-527-40233-0 of M. Noether, and was further developed by Variational and Potential Methods in the This book consists of six papers describing F. Enriques. Most of the results presented Theory of Bending of Plates with Transverse recent progress in several topics concerning here have appeared in the literature, but the Shear Deformation, Monographs and Surveys evolution partial differential equations; all description based on infinitely near points is in Pure and Applied Mathematics 115, Chapman the contributions are self-contained. somewhat new. To read the book, the only & Hall, CRC, Boca Raton, 2000, 236 pp., The first article by G. Lumer studies the prerequisites are a basic knowledge of alge- £46.99, ISBN 1-58488-155-0 asymptotic behaviour of solutions of singular bra and complex analysis. The basic facts, This volume presents the analysis of linear parabolic transition/interaction problems needed throughout the book are summa- models of thin plates which yield the deflec- with distribution or hyperfunction data. The rized in the introductory chapter. tion of the middle section, as in Kirchhoff’s paper by G. Lumer and F. Neubrander is In the first two chapters, the proof of the theory, and account for transverse shear devoted to applications of asymptotic Puiseux theorem on roots of a power series deformation. The authors consider a num- Laplace transform to semigroups generated in two variables is presented. The main alge- ber of boundary value problems concerning by operators whose resolvents have large braic properties can be deduced, including the equilibrium bending of an elastic plate: growth (existence, uniqueness, well-posed- the Weierstrass theorems and geometrical these include the Dirichlet and Neumann ness). The third contribution, by G. Lumer properties of germs of a curve. In the third problems, the problem with mixed bound- and R. Schnaubelt, is on local operator and fourth chapters, the basic ideas of ary conditions, the plate on a generalised methods for linear and semilinear parabolic geometry of infinitely near points are intro- elastic foundation and the model of the plate problems with time-dependent coefficients duced and used to describe the singularities weakened by a crack. Existence, uniqueness in non-cylindrical domains or on networks. of a curve; in particular, the Enriques dia- and stability of weak solutions of variational The well-posedness is characterised by barri- grams and dual graphs are treated here. In formulations of the problems are studied. er conditions which are verified for a large the other chapters, the Plücker formula, a The solutions are sought in the form of plate class of singular domains. computation of the Milnor numbers, and the potentials: the problem is reduced to inte- The second part of the book is devoted to study of linear families of germs of the curve gral equations on the boundary of the more abstract topics connected with pseudo- (including the Bertini theorem) are studied. domain. In the appendix, some basic mate- differential operators. The article by M. In the last chapter, a geometric theory of val- rial on distribution theory and on Sobolev Rouleux is about resonances for a self- uations is presented. Each chapter includes spaces is given. adjoint h-pseudodifferential operator on a sufficient number of exercises. The book will be useful for mathemati- L2(R+)⊕C2 with Dirichlet boundary condi- The book will be useful for graduate stu- cians, theoretical engineers and all interest- tions and a conical intersection of the char- dents as a first step in the study of singulari- ed in mathematical modeling in elasticity. acteristic variety. This problem arises in the ties, and for non-specialists who wish to learn (oj) one-dimensional Born-Oppenheimer the basic facts about singularities of plane approximation of the transitions of nuclei. curves. (jbu) J. H. Davis, Differential Equations with A. Boulet de Monvel and R. Purice present a Maple. An Interactive Approach (CD-ROM variant of the Mourre theory of conjugate K. Chen, P. Giblin and A. Irving, incl.), Birkhäuser, Boston, 2001, 409 pp., operators and its application to various Mathematical Explorations with MATLAB, DM148, ISBN 0-8176-4181-5 and 3-7643- Hamiltonians in a class of Besov spaces. The Cambridge University Press, Cambridge, 1999, 4181-5 typical feature of this approach is the very 238 pp., £15.95, ISBN 0-521-63078-9 and 0- This introduction to differential equations weak assumptions on the regularity of 521-63920-4 features an exciting interactive approach to Hamiltonians. Finally, the contribution of This book is another attempt to use comput- the subject, integrating the basics of ODE B.-W. Schulze and N. Tarkhanov describes ers and mathematical software in basic uni- and the symbolic computation package elliptic complexes of pseudodifferential versity mathematics courses. The computer Maple. The book provides a solid introduc- operators on manifolds with edges. To each system chosen is the package MATLAB, but tion to Maple in parallel with a standard complex there correspond two sequences of no a priori knowledge of this package is ODE course for advanced undergraduate symbols controlling interior ellipticity and assumed. (There is a short introduction to and beginning level graduate students. ellipticity at the edges; in this setting, the MATLAB in Chapter 1.) The aim of the The material covers many topics authors establish the Fredholm property of book is to promote some mathematical skills (Introduction to Maple, Introduction to DE, complexes in weighted Sobolev spaces and to students by solving various mathematical First order equations, Introduction to present the Hodge theory for them. (jmil) problems with the help of MATLAB. numerical methods, Higher order DE, The book is divided into three parts. The Laplace transform methods, Systems of F. J. E. Dillen and L. C. A. Verstraelen first part introduces techniques of MATLAB equations, Stability, Periodic problems, (eds.), Handbook of Differential Geometry, that can be used in the projects later in the Impedances and DE, Partial DE, Vol. I, North-Holland, Amsterdam, 2000, 1054 book. The topics in Part 1 include matrices, Introduction to Maple applications, Plotting pp., US$177.50, ISBN 0-444-82240-2 integers and elementary number theory, with Maple, Maple and Laplace transforms, This book is the first volume of a series curve plotting, data analysis, simulation of Maple linear algebra applications, Runge- whose aim is to give a rather complete survey random number generation and differential Kutta designs, Maple