# TTT45: Leicester

Department of Mathematics and Computer Science, University of Leicester.

## Date

16 June 2004

## Speakers

Daniel Singh (Sheffield)

The moduli space of stable n-pointed curves of genus zero

Peter Jorgensen (Leeds)

Rings and spaces

Assaf Libman (Aberdeen)

On the homotopy type of the uncompleted classifying spaces of p-local finite groups

## Abstracts

### The moduli space of stable n-pointed curves of genus zero

After introducing the moduli space of stable n pointed curves of genus zero I intend to give a new description for this space and describe a natural isomorphism between them. I will then briefly describe the cohomology of this space if time permits.

### Rings and spaces

Ring theory and algebraic topology have a convenient meeting point in the form of differential graded algebras (DGAs). On one hand, rings are special DGAs, and the homological machinery built to study DGAs specialises to a slick version of homological ring theory. On the other hand, each topological space gives rise to a singular cochain DGA which encodes information about the space.

We shall see how the study of DGAs gives rise to theorems which are simultaneous generalisations of theorems in ring theory and algebraic topology.

### On the homotopy type of the uncompleted classifying spaces of p-local finite groups

I will report on an ongoing project whose aim is to understand the classifying space of a p-local finite group before it is p-completed. This work is joint with Antonio Viruel. Some time ago the normaliser decomposition for p-local finite groups was constructed. Its advantage is in being defined over a poset.

We use this construction to show that in some interesting cases the classifying space of a p-local finite group is an Eilenberg-MacLane space. Some interesting consequences in group cohomology are drawn. We can also show that the universal space of this classifying space is finite dimensional if the p-local finite group is not exotic.

## Further information

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