# Fixed Point Properties of Random Groups

 COMPUTER SCIENCE/DISCRETE MATH SEMINAR, II Topic: Fixed Point Properties of Random Groups Speaker: Lior Silberman Affiliation: Princeton University Date: Tuesday, February 15 Time/Room: 10:30am - 12:30pm/S-101

In a sequence of preprints M. Gromov introduced a new model of a random quotient of a finitely generated group and indicated that under favourable conditions the quotient groups should be non-trivial and satisfy Kazhdan's Property (T), both with high probability. The proof of the first assertion (using techniques of small cancellation theory) was completed by T. Delzant and Y. Ollivier. I will present a proof of the second assertion (analyzing the averaging properties of random walks). In this model quotients are constructed using a finite graph. Property (T) of the group arises from the spectral gap of that graph.