packages, Review of the field of differential geometry. To equations. Each chapter in this part ends problems, Laplace transform table). The realise this project, the editors asked experts with exercises, designed to check knowledge book contains many user-friendly presenta- in specific topics to prepare review papers of the topic and of MATLAB techniques. tions of rigorous mathematics, excellent containing both old and recent research The second part of the book contains a lot of examples, numerous graphical interpreta- results. The authors had freedom in length, projects built on ideas from Part 1 – for tions of solutions, a careful introduction to style and depth, so the volume contains dif- instance, the project Magic squares is an Maple, harder Maple programming pro- ferent types of papers. application of matrices. The projects jects, Maple worksheets, and supplementary Volume I contains contributions by M. A. explore mathematical problems that include material for instructors. Akivis and V. V. Goldberg (Differential 32 EMS June 2001 RECENT BOOKS geometry of webs), D. E. Blair (Spaces of nine chapters, notes and bibliography. ate students and is also suitable as a general metrics and curvature functionals), B.-Y. Chapter 1 is a summary of tools from the self-study resource for professionals in Chen (Riemannian submanifolds), A. theory of orthogonal polynomials of one Fourier analysis. (knaj) Derdzinski (Einstein metrics in dimension variable. In Chapters 2 and 3, the authors four), P. B. Gilkey (The Atiyah-Singer index give various examples of families of orthog- J. Elschner, I. Gohberg and B. Silbermann theorem), U. Lumiste (Submanifolds with a onal polynomials in several variables and (eds.), Problems and Methods in parallel fundamental form), K. Shiohama present their properties. Coxeter groups are Mathematical Physics, Operator Theory (Sphere theorems), U. Simon (Affine differ- treated systematically in a self-contained way Advances and Applications 121, Birkhäuser, ential geometry), G. Thorbergsson (A survey in Chapter 4. A key part of this chapter are Basel, 2000, 523 pp., DM248, ISBN 3-7643- on isoparametric hypersurfaces and their the fundamental theorems for the differen- 6477-7 generalizations) and T. Willmore (Curves). tial-difference Dunkl operators. Chapter 5 This volume presents the proceedings of the In particular, the contribution by A. presents h-harmonics, the analogue of har- 11th Conference on Problems and Methods Derdzinski is a nice and detailed exposition monic homogeneous polynomials associated in Mathematical Physics, held in Chemnitz (288 pp.) on the local and global theory of with reflection groups. Chapter 6 is a in March 1999. The conference was dedi- four-dimensional Einstein manifolds, detailed treatment of orthogonal polynomi- cated to the memory of Sigfried Prössdorf including indefinite Einstein metrics and als on the simplex, the ball, and of Hermite who made important contributions to the Petrov’s classification of its curvature types, type. Summability theorems for expansions theory and numerical analysis of operator and topological obstructions for the exis- in terms of these polynomials are presented equations and their applications in mathe- tence of Einstein metrics on a given compact in Chapter 7, and the non-symmetric Jack matical physics and mechanics. four-dimensional manifold. The contribu- polynomials appear in Chapter 8; this chap- The book starts with articles describing his tion by P. B. Gilkey presents a nice and short ter treats analysis associated with symmetric life and mathematical achievements, togeth- overview of index theory, including the main groups. Finally, Chapter 9 shows how to use er with the list of his publications. The main ideas, results and applications. Finally, in T. non-symmetric Jack polynomials to produce part of the book consists of original research Willmore’s contribution discusses the role of bases associated with the octahedral groups; papers containing new and interesting curves in geometry, and shows how the con- this chapter contains a short discussion of results. The topics range from integral and cept of a curve has evolved through the ages; how these polynomials and related operators pseudodifferential equations, boundary in particular, he presents a study of special are used to solve the Schrödinger equations value problems, operator theory, boundary curves related to some geometrical problems of the Calgero-Sutherland systems. element and wavelet methods, approxima- (immersions of manifolds into a Riemannian This book will be welcomed by research tion theory and inverse problems to various manifold, holonomy groups of Riemannian mathematicians and applied scientists, concrete problems to applications in physics manifolds, etc.). All the contributions are including mathematicians, physicists, and engineering. They reflect Prössdorf’s very interesting, and the book can be recom- chemists and engineers. (knaj) broad spectrum of research activities. mended to all mathematicians interested in The book is addressed at a wide audience geometry. (jbu) J. Duoandikoetxea, Fourier Analysis, in the mathematical and engineering sci- Graduate Studies in Mathematics 29, American ences. (kn) R. M. Dudley, Uniform Central Limit Mathematical Society, Providence, 2001, 222 Theorems, Cambridge Studies in Advanced pp., US$35, ISBN 0-8218-2172-5 E. Flapan, When Topology Meets Chemistry. Mathematics 63, Cambridge University Press, This book is a translation of Analisis de A Topological Look at Molecular Chirality, Cambridge, 1999, 436 pp., £55, ISBN 0-521- Fourier by Javiar Duoandikoetxea Zuazo, Cambridge University Press, Cambridge, 2000, 46102-2 published in Spanish by Addison-Wesley and 241 pp., £16.95, ISBN 0-521-66254-9 and 0- Central limit theorems for independent Universidad Autónoma de Madrid in 1995. 