the inaugural

University of Sheffield

Tuesday

06/06/06

This will be a working meeting. There will therefore be the usual time for
participant discussion.

- 11.00 am: Coffee in I15

- 11.30 am, Northcott Room J11: Assaf Libman (Aberdeen)

"Minami type splitting and some exotic p-local finite groups". - 1.45 pm, Northcott Room J11: Johann Sigurdsson (Sheffield)

``Some applications of parametrized homotopy theory'' - 2.45 pm, I15: Tea
- 3.00 pm, Northcott Room J11: GATA Lecturer, Bertrand Toen (Toulouse)

"Stacks and derived categories I"

I will present a new proof of Minami's stable splitting of classifying spaces of finite groups which depends on Peter Symonds's resolution of Webb's conjecture and the Bredon cohomology groups of certain spaces. I will show how the method applies to obtain a stable splitting of the classifying spaces of certain exotic p-local finite groups.

Johann Sigurdsson

I will give an introduction to the basic techniques of
parametrized homotopy theory and then apply them to derive well known
classical results such as Poincar\'e duality and the Wirthm\"uller isomorphism.

Bertrand Toen

The purpose of these two talks (the second is on Wednesday 7th)
is to report on recent works which use stack theory to study derived categories.
In the first talk I will discuss the problem of constructing
a reasonable moduli space for compact objects in a given triangulated category
(or rather a triangulated "dg-category"). In a first part I will explain some
motivations coming from algebraic geometry and
representation theory (e.g. the contruction of moduli spaces of complexes of
sheaves on an algebraic variety, the definition of "Hall algebras" for
derived categories). The second part of the talk will be devoted to
present a solution to this problem using a notion of "derived \infty-stack": the
main theorem states that the (derived \infty-) stack of compact objects in a
given "saturated" dg-category is algebraic. Some
corollaries and possible future applications will be discussed.

Anyone who wishes to participate is welcome: we shall operate the usual
arrangements for assistance with travel expenses. We expect to assemble for tea
and coffee in I15, Floor 5, from 11.00 am until the first talk. Each lecture
will take place in Room J11 of the Hicks Building, Hounsfield Road,
Sheffield.

Tea and Coffee will be served in the common room I15.

For
further information email John Greenlees j.greenlees@sheffield.ac.uk, (or
John Hunton jrh7@mcs.le.ac.uk or Nige Ray
nige@ma.man.ac.uk) if you are interested,
so we can make approximately the right amount of tea and coffee.

The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

To TTT54

To TTT56