THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 318 September 2003 Forthcoming COUNCIL DIARY degree institutions for post- graduate study. Could the LMS Society 20 June 2003 establish a forum providing Meetings Ursula Martin was present at advice on PhD study? It was the June Council meeting to suggested that this might be a report on the work of the function of the planned 2003 Computer Science Committee, Mathematics Promotion Unit, Friday 24 October which she chairs. The commit- and that the Society might well Southampton tee is focusing on three initia- play a coordinating role, and South West and tives. As MathFIT draws to an establish a web page. South Wales Regional end, the question of succession The Treasurer reported on the Meeting is a natural one, and is under meeting of the Finance Nonlinear Dynamics discussion. A meeting of past Committee two weeks earlier. 1 grantholders, planned for the For the first time the specialist Autumn, will allow consulta- advisors had been present, who Friday 21 November tion. Following the success of had agreed to supplement London the e-Science meeting held at Finance Committee and join an L.C.G. Rogers, De Morgan House in March, a Investment Advisory Committee. M.H.A. Davis (Naylor proposal for a mathematics pro- They had provided very valuable Lecture) gramme scheme for e-Science input to a broad-ranging discus- similar to, but on a smaller scale sion of the Society’s investments than, MathFIT is also being and investment policies, and at a 2004 debated. And Robert Leese’s meeting with the Society’s pro- Friday 20 February seminar at De Morgan House on fessional advisors. It was agreed London the work of the Smith Institute, that the Investment Advisory D. Schleicher, highlighting useful opportuni- Committee would meet again in S.M. Rees (Mary ties for collaboration with the September. Cartwright Lecture) industrial and commercial sec- The Treasurer presented the tors, has raised some interesting budget proposals for 2003/04, questions on ways in which the which are tougher than they Society might contribute. have needed to be in the past, Miles Reid initiated discus- due in part to the poor per- sion on the recruitment and formance of investments. We distribution of PhD students to are lucky that publications UK mathematics departments. income remains healthy, but it He asked if the LMS should would be unwise to rely too consider helping with this. It heavily on this. The was widely recognised that it Administration, Computer was in students’ best interests Science Committee and to move on from their first Programme Committee have THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 318No. September 318 June 2003 had to accept lower budgets than were UK mathematics community. Let us know HONORARY MEMBERSHIP A tour of his achievements includes: his requested; Programme Committee needs to your opinions: my address is at the bottom of famous 1974 proof of the last of the Weil consider seriously ways in which it can tight- this page. Naturally we are unable to please conjectures (the ‘Riemann Hypothesis’ for en up its procedures in order to be more everybody, and we apologise to those read- varieties over finite fields); his construction selective. The Treasurer commented that this ers who will miss the handcrafted style of the in 1968 of the l-adic representation associ- year’s projection figures are definitely pes- old Newsletter with its sober monochrome ated to a modular form, yielding the proof simistic; the budget is a cautious one. The and incongruous juxtapositions. As always, of the Ramanujan–Petersson conjecture, as Society’s membership subscription is due to we welcome suggestions for articles and well as providing substantial evidence for increase to £30, but Council still considered it reviews, as well as news of conferences and the Langlands program, and motivation for to be a good deal, considering the services meetings – especially of course those sup- the solution by Wiles and others of the the Society provides for members. ported by the LMS. Taniyama–Shimura–Weil conjecture; the The meeting adjourned early to allow And this isn’t all ... the new web version of development of the theory of weights and members of Council to attend the Society’s the Newsletter will also appear each month mixed sheaves; the algebraic study of inter- very first Fröhlich lecture. simultaneously with the printed version, section cohomology (with Beilinson and Sarah Rees complete with relevant links to conference Bernstein), perverse sheaves, t-structures sites, reports and other background docu- and derived categories, and the decompo- NEW LOOK NEWSLETTER ments, such as archives of more photographs sition theorem; the existence of mixed of Council members and other mathemati- Hodge structures on the cohomology of 2 So, here it is: the New Look Newsletter. cians at various meetings than you (or they) varieties over the complex numbers; differ- 