Optimal embeddings of groups into Hilbert spaces

Optimal embeddings of groups into Hilbert spaces

Wed, 18/05/2011
16:00 		David Hume (University of Oxford) Junior Geometric Group Theory Seminar Add to calendar SR1
Optimal embeddings of groups into Hilbert spaces
We begin by showing the underlying ideas Bourgain used to prove that the Cayley graph of the free group of finite rank can be embedded into a Hilbert space with logarithmic distortion. Equipped with these ideas we then tackle the same problem for other metric spaces. Time permitting these will be: amalgamated products and HNN extensions over finite groups, uniformly discrete hyperbolic spaces with bounded geometry and Cayley graphs of cyclic extensions of small cancellation groups.