521-66489-9 identically distributed random variables with Its purpose is to develop Fourier analysis This book describes topological techniques values in general spaces form the main topic using the real variable methods introduced with applications in chemistry and molecular discussed in this book. A number of recent by A. P. Calderon and A. Zygmund in the biology. Recently, there was substantial results of Talagrand and others are surveyed 1950s. interaction among these different scientific without proofs, in separate sections. At the The book consists of 9 chapters. The first disciplines with an interesting impact of end of each section, there are problems for three chapters give a review of Fourier series topology itself. solution, various notes and a list of refer- and integrals, and introduce the Hardy- The main topics treated here are knot the- ences. Littlewood maximal functions and the ory, topology of embedded graphs and The book consists of ten chapters (includ- Hilbert transform. Its higher dimensional three-dimensional manifold theory. Each ing chapters on Gaussian measures and analogues are known as singular integrals, chapter starts with an explanation of the cor- processes, the Donsker classes, Vapnik- and are discussed in Chapters 4 and 5 along responding topic from biology or chemistry Cervonenkis combinatorics and correspond- with their modern generalizations. In and a description of their relations to specif- ing limit theorems, metric entropy, universal Chapter 6 the author studies the relation- ic geometric or topological structures. In the and uniform central limit theorems) and a ship between H1, BMO and singular inte- first chapter, stereochemical topology is number of appendices. The reader is grals. Chapter 7 presents the elementary introduced as a study of three-dimensional assumed to be familiar with some real analy- theory of weighted norm inequalities. structure of molecules, using the topology of sis, including Lebesgue integration and Littlewood-Paley theory is discussed in graphs embedded in three-dimensional probability based on it, and the finite-dimen- Chapter 8; its origins date back to the 1930s, space. In the second chapter, the chirality of sional central limit theorem. but it has had extensive later development complex molecules and its relation to the The book should be of interest to mathe- which includes a number of applications; theory of knots and links are studied. One maticians working in probability, to mathe- those presented in this chapter are useful in interesting geometrical object used here is matical statisticians and to computer scien- the study of Fourier multipliers, which also the Möbius ladder, which is a special type of tists working in computer learning theory. uses the theory of weighted inequalities. graph; its embeddings into three-dimen- (mahus) The book concludes with an important result sional manifolds, and into the sphere S3 in from the 1980s, the T1 theorem which has particular, are studied in the context of topo- C. F. Dunkl and Y. Xu, Orthogonal been of crucial importance to the field. logical chirality. Some non-trivial results Polynomials of Several Variables, At the end of each chapter there are from graph theory concerning their possible Encyclopedia of Mathematics and its Applications extensive references and notes on additional embeddings in the plane or space are used 81, Cambridge University Press, Cambridge, results. The bibliography at the end con- here, and the symmetries of embedded 2001, 390 pp., £55, ISBN 0-521-80043-9 tains only books that treat in depth the pre- graphs of different types are applied in the This modern book presents a comprehen- sented ideas. The material in the book theory as well. The last chapter is devoted to sive theory of orthogonal polynomials of sev- comes from a graduate course taught at the a study of DNA using topological techniques; eral variables in an elegant form and with Universidad Autónoma de Madrid in 1988- the main topic used here is the theory of tan- modern concepts and notation. It consists of 89. The book is an excellent text for gradu- gles (originally developed by Conway), and EMS June 2001 33 RECENT BOOKS their equivalences and properties. At the have read in recent years. It proves that all sent the main trends of contemporary alge- end of each chapter, there are exercises. specialists in mathematics or physics should braic geometry; it was exactly this idea which The book is interesting from different be well informed about the history of their was behind the choice of the articles. points of view, and in particular because of field, because it definitely (and sometimes Five of the articles are expository and sur- its interdisciplinary character and its surprisingly) brings ideas for their own vey articles, and in the rest there is a survey description of applications of topology in research. aspect. The intention of the editors was to biology and chemistry. An effort was made This collection will be interesting for assemble a collection of articles that could to make the material accessible also to mathematicians working in differential create a picture of contemporary algebraic chemists and molecular biologists, and the geometry and for physicists interested in rel- geometry, even for non-specialists in the technicalities are kept to a minimum when- ativity. But there is a lot of interesting mate- field. We do not want to pretend that a read- ever possible. (jbu) rial for geometers in general, for people er with no knowledge of algebraic geometry working in analysis (especially complex is able to read these articles; nevertheless, J. Gil, D. Grieser and M. Lesch (eds.), analysis), representation theory of groups, the editors have been quite successful, and a Approaches to Singular Analysis. A Volume of topology, and other areas. The articles non-specialist with certain background from Advances in PDE, Operator Theory Advances should also attract the attention of physicists algebraic geometry, who likes this field, can and Applications 125, Birkhäuser, Basel, 2001, interested in optics, field theories, quantum probably understand a lot; this applies also 256 pp., DM170, ISBN 3-7643-6518-8 physics, and other areas. The great pioneers to postgraduate students. This book, based on the Workshop of mathematics and physics, whose lives and The articles can be divided into three ‘Approaches to Singular Analysis’ held in work this collection describes, cannot be main groups. The first group, consisting of 1999 in Berlin, presents various approaches associated with one or two subjects only. four papers, is devoted to the Gromov- to analytic problems arising in analysis on (jiva) Witten invariants. The second group, also singular spaces, in particular on manifolds consisting of four articles, deals with Calabi- with corners. The approaches to analysis via D. F. Griffith and G. A. Watson (eds.), Yau 3-folds and mirror symmetry. The third partial differential equations on singular Numerical Analysis 1999, Research Notes in group covers various other topics; these are spaces may be divided into pseudodifferen- Mathematics 420, Chapman & Hall/CRC, Boca very interesting and high quality articles that tial calculus adapted to the underlying con- Raton, 2000, 279 pp., £45, ISBN 1-58488- deserve attention. This collection