|
REPORTS AND RECORDS OF SOCIETY MEETINGS Contents LMS Spitalfields
Day 30 March 2004 - report LMS SPITALFIELDS DAY Applications of K-theory and Cohomology The workshop with the same title, which was held at the University of Southampton during 31 March – 2 April 2004, was designed as a follow-up to the research programme entitled New Contexts for Stable Homotopy Theory organised by John Greenlees, Haynes Miller, Fabien Morel and Victor Snaith at the Newton Institute during September-December 2002. Accordingly the main themes of the workshop focused on the Fields Medal winning work of Voevodsky and the related work of Suslin, Rost, Levine, Morel et al. which has resulted in a burst of progress on a host of famous conjectures due to Bloch-Kato, Beilinson, Birch-Swinnerton-Dyer, Coates-Sinnott, Lichtenbaum and others. Many of these applications were reported on in the subsequent workshop, which was attending by about 40 people and featured seventeen speakers from Canada, Denmark, France, Japan, Poland, Russia, Britain and the USA. The accompanying Spitalfields Day consisted of three lectures designed to show how algebraic K-theory impinges on group cohomology, number theory and algebraic geometry. Rick Jardine outlined the history of the problem, initiated by John Milnor in the context of Lie groups, of comparing the cohomology of an algebraic group viewed on the one hand as a discrete group and on the other as a topological group with the classical topology. The case of the general linear group is particularly closely related to algebraic K-theory where such a comparison isomorphism, due originally to Suslin and Jardine independently, states that the mod p Quillen algebraic K-theory of the complex numbers and the topological K-theory coincide. Mark Levine explained the significance of Grothendieck’s notion of a motive in algebraic geometry, of the search for Deligne’s category of mixed motives and of the significance of the recent construction of the derived category of mixed motives by Levine, Hanamura and others, explaining how it fits in with the motivic cohomology of Voevodsky-Suslin-Friedlander. In the third Spitalfields Day lecture I explained, by way of illustrating algebraic K-theory at work in arithmetic, how the long conjectured non-vanishing of Kubota-Leopoldt p-adic L-functions at positive integers is equivalent to the injectivity of a natural map between algebraic K-groups. This result was originally proved by Soulé in the 1980's but I presented a simpler approach using more recent results due to Bruno Kahn, based on work of Merkuryev-Suslin. The Spitalfields Day served very effectively both as an overview of the outstanding recent progress in algebraic K-theory and as a taste of the many resulting applications to other central subdisciplines of pure mathematics. V.P. Snaith
ORDINARY MEETING held on Friday 18 June 2004 at University College London. At least 70 members and visitors were present for all or part of the meeting. The meeting began at 3.30 pm, with the President, Professor F.C. KIRWAN, FRS, in the Chair. The President invited Professor J.C. Rickard, of the University of Bristol, Senior Berwick Prize-winner for 2002, to give a lecture, postponed from last year, on The stable module category of a finite group algebra. After tea, a GENERAL MEETING was held, with Professor Kirwan in the Chair. On a recommendation from Council it was agreed to elect Dr D.J. Collins and Professor P.T. Saunders as scrutineers in the forthcoming Council elections. The Ordinary Meeting then resumed. The President, on Council’s behalf, proposed that Professor I.M. Singer, of MIT, be elected to Honorary Membership of the Society. This was approved by acclaim. The President read a short version of the citation, to be published in full in the Bulletin. Eight people were elected to Ordinary Membership: R. Ahmad, Y.D. Barnea, Y. Chen, R.O. Jozsa, J.B. Lawrie, K. Liu, N.C. Snaith, J.R. Winkler; five people were elected to Associate Membership: M.R. Clelland, S.B. Connor, M.J. Heath, T.W.S. Hodge, G.L. Titchener; one person was elected to Reciprocity Membership: E. Bayer-Fluckiger. The President announced the awards of the medal and prizes for 2004:
The President read short versions of the citations, to be published in full in the Bulletin. The Hardy Lecture was given by Professor T. Tao, on Long arithmetic progressions in the primes. After the meeting, a reception was held in De Morgan House, followed by dinner at the Bloomsbury Park Hotel.
ORDINARY MEETING held on Wednesday 30 June 2004 at the Aula Magna, Stockholm University, during the Fourth European Congress of Mathematics. At least 70 members and guests were present. The meeting began at 6.00 pm, with Professor F.C. KIRWAN, FRS, President, in the Chair. Professor Kirwan welcomed members and guests: the meeting provided an opportunity for overseas members to meet other members of the Society. She gave a particular welcome to Professor Lennart Carleson and Professor Serge Novikov, Honorary Members of the London Mathematical Society. She then welcomed guests, with a special welcome to Professor Ari Laptev, organiser of the European Congress of Mathematics, Sir John Kingman, President of the European Mathematical Society and Jean-Pierre Bourguignon. Fifteen members signed the membership book. The meeting was followed by a reception.
Stockholm, 28 June – 2 July 2004
|
|||||||||||||||
