# Sheffield GATA Lecture

## Department of Pure MathematicsUniversity of Sheffield Tuesday 06/06/06

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

## Programme

• 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"
We expect to go to eat nearby, soon after the last talk.

### GATA Lectures

The Sheffield GATA lectures are a principle activity of the Sheffield GATA Centre (directed by Prof Tom Bridgeland). The GATA lecturer is invited to spend an extended period in Sheffield and to give a series of lectures on a current topic of broad interest.

### Abstracts

Assaf Libman
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.

## How to get there

From the rail station, you can catch the Number 60 bus, and get off where it crosses the ring road. Or take the supertram to the University stop. There is more information at School of Mathematics and Statistics Homepage
The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

## Escape routes

Back to TTT Homepage
To TTT54
To TTT56