is indis- figuration, and a direct approach consisting 020-1 pensable for specialists in algebraic geome- of an analysis of geometric differential oper- This text is based on lectures presented at try, and for postgraduate students in this ators (Laplace, Dirac) in special geometric the 18th Dundee Biennial Conference on field. (jiva) situations. Numerical Analysis, held at the University of This book contains articles by workshop Dundee in July 1999. It contains full ver- S. Jiang and R. Racke, Evolution Equations participants and invited contributions. sions of all the invited papers and the list of in Thermoelasticity, Monographs and Surveys There are introductory lectures on the b-cal- titles of all contributed talks together with in Pure and Applied Mathematics 112, Chapman culus of R. Melrose and cone algebras. B. W. names and addresses of the lecturers. & Hall/CRC, Boca Raton, 2000, 308 pp., Schulze proposes a systematic study of ellip- The papers cover a wide range of topics £53.99, ISBN 1-58488-215-8 tic PDEs on manifolds with singularities, in from partial differential equations to linear The aim of this book is to present the state of terms of pseudodifferential algebras with algebra and approximation theory and con- the art in the theory of evolution equations hierarchies of symbols. J. Bruning examines tain contributions from leading experts in in thermoelasticity, to which the authors resolvent expansions for Laplace-type oper- the field (adaptive and mixed hp-finite ele- have also contributed. The evolution prob- ators on a certain class of isolated singulari- ment methods; optimal control problems; lem under consideration is a coupled system ties. The index theorem for elliptic opera- finite volume approximations; variational of a parabolic and a hyperbolic equation, tors on toric manifolds with conical singular PDE methods; subgrid scales; Krylov sub- considered either on the whole space Rn or points is studied by Fedosov, Schulze and space methods for radial basic function on a bounded domain in Rn with boundary Tarkhanov. (pso) interpolation; homotopy methods for mixed conditions. Local existence and asymptotic complementary problems based on PATH behaviour for one- and multi-dimensional J. J. Gray (ed.), The Symbolic Universe: solvers; Störmer-type numerical integrators; models are studied separately, both for lin- Geometry and Physics 1890-1930, Oxford domain decomposition methods; a polyno- ear and non-linear equations. The impact of University Press, Oxford, 1999, 289 pp., £55, mial interpolation on the sphere). The the parabolic and hyperbolic structures is ISBN 0-19-850088-2 applications range from image processing demonstrated on the propagation of singu- This book is a collection of nine articles that and molecular dynamics to superconductivi- larities. The last two chapters are devoted to were presented at a conference held at the ty (an incompressible flow; a problem of contact problems and other related results. Open University in March 1996. They are boundary control in superconductivity; To help the reader, there is a short deriva- devoted to history of mathematics and image processing; a model of superconduct- tion of the equations in Chapter 1 and a gen- physics and their mutual interrelations in ing vortices; a perturbed Hamiltonian sys- eral existence theory and other tools that are the period 1890-1930. The authors are tem; reduction techniques for large-scale used throughout the book, are summarised highly competent, with a profound under- dynamical systems; data fitting problems). in an Appendix. This book is essentially standing of the subject and a good knowl- The book offers inspiration for further devoted to one type of evolution problem edge of history, and the articles are far from research. It can be strongly recommended and describes several theories applied to its being a mere collection of data and facts – on to researchers and postgraduate students different modifications. It might thus be the contrary, they offer deep analyses of the involved in numerical analysis, and to engi- suitable for demonstrating the theory of evo- situation in mathematics and physics in the neers or scientists using numerical methods. lution equations on a special, although periods of interest, explain why mathemati- (knaj) advanced, example. Graduate students will cians and physicists were interested in these appreciate that material previously pub- and not other problems, and why they used K. Hulek, F. Catanese, C. Peters and M. lished only in papers is collected in this certain methods. They take into account the Reid (eds.), New Trends in Algebraic book, and experts will find some new results general ambience and the country where the Geometry, London Mathematical Society, Lecture here. A basic knowledge of linear partial dif- work took place. Moreover, many notions Note Series 264, Cambridge University Press, ferential equations is assumed. (efa) are explained from the point of view of con- Cambridge, 1999, 484 pp., £29.95, ISBN 0- temporary mathematics and physics, which 521-64659-6 W. J. Kaczor and M. T. Nowak, Problems in can be very helpful; they show mathemati- Formally, this volume contains seventeen Mathematical Analysis I. Real Numbers, cians and physicists of those times as com- contributions from the July 1996 Warwick Sequences and Series, Student Mathematical plex personalities, and this enables us also to European algebraic geometry conference, Library 4, American Mathematical Society, understand better their work. I do not often which is considered one of the major alge- Providence, 2000, 380 pp., US$39, ISBN 0- read books on the history of mathematics braic geometry events of the last decade – 8218-2050-8 and physics, but this collection is the best I but the real aim of this collection is to pre- This book is the first volume of a series of 34 EMS June 2001 RECENT BOOKS problem books in mathematical analysis. It nary knowledge from parts of the textbooks Institut für Mathematik in Bonn. The first contains 78 problems on real numbers, 244 of J. K. Hale, S. M. Verduyn Lunel or O. part (Chapters I-IV) is devoted to abstract problems on sequences, and 299 problems Diekmann, S. A. van Gils, S. M. Verduyn Frobenius manifolds and to implications of on series. The problems are nicely chosen Lunel, H.