Applications of K-theory and Cohomology, Southampton 30 March-2 April 2004.

General Information

The meeting will address recent exciting developments on the boundaries where Algebraic K-Theory meets with arithmetic, algebraic geometry and algebraic topology. The interplay between these topics has been thematic in the long research career of Professor Victor Snaith, a faculty member at the University of Southampton whose sixtieth birthday will be marked by holding this workshop. The workshop itself will serve as a follow-up to the research programme entitled ``New Contexts for Stable Homotopy Theory'' organised by Greenlees, Miller, Morel and Snaith at the Newton Institute during September-December 2002.

Main themes of the workshop will include motivic homotopy theory and K-theory, algebraic cobordism of Levine, Morel, and Voevodsky, recent progress on the Bloch-Kato and Beilinson conjectures and applications of algebraic K-theory to the Kummer-Vandiver conjecture in number theory and current ramifications of these topics. There has been much intense activity in this area and the workshop is intended to stimulate exchange of ideas and to facilitate further progress in this exciting and very active area of research.

We have been given permission by the London Mathematical Society to hold a Spitalfields Day on 30th March 2004. This will be a day consisting of three one-hour lectures aimed at introducing the topic of the conference to mathematicians who are not necessarily specialists in K-theory and cohomology.

There will be talks on each of Tuesday (LMS Spitalfields Day), Wednesday, Thursday and Friday. Participation of postgraduate students and recent postdoctoral mathematicians will be encouraged. This meeting will be organized by J. Brodzki, B. Koeck and I. Leary. Please contact Jacek Brodzki (j.brodzki@soton.ac.uk) if you are interested in attending the conference.

Conference Participation form

It would help us a lot if all prospective participants could provide the details of accommodation requirements by filling out the Participation Form.

Participants

Expected participants include the following mathematicians, where an asterisk indicates acceptance:

G. Banaszak* (Poznan), D. Burns* (KCL), Rob de Jeu* (Durham), I. Fesenko* (Nottingham), J.P. Greenlees* (Sheffield), J.F. Jardine* (Western Ontario), B. Kahn* (Paris VII), M. Levine* (Northeastern), I. Madsen* (Aarhus), K. Sato* (Nottingham), B. Totaro*(Cambridge), A. Vishik* (Moscow), A. Weiss* (U. Alberta)

Financial arrangements

The workshop is supported by a grant from the London Mathematical Society under Scheme 1. Part of the grant is specifically set aside to support UK based postgraduate students, who are therefore encouraged to apply. As the funds are limited, please contact the organizers as soon as possible. There is a certain amount of money to support interested mathematicians from the fSU and countries of Central Europe (e.g. Poland). Again, it is worthwhile to contact the organizers as soon as possible.

There will be a conference registration fee, to cover some local expenses.

Travel

Southampton is easy to reach by air, rail, sea and road. If you want to fly here, London's Heathrow airport is only about an hour away from Southampton. Southampton has a small airport with direct flights from Paris, so if you can arrange a flight on Air France, you could fly all the way to Southampton. The budget airlines tend to use the airports north of London (Luton and Stansted) although there may be some budget flights into Gatwick, which is about 2 hours away from Southampton.

The Eurostar train, connecting Paris with London, arrives at London Waterloo station, where trains to Southampton originate. It takes about 1h15 to get to Southampton from London by train.

Detailed instructions, suitable more for the UK participants, on how to get to Southampton are given at http://www.soton.ac.uk/~indexes/maps/. The organizers will be happy to answer any further queries.

To get to Southampton from Heathrow airport, you can do one of the following:

1. Take a National Express coach from the main coach station (cost about 15 pounds) to Southampton. This deposits you at the coach station in the south part of town (about 3 miles from campus), so it's best to take a taxi from there to Highfield campus (and the Glen Eyre complex).

2. Take a Rail Link coach to Woking and from there a train to Southampton. The coach leaves from the same main coach station at the airport. The coach/train service offered by Rail Link is one service, so the ticket person should be able to sell you a ticket to Southampton. The nearest rail station to campus in Southampton is Southampton Airport Parkway (small station with a long name), there are normally taxis waiting outside. There is also a bus service.

The only other rail station in Southampton is called Southampton Central, there is a bus service (and taxis) from there to the main Campus.

The University is running a bus service connecting the two stations with the Highfield campus. Timetables are given here:

http://www.unilink.soton.ac.uk/timetables.html

Accommodation

The Department of Mathematics is located on the Highfield Campus of the University, and its location is shown on the following map:

http://www.soton.ac.uk/~indexes/maps/highfield.html

The Spitalfields Day

Applications of K-theory and Cohomology

30th March 2004

Lectures will take place in the Department of Mathematics, Building 54, room 4A
10.30 Coffee
11:00 am Rick Jardine (University of Western Ontario): The discrete cohomology of algebraic groups.
12:30-13:45 Lunch
14:00 Victor Snaith (University of Southampton): Algebraic K-theory and Arithmetic.
15:00 Tea
15:30 Marc Levine (Northeastern University): Motives, Mixed Motives and Motivic Cohomology.
17:00 Wine and Cheese party

Titles of talks at the workshop:

G. Banaszak: Detecting linear dependence of nontorsion points in K-groups and Mordell Weil groups via reduction maps. (joint work with W. Gajda and P. Krason)
Jacek Brodzki: Entire cyclic cohomology of Schatten classes.
I. Fesenko: Steps in analytic arithmetic geometry.
J. P. C. Greenlees: Equivariant forms of connective K-theory
Bruno Kahn: 1-motives and triangulated motives
Rob de Jeu: K2 of hyperelliptic curves and Beilinson's conjecture.
Bernhard Koeck Euler characteristics of nearly perfect complexes.
Ian Leary: The L2 cohomology of Artin groups.
I. Madsen: K-theory and the deRham-Witt complex.
K. Sato: p-adic etale Tate twists and arithmetic duality.
Burt Totaro: Torsion in cohomology and torsors for simple algebraic groups.
Al Weiss: Equivariant Iwasawa Theory.

Programme of talks:

Wed, 31st March Thu, 1 April Fri, 2 April
9.30-10.15 B. Koeck I.J. Leary A. Weiss
10.45-11.45 I. Madsen I. Fesenko A. Vishik
12.00-13.00 B. Kahn G. Banaszak D. Burns
14.30-15.30 B. Totaro R. de Jeu J. Brodzki
16.00-17.00 J. P. Greenlees K. Sato

Conference dinner

There will be a conference dinner at 19.45 on Wednesday, 31st March, at the POSH Indian Restaurant, 1 Queensway, Southampton, tel: 8022 6388.

Theatre opportunity

From 31st March until 3rd April, the critically acclaimed Scottish Babel Theatre Company presents Ibsen's A Doll's House at the Nuffield Theatre which is on the University of Southampton campus a stone's throw from the Mathematics Building.