Cornell Math - MATH 762, Fall 1999

MATH 762 — Fall 1999
Seminar in Geometry: Property (T), random walks and discrete groups

Instructor: Andrzej Zuk

Time: MWF 11:15-12:05

Room: Malott 206

Property (T) was introduced by Kazhdan in order to solve Siegel's conjecture which states that discrete subgroups of some Lie groups are finitely generated. Since then this property of unitary representations of groups was used to solve several other outstanding problems related to different branches of mathematics like expanding graphs (Margulis), invariant measures on spheres (Margulis, Sullivan), operator algebras (Connes) and others. We would like to present an elementary introduction to this property, its applications and recent results concerning constructions of discrete groups with property (T). We will also discuss its relation to random walks, Ramanujan groups and L² cohomology.