-O. Walther would be useful. this notion, while the construction of the and solutions of all of them are provided. It Specialists will find recent results here. (jmil) quantum cohomology itself is postponed to is an ideal book for problem seminars and Chapters V and VI. While the first part of also for self-study. The problems are by no H. G. Kwatny and G. L. Blankenship, the book is more-or-less self-contained, the means new, but books of this type in English Nonlinear Control and Analytical construction of the quantum cohomology are still rare. The second volume already Mechanics. A Computational Approach, needs quite advanced techniques of algebra- exists in Polish and is being translated into Control Engineering, Birkhäuser, Boston, 2000, ic geometry, and the reader is supposed to English. Problems on structures, such as 317 pp., DM128, ISBN 0-8176-4147-5 and 3- work with references. metric or topological spaces, will be pub- 7643-4147-5 Although the book assumes a rather broad lished in a separate volume. This monograph is devoted to a modern preliminary knowledge of algebraic and dif- This book can be recommended for treatment of analytical mechanics and non- ferential geometry, it might yet give, even to libraries and for students with a deeper linear control theory with very strong com- a non-specialist, some basic orientation in interest in mathematical analysis. (jive) putational aspects. After introducing the the above topics which belong to the main basic concepts of Banach spaces and stability stream of research in mathematics and have, H. Krause and C. M. Ringel (eds.), Infinite theory for ordinary differential equations, moreover, a strong physical flavour. (mm) Length Modules, Trends in Mathematics, the basic geometric properties of dynamical Birkhäuser, Basel, 2000, 439 pp., DM198, systems are introduced. The authors pre- V. Maz’ya, S. Nazarov and B. Plamenevskij, ISBN 3-7643-6413-0 sent these basic properties in an easily Asymptotic Theory of Elliptic Boundary This book is based on invited lectures at a understandable form, without unnecessary Value Problems in Singularly Perturbed Euroconference held at the University of details but in a clear and correct manner. Domains, I, II, Operator Theory Advances and Bielefeld in September 1998. The main The authors also provide a short introduc- Applications, 111, 112, Birkhäuser, Basel, 2000, topic is the role of infinite length modules in tion to differential geometry and introduce 435 pp., 323 pp., DM268, ISBN 3-7643-6397- the representation theory of algebras. necessary concepts (vector fields, flaws, dis- 5 and 3-7643-6398-3 The book consists of 23 survey papers tributions, Lie groups and algebras) for the This book is devoted to the development written by the leading experts in the field. formulation of dynamic equations. This and applications of asymptotic methods to The scene is set by a survey by Ringel, with makes the book an excellent introduction boundary value problems for elliptic equa- many illuminating examples. There follow into the subject. tions in singularly perturbed domains. The papers on algebraically compact modules The much developed numerical aspects of first volume contains Parts I-IV, in which (Huisgen-Zimmermann, Prest), decomposi- the treatment make it possible to demon- boundary value problems with perturbations tion theory (Eklof, Facchini, Göbel, strate the behaviour of dynamical systems on near isolated singularities of the boundary of Pimenov-Yakovlev), dimension theory a computer. Each copy of the book is the domain are studied. The second volume (Bavula, Lenagan, Schröer), functor cate- equipped with a CD-ROM containing the contains Parts V-VII, which deal with other gories (Kuhn, Powell), homological methods package ProPac, which can be used as a kinds of perturbations (problems with per- (Martsinkovsky, Schwartz, Smalo), localisa- MATHEMATICA (3 or 4) package for simu- turbations of the boundary of singular man- tion and moduli spaces (Rickard, Schofield), lation of motions of dynamical systems. It ifolds, problems in thin domains, and prob- modular representations of finite groups can also be used in MATHLAB/SIMULINK. lems with rapid oscillations of the boundary (Benson, Carlson), and tameness (Bautista, Using this software, the authors give many of domain or coefficients of differential Krause, Lenzing, Zwara). This book is indis- examples of how to simulate the behaviour operators). pensable for anyone interested in current of simple multibody systems (for instance, In Part I the authors discuss boundary trends and methods of representation theo- planar mechanisms) or smooth affine con- value problems for the Laplace operator. ry. (jtrl) trol systems. The last two chapters of the Part II is devoted to the study of general book are devoted to robust and adaptive elliptic boundary value problems. Parts III T. Krisztin, H.-O. Walther and J. Wu: controls for non-linear systems and to appli- and IV deal with the expansion of function- Shape, Smoothness and Invariant cations of feedback linearisation methods for als over solutions of boundary value prob- Stratification of an Attracting Set for Delayed uncertain systems. Discontinuity of control lems and eigenvalues in the asymptotic Monotone Positive Feedback, Fields Institute functions over smooth surfaces is also con- series. In Part V, the authors study boundary Monographs 11, American Mathematical Society, sidered. The book provides an excellent value problems in domains perturbed near Providence, 1999, 245 pp., US$69, ISBN 0- introduction to dynamical systems and con- multidimensional singularities of the bound- 8218-1074-X trol theory for anyone interested in exam- ary. The behaviour of solutions of boundary This book is devoted to the study of global ples and practical applications. The use of value problems in thin domains is investigat- dynamics for a delay differential equation of its software package could considerably ed in Part VI. Part VII deals with elliptic the type (dx/dt)(t) = –µx(t) + f(x(t–1)) with a improve the understanding of the subject. boundary value problems with oscillating monotone feedback f. Such equations arise (ak) coefficients. (dmed) in various applications in engineering, biolo- gy, or neural networks. A natural object for Yu. I. Manin, Frobenius Manifolds, H. Nakajima, Lectures on Hilbert Schemes of studying long-time behaviour of solutions is Quantum Cohomology, and Moduli Spaces, Points on Surfaces, University Lecture Series a global attractor (provided it exists) or, Colloquium Publications 47, American 18, American Mathematical Society, Providence, more generally, an unstable manifold of the Mathematical Society, Providence, 1999, 303 1999, 132 pp., US$21, ISBN 0-8218-1956-9 stationary point 0. pp., US$55, ISBN 0-8218-1917-8 The purpose of this book is to describe vari- This book