3 More attractive, easier to read, better organ- could ever want. There isn’t yet a webcam at ential equations with regular singular ised, we hope, and of course in colour (which De Morgan House, but as always the LMS is points, and the solution of Hilbert’s 21st need not remain constant). We aim to widen keen to innovate and is ready to embrace problem; the theory of absolute Hodge the scope of material included, with more enthusiastically any realistic suggestions as cycles on Abelian varieties, and the identi- opinion, polemics, politics, pictures, poems, to how we might advance to meet with cre- fication of the Taniyama group with the singing and dancing – well, perhaps that will ativity and panache the stimulating chal- Galois group of the category of CM come later – while maintaining the brief of lenges of the twentieth century, or even the motives; his ingenious proof of the exis- the Newsletter to inform members of current twenty-first. The London Mathematical Society has elect- tence of local ε-factors, a key ingredient of events and news particularly relevant to the David Chillingworth ed Professor Pierre Deligne to Honorary the Langlands program; his discovery of Membership of the Society in recognition of the motivic structure on the fundamental his monumental contributions to algebraic group of an algebraic variety, providing in LMS Newsletter geometry. the simplest case of the projective line Viewed as a whole, Deligne’s work con- minus three points a link between polylog- General Editor: Dr D.R.J. Chillingworth ([email protected]) cerns many different aspects of the cohomol- arithms and mixed Tate motives, and (with Reports Editor: Dr S.A. Huggett ([email protected]) ogy of algebraic varieties. It has turned Beilinson) giving a motivic interpretation Reviews Editor: Professor M.P.F. du Sautoy ([email protected]) Grothendieck’s philosophy of motives from a of Zagier’s conjecture on special values of Administrative Editor: Miss S.M. Oakes ([email protected]) conjectural program into what is the driving the Dedekind zeta-function of a number Editorial office address: London Mathematical Society, De Morgan House, force behind many of the most subtle areas field. 57-58 Russell Square, London WC1B 4HS (tel: 020 7637 3686; fax: 020 7323 3655, of current algebraic geometry and arith- Professor Deligne is a member of the email: [email protected], web: www.lms.ac.uk) metic. Through an unparalleled blend of Paris Académie des Sciences, of the Designed by CHP Ltd (tel: 020 7240 0466, email: [email protected], web:www.chpdesign.com). penetrating insights, fearless technical American Academy of Arts and Sciences, Printed by: Armstrong Press Ltd, Southampton (tel: 023 8033 3132, email: [email protected]) mastery and dazzling ingenuity, Deligne has and of the Académie Royale de Belgique. Publication dates and deadlines: published monthly, except August. single-handedly brought about a new under- He was awarded a Fields Medal in 1978, Items and advertisements by first day of the month prior to publication. standing of the cohomology of varieties, and the Crafoord Prize of the Swedish Information in the Newsletter is free to be used elsewhere; attribution is requested when reproducing both classical and in finite characteristic, with Academy in 1988. He is currently Professor whole articles. The LMS cannot accept responsibility for the accuracy of information in the Newsletter. numerous applications to deep problems in at the Institute of Advanced Study in Charity registration number: 252660 geometry and number theory. Princeton. THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 318No. September 318 June 2003 THE INTERNATIONAL with the academic staff and particularly meet- ing and interacting with young postgrad and LONDON MATHEMATICAL SOCIETY SOUTH WEST REVIEW OF MATHEMATICS postdoc research mathematicians. Report 6 Stephen Huggett, the Scientific Secretary AND SOUTH WALES REGIONAL MEETING to the Review, is in contact with the venues Invitations have been sent to the eight insti- and hosts, discussing each of the pro- Nonlinear Dynamics tutions selected as venues for the Review grammes. It is recognised that the specific Panel to visit during the Review Week, programmes will vary, drawing on the differ- University of Southampton, 24 October 2003 Monday 1 December to Saturday 6 ing strengths and natures of the regions and December. their institutions. The South West and South Wales Regional Meeting of the London Mathematical At each venue, key institutions of high There is a contact point on the Review Society will be held on Friday 24 October. There will be a reception and dinner afterwards. standing in the region centred on the venue website for feedback ([email protected]). Please 3.30 - 4.30 Marcelo Viana (IMPA, Brasil) have been asked jointly to act as “hosts” to use this to send in your own comments and 4.30 - 5.00 Tea/coffee present the core material to the sub-Panel.