Mathematical Sciences Geometry/Topology Seminar

October 28:
Speaker: Andrzej Zuk (Cornell)
Title: Generic hyperbolic groups with property (T)

Property (T) is a property of unitary representations of groups. It was used to solve several important problems related to different branches of mathematics like lattices in Lie groups, expanding graphs, invariant measures on spheres and operator algebras. We give a simple condition for a discrete group to have Kazhdan's property (T). This condition is easy to check and gives Kazhdan constants. We give examples of groups to which this method applies. We show that generic finitely presented groups in the sense of Gromov satisfy this condition and thus have property (T). Moreover we prove that small changes in the presentation of a group satisfying this condition do not change the fact that the group has property (T).