follows this approach and Quantum cohomology is a specific formal ous properties of Hilbert schemes of points demonstrates the richness of dynamics of deformation of the cohomology ring H = on surfaces. The subject has its origin in delay differential equations. Although the H*(V) with complex coefficients of a projec- algebraic geometry and is related to many subject is rather technical, it is not too diffi- tive algebraic variety V. The resulting other branches of mathematics, such as sin- cult to read this text. The presentation is abstract algebraic structure is called the gularities, symplectic geometry, representa- clear and the book is self-contained, since it Frobenius manifold and can be described by: tion theory and even theoretical physics. contains appendices on basic facts from the (i) a ‘potential’ Ψ in coordinates on H; (ii) The topic can be explained from various theory of (smooth) dynamical systems an action of an operand on H; (iii) a com- points of view. The presented lectures are (invariant manifolds, Floquet and Poincaré- pletely integrable system on the formal man- intended for graduate students having Bendixson theory for delay equations, etc.). ifold H; structure (ii) is also called the coho- already a basic knowledge of algebraic This book will be suitable for graduate stu- mological field theory. geometry and homology groups of mani- dents with interests in differential equations The book is a compendium of lectures folds, but some chapters require a more and/or dynamical systems. Some prelimi- given by the author at the Max-Planck- extended background, such as spectral EMS June 2001 35 RECENT BOOKS sequences, intersection cohomology and pendent study or as an interesting text for ed by direct applications to physics. perverse sheaves. seminar lectures. (pp) Recently the theme has become a favourite The first chapter collects basic facts, need- topic, and is topical because there remain ed in later chapters, on the Hilbert scheme M. S. Osborne, Basic Homological Algebra, many basic open problems to be solved or of points on a surface; other chapters in the Graduate Texts in Mathematics 196, Springer, better understood. Many interconnections book can be read independently. New York, 2000, 395 pp., DM98, ISBN 0-387- with other areas of analysis can be observed; Resolutions of simple singularities are stud- 98934-X among methods used in the authors’ ied in Chapter 4, and the Poincaré polyno- The title characterises this book very well. approach, we mention glueing theorems, mial of Hilbert schemes in Chapters 5 and 6. The author wrote it when teaching courses functional analysis on weighted Hölder Chapter 8 contains a description of the on homological algebra: he needed a text- spaces, conservation laws, Pohozaev formula homology group of Hilbert schemes. This book leading quickly to the functors Tor and for conformal fields, and comparison princi- book is not the first (and hopefully not the Ext which would then offer possibilities for ples. The book is a nicely written and inter- last) on Hilbert schemes of points on sur- proceeding further in several different direc- esting treatment of the topic. (jama) faces, but the author has avoided repetition tions. The possibilities are best depicted in of material from earlier books on the same his diagram on Chapter/Appendix T. Peterfalvi, Character Theory for the Odd subject. (ae) Dependencies. One can continue, for exam- Order Theorem, London Mathematical Society ple, with dimension theory, applications in Lecture Note Series 272, Cambridge University R. Narasimhan and Y. Nievergelt, Complex ring theory, and abstract homological alge- Press, Cambridge, 2000, 154 pp., £24.95, ISBN Analysis in One Variable, Birkhäuser, Boston, bra. 0-521-64660-X 2001, 381 pp., DM148, ISBN 0-8176-4164-5 The book is well written. We find here The famous theorem of W. Feit and J. G. and 3-7643-4164-5 many examples. Each chapter is followed by Thompson states that every finite group of This book is an extended version of a book exercises, and at the end of the book there odd order is soluble. The proof of this the- published by the first author. It now appears are outline solutions to some of them. The orem consists of two parts; the first part has with slight changes and enlarged by the sec- organisation of the book is such that the been revised by H. Bender and G. ond author, with 365 carefully chosen exer- readers meet the more abstract notions only Glaubermann in the LMS Lecture Notes 188 cises. It is based on graduate courses given when they are already familiar with their (Cambridge, 1994). Throughout the proof a by the authors, with the aim of relating com- special instances. I especially appreciated minimal counter-example is considered, and plex analysis to other fields of mathematics. the lively style of the book; compared with the first part consists of describing its maxi- In about 250 pp., it contains traditional some other books on homological algebra, mal subgroups. These are classified into five material and also such topics as functions of one has here the good feeling that one types, the first of which is associated with a several complex variables, compact understands why a notion is defined in this Frobenius subgroup, while the others are Riemann surfaces, the Corona theorem, and way, that one can easily remember at least associated with a cyclic subgroup. A revision more than 40 pages on subharmonic func- the structure of the theory, and that one is of the second part of the proof is presented tions and related topics. The second part quickly able to find necessary details. The in the first 95 pages of Peterfalvi’s book. He with exercises (about 110 pp.) follows the prerequisite for this book is a graduate uses character theory to show that none of structure of the first part and contains refer- course on algebra, but one can get quite far the settings described in the first part of the ences to other sources. Most exercises are with a modest knowledge of algebra. The proof can be actually realised. chosen to complete the exposition of the book can be strongly recommended as a In the book there are seven chapters of theory rather than to master more-or-less textbook for a course on homological alge- preparatory computations that concern routine calculations. Carefully written com- bra. (jiva) Dade isometries of class functions, and Z-lin- ments and bibliography at the end of each ear isometries of irreducible characters chapter of the first part, as well as final com- F. Pacard and T. Rivière, Linear and (coherence theorems). Chapter 