# TTT79: Sheffield

The University of Sheffield.

Supported by the London Mathematical Society.

## Date

8 June 2011

## Speakers

### Pokman Cheung (Sheffield)

Equivariant chiral differential operators and associated modules

Equivariant chiral differential operators and associated modules

After an introduction of chiral differential operators (CDOs) on a manifold with a mention of their relation to 'formal loops', I will discuss how they interact with a Lie group action. Let G be a compact Lie group, g its Lie algebra and g' a central extension of the formal loops in g. Under a condition on the equivariant first Pontrjagin class, a G-action on a manifold can be lifted to a (g',G)-action on CDOs. The latter may provide a construction of vector bundles on 'formal loops' (e.g. the spinor bundle).

### Ken Deeley (Durham)

Configuration spaces of thick particles on graphs

Configuration spaces of thick particles on graphs

We discuss topological properties of configuration spaces of particles of positive radius on a metric graph G. In topological robotics, these spaces model the collision-free motion of autonomous robots moving on the guidepath network G. Our main tool for studying these spaces is a piecewise linear (PL) Morse-Bott theory extending the PL Morse theory developed by Bestvina and Brady.

### Ieke Moerdijk (Utrecht/Sheffield)

Rectification of infinity-operads

Rectification of infinity-operads

Combined work of Bergner, Joyal-Tierney and Lurie shows the Quillen equivalence between infinity categories and simplicial categories. I will present an extension of this result, establishing a similar equivalence between infinity operads and simplicial operads. The talk is based on joint work with D-C Cisinski.