Title: Computing Kazhdan Constants

Martin Kassabov (Cornell University)

Tuesday, September 14 at 1:30pm in Malott 406

Abstract:

It is well known that a lattice in high rank simple Lie group have Kazhdan property. Unfortunately that the classical proof does not lead to any Kazhdan constants. The Kazhdan constants are necessary for a quantitative bounds for the working time of some algorithms in computational group theory. One of the first lower bounds for a Kazhdan constant of an infinite group with property T, was obtained by Y. Shalom. I will describe a generalization of this result which leads to an asymptotically exact bound for the Kazhdan constant for the groups SL_n(R), for some rings R. If time permits I will discuss how this idea may be used to prove that some groups have property tau.