LMS Scheme 9: Celebrating New Appointments

Titles and abstracts:

David Hume: Regular embeddings, topological expanders and waist inequalities

This talk introduces regular embeddings as a large-scale geometric generalisation of both subgraph inclusion (between bounded degree graphs) and subgroup inclusion (between finitely generated groups).  I will describe a family of very new tools that yield obstructions to regular maps coming from graph theory (separators and cutwidth), analysis (Poincaré inequalities) and topology (waist inequalities), explain some highlights of the current theory and raise many many open questions.

John Mackay: Connectivity of low dimensional hyperbolic groups

Hyperbolic groups are ubiquitous in geometric group theory, indeed in some sense "almost every" finitely presented group is hyperbolic.  I'll discuss the relationship between two ways to measure how big such a group is: the conformal dimension of its boundary at infinity, and its separation profile, with a particular focus on the case the boundary is one-dimensional.  Based on joint work with Hume and Tessera. 

Cornelia Drutu: Property (T) and a-T-menability for Banach spaces

This talk will discuss various versions of fixed point properties, generalizing property (T), and of proper actions on Banach spaces, generalizing a-T-menability. In particular, I will describe a notion of spectrum providing an optimal way to measure ``the strength'' of the property (T) that an infinite group may have, and what can be said about this spectrum, in particular for hyperbolic groups. I will also describe weak versions of a-T-menability for (acylindrically) hyperbolic groups and for mapping class groups.

This is on joint work with Ashot Minasyan and Mikael de la Salle, and with John Mackay.