8 presents ments to exercises, are very useful. This is a Nonlinear Aspects of Vortices. The Ginzburg- the output theorems of Bender’s and good source for teachers leading seminars Landau Model, Progress in Nonlinear Glaubermann’s book, and the following six on complex function theory and for self- Differential Equations and Their Applications 39, chapters apply the preparatory computa- study by graduate students. (jive) Birkhäuser, Boston, 2000, 342 pp., DM178, tions to show the non-existence of the ISBN 0-8176-4135-5 and 3-7643-4133-5 counter-example. The rest of the book J. Oprea, The Mathematics of Soap Films: The Ginzburg-Landau functional is studied gives, in 35 pages, a revised proof of a theo- Explorations with Maple, Student as a model for superconductivity. Critical rem of M. Suzuki, that a doubly transitive Mathematical Library 10, American points of the functional are called Ginzburg- finite group, whose stabiliser is a semidirect Mathematical Society, Providence, 2000, 266 Landau vortices. The existence part uses the product of an even-order and odd-order pp., US$29, ISBN 0-8218-2118-0 fixed-point method to obtain a solution of group, has to contain (if involutions satisfy Nature tries to minimise the surface area of the problem, with a given small parameter ε an additional condition) a normal subgroup a soap film through the action of surface ten- which is close to an approximate solution, isomorphic to PSL(2, q), Sz(q)orPSU(q). sion; the process can be understood mathe- previously constructed with the aid of the lin- The proof uses various properties of linear matically by using differential geometry, earised problem. Letting ε→0, the solu- groups, and some other facts, most of which complex analysis, and the calculus of varia- tions converge to one of solutions of the limit are gathered on 15 pages in four appendices tions. This book employs ingredients from problem and the zeros of the solutions con- (a theorem of Huppert, near-fields, Suzuki each of these subjects to tell the mathemati- verge to singular points of the limit problem. 2-groups, and the Feit-Sibley theorem). (ad) cal story of soap films. The text is fully self- The solution of the limit problem is a har- contained, combining a mixture of types of monic map with values in S1, and its topo- M. H. Protter, Basic elements of real analy- mathematics with a bit of physics that under- logical degree plays an important role. The sis, Undergraduate Texts in Mathematics, lies the subject, and requires no advanced uniqueness consists of proving that, roughly Springer, New York, 1998, 273 pp., DM79, background material from either mathemat- speaking, for sufficiently small values of the ISBN 0-387-98479-8 ics or physics. Through Maple applications, parameter such a solution is unique, provid- While A First Course in Real Analysis by the reader is given tools for creating shapes ed that the asymptotic behaviour and Morrey and Protter is designed for a com- that are being studied. Maple procedures boundary data are prescribed; this concerns prehensive one-year course in analysis, this creating the surfaces of soap film are pre- the simplified model Eε(u). In the last chap- book is intended for a ‘shortened’ course sented, together with many figures as their ter, a more complicated model is investigat- aimed at students who intend to study the output in various situations. The author also ed, which better reflects the physical reality. physical sciences or computer science. It includes descriptions of experiments and Deep uniqueness results are achieved here, covers the most important topics in an ele- photographs that let one see real soap films making a step towards a solution of the so- mentary way. Apart from traditional mater- on wire frames. called Jaffe and Taubes conjecture. ial, some basics of metric space theory, dif- The book is an excellent presentation of a The theory of Ginzburg-Landau vortices ferentiation and integration in Rm, the deriv- beautiful subject. It can be used for inde- is a beautiful piece of mathematics, motivat- ative of the integral and the theorems of 36 EMS June 2001 RECENT BOOKS Green and Stokes are included. The course provide the background for a course on matical courses. It is not a manual of does not leave major items to be filled in by numerical analysis, for example. Some read- Mathematica, or a calculus or algebra text- readers. One cannot expect advanced ers might miss applications to linear pro- book with exercises for students, but is a very results to be included, but the course gives a gramming or Markov chains. (jstep) helpful text that explains what commands good knowledge of the important basic con- and features of Mathematica can be used to cepts for non-specialists. Many problems M. Schechter, Linking Methods in Critical solve problems in calculus and/or algebra (the odd-numbered ones with answers) are Point Theory, Birkhäuser, Boston, 1999, 294 courses. No prerequisites other than high included. pp., DM118, ISBN 0-8176-4095-9 and 3- school level mathematics are assumed. The book can be recommended to stu- 7643-4095-9 There is a very nice introduction to the dents desiring a good solid background in This carefully written monograph addresses Mathematica program in Chapters 1 and 2. mathematics for the study of other sciences several interesting topics from critical point The different features of Versions 3 and 4 without unnecessary detours. (jive) theory and semilinear elliptic partial differ- are shown, as are platform specific informa- ential equations. In the first area, the book tion for Apple Macintosh and Microsoft E. Risler, Linéarisation des perturbations presents the first systematic study of finding Windows. A warning sign indicates para- holomorphes des rotations et applications, critical points of the functionals, defined in a graphs that can be skipped by beginners but Mémoires de la Société Mathématique de France Banach space, that are neither minima nor can be interesting for advanced users. The 77, Société Mathématique de France, Paris, maxima. The key role is the method of link- topics in Chapters 3-7 are typical ones from 1999, 102 pp., Ffrs150, ISBN 2-85629-076-0 ing: a set A links another set B if the supre- precalculus, calculus, multivariable calculus This little book is devoted to a typical prob- mum of the functional values over A does not and linear algebra courses: functions, lem from the theory of quasi-periodic exceed the infimum of the values of the func- graphs, equations, limits, integrals, vectors, dynamical systems, which has attracted a lot tional over B. (In the mountain pass geom- matrices, etc. of attention in recent years. It contains part etry, A consists of two points: one lies inside The book can be used as a supplementary of the author’s thesis, prepared under the an open set Q, the second outside the closure text in calculus or algebra courses and also as guidance of J.