# Geometric Analysis and Topology Seminar

#### Expanders with no Uniform Embedding in a Uniformly Convex Banach Space

**Speaker:**
Vincent Lafforgue, Jussieu

**Location:**
Warren Weaver Hall 1013

**Date:**
Friday, February 29, 2008, 1 p.m.

**Synopsis:**

We show that if \(F\) is a local non-archimedian field the trivial representation of \(S L_3(F)\) is isolated among isometric representations in uniformly convex Banach spaces and deduce from this strong form of property \((T)\) that the expanders constructed as finite quotients of a lattice in \(S L_3(F)\) do not embed uniformly in a uniformly convex Banach space. The same question for Ramanujan expanders associated to quaternions is open: a strong form of property (tau) would be needed. Notes from a previous talk on this subject are available at the address http://www.institut.math.jussieu.fr/~vlafforg/edimbourg.pdf.