# TTT86: Sheffield

The University of Sheffield.

Supported by the London Mathematical Society.

## Date

10 January 2013

## Speakers

### Magda Kedziorek (Sheffield)

Towards the algebraic model of rational equivariant cohomology theories.

Towards the algebraic model of rational equivariant cohomology theories.

Cohomology theories are represented by spectra. However the category of spectra is quite complicated. The machinery of model categories allows us to look for different (easier, algebraic) models with the same homotopy information as the category of spectra. It is well known that rational chain complexes give an algebraic model for the rational cohomology theories. However, for G-equivariant cohomology theories, no general result of this form is known when G is a compact Lie group.

In this talk I will describe some earlier work and introduce a framework for constructing algebraic models in general. It is conjectured that the models will take the form of sheaves of modules over a topological category of subgroups of G.

I will assume only basic knowledge of algebraic topology and I will remind the audience of the ideas of model structures.

### Armindo Costa (Warwick)

The topology of random 2-complexes

The topology of random 2-complexes

In this talk I will describe some models for random simplicial complexes introduced in recent literature. Although these models generalise the celebrated Erdos-Rényi model for random graphs it makes sense to study their probabilistic topology, ie estimating topological invariants of random spaces.

I will survey some of the known topological phase transitions, connections to Gromov’s theory of random groups and some challenges that lay ahead.

### Teimuraz Pirashvili (Leicester)

Polynomial functors, functor cohomology and applications

Polynomial functors, functor cohomology and applications