-C. Yoccoz. The main topic is of Q, and B = ∂Q.) It is proved that A links a textbook for students who wish to learn a study of holomorphic maps F from an B if they are disjoint and A cannot be contin- Mathematica and use it to solve mathemati- annulus A in the complex plane to itself, uously shrunk into a point without intersect- cal problems. The book is nicely written and which are conjugates to rotations – that is, ing B. With this general approach the is recommended to anyone studying mathe- for which there is a rotation Ta of (a possibly author obtains new results and applies them matics. (ml) smaller) annulus A′ and a holomorphic map to semilinear elliptic PDEs, analysing such h from A′ to A such that F ° h = h ° Ta in A′. questions as the solvability of boundary value N. Weaver, Lipschitz Algebras, World In the book, the attention is restricted to problems, the existence of non-trivial solu- Scientific, Singapore, 1999, 223 pp., £30, ISBN local problems – that is, to maps which are tions, the multiplicity of solutions, non-lin- 9-81-023873-8 close to rotations. ear eigenvalues and resonance effects. Let X = (X, ρ) be a metric space. The The first part contains results in a neigh- Although the subject is technical, the book is Lipschitz number L(f) of a function f : X→ R bourhood of a map conjugated to a rotation clearly organised. is the infimum of all a = 0 with the property with a parameter satisfying the so-called With its pedagogical presentation, various that |f(y) – f(x)| = a ρ(y, x) for each x, y in Bruno condition. The main tool used is a new results in important fields, greatly gen- X. The space Lip X, the class of all bounded renormalisation of the dynamics analogous eralised approaches and an extensive bibli- Lipschitz functions on X, endowed with the to one used by J.-C. Yoccoz for the case of ography, the book can be recommended to norm || f || L = max {||f||∞ , L(f)}, is one of diffeomorphisms of the circle. This renor- specialists and to anyone interested in criti- the spaces studied in the book. malisation concerns an analytic family of cal point theory or non-linear PDEs. (jmal) First of all, they are Banach spaces, and maps instead of one map, and additional this point of view is considered in Chapter 1. tools needed include methods of several J. Stalker, Complex Analysis. Fundamentals They are also dual spaces, and the proof is complex variables. In the second part, earli- of the Classical Theory of Functions, based on non-trivial constructions studied in er results are extended from real parameters Birkhäuser, Boston, 1998, 228 pp., DM84, Chapter 2; applications to the mass transfer to complex ones, and the resulting corre- ISBN 0-8176-4038-X and 3-7643-4038-X problem are given. The little Lipschitz spondence is regular in the sense of This is an unusual textbook, incorporating spaces are studied in Chapter 3; they consist Whitney. The third part describes some material showing how classical function the- of functions for which lim(x,y)→0 |f(y) consequences for previous results of singular ory can be used. It has three chapters: –f(x)|/ρ(x, y) = 0. This space is trivial if X = rotation domains of rational maps on a Special functions, Analytic functions, and Rn with the Euclidean metric, but in the gen- Riemann sphere. Elliptic and modular functions, and an eral theory their role is significant. In The book will be valuable for mathemati- appendix containing a quick review of real Chapter 4, Lipschitz spaces are studied as cians interested in dynamical systems. (vs) analysis. The general scheme is to show the Banach algebras. Among the main goals are reader how things were developed without results of Stone-Weierstrass type, studies of J.-E. Rombaldi, Analyse matricielle: Cours et following the traditional approach of most carrier spaces and spectral synthesis. Lattice exercises résolus, EDP Sciences, Les Ulis, 1999, books on function theory. Thus, the first properties are studied in Chapter 5. The 304 pp., Ffrs210, ISBN 2-86883-425-6 chapter contains information on the distrib- definition of a Lipschitz function can be This is a thorough and mathematically neat ution of primes and on the gamma, beta and adapted to measurable metric spaces; this textbook on matrix theory. The algebraic hypergeometric functions, while the second topic is studied in Chapter 6. The last chap- and topological properties of the matrix vec- chapter is devoted to contour integration, ter is devoted to derivations, functionals sat- tor algebra (over both real and complex power series, the Cauchy integral formula, isfying the product rule D(fg) = f Dg + g Df. numbers) are presented in a self-contained etc. Generally, the book deals with topics manner, starting with a condensed treat- This book can be recommended to those based on the general metric structure of X; ment of the normed vector spaces that can who like to see applications of the theory problems such as differentiability of be easily followed by any reader familiar with taught in ‘classical courses’. (jive) Lipschitz functions on Euclidean domains elements of linear algebra. Standard results are beyond its scope. The author is one of of classical matrix theory are proved com- B. F. Torrence and E. A. Torrence, The the best experts in the field, and the book, fortably via the endomorphism interpreta- Student’s Introduction to Mathematica, A probably the first monograph devoted exclu- tion, and applications to systems of linear Handbook for Precalculus, Calculus, and sively to Lipschitz algebras, is a valuable differential equations are carefully presented Linear Algebra, Cambridge University Press, guide to a modern, little known, part of func- with respect to possible numerical problems. Cambridge, 1999, 280 pp., £16.95, ISBN 0-19- tional analysis. Some open problems are Each chapter is accompanied by a collection 853576-7 mentioned, and possible interesting future of relevant solved exercises. This book is another member of the family developments are considered. It should be The textbook is meant as a teaching text of books devoted to the computer algebra interesting for both researchers and stu- at first- or second-year graduate level, to system Mathematica and its use in mathe- dents. (jama) EMS June 2001 37