Texas A&M University, Department of
Mathematics, 216 Milner Hall, 8th of November 2005, 3:00-3:50
Groups and Dynamics Seminar
Compression of
uniform embeddings of groups into Hilbert spaces
Romain Tessera of Vanderbilt University
In this talk, we will show that for amenable groups, there exists a
relation between the compression functions associated to uniform
embeddings of the group into a Hilbert space, and the first eigenvalue
of the laplacien in balls. For a certain class of groups, including all
amenable Lie groups, this relation is "optimal" in an asymptotic sense.
We also caracterize quantitatively how one can uniformly embed a
3-regular tree into a Hilbert space.