# TTT71: Leicester

Department of Mathematics and Computer Science, University of Leicester.

## Date

7 December 2008

## Speakers

### John Jones (Warwick)

Calculating string homology

Calculating string homology

### Chris Braun (Leicester)

Topological field theory and moduli spaces of Klein surfaces

Topological field theory and moduli spaces of Klein surfaces

Abstract: The ribbon graph decomposition of moduli space gives orbi-cell complexes homotopy equivalent to moduli spaces of Riemann surfaces. Ribbon graphs are related to the A-infinity operad which gives a dual interpretation (due to Kevin Costello) of this in terms of topological conformal field theory.

I will explain a generalisation of TFTs allowing unorientable manifolds and outline how this leads to a Möbius graph decomposition for moduli spaces of Klein surfaces (real algebraic curves). I will also mention another quite different partial compactification of these spaces, closer in spirit to the operad of Deligne-Mumford moduli spaces, with a different graph complex.

### Nick Gurski (Sheffield)

Categorical models for stable homotopy types

Categorical models for stable homotopy types

Abstract: One of the guiding principles of higher category theory is the Homotopy Hypothesis: whatever 'n-dimensional groupoids' are, they should model homotopy n-types (spaces whose homotopy groups vanish above dimension n).

This talk will be about the stable version of this hypothesis in low dimensions. In particular, I will emphasise how coherence theorems for certain categorical structures are central to the question of modeling stable homotopy types. The work in this talk is joint with Mikhail Kapranov.