Event
Damian Orlef, Univeristy of Warsaw
Wednesday, November 23, 2016 15:00to16:00
Burnside Hall
Room 1234, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Kazhdan's property (T) of random groups in the square model for d>5/12.
A random group in the square model is obtained by fixing a set of n generators and introducing at random about (2n)^(4d) relations of length 4 between them, where d is a fixed parameter called the density and n tends to infinity. By results of T. Odrzyg贸藕d藕, if d<1/2, then these groups are with overwhelming probability (w.o.p.) infinite and hyperbolic. We prove that for d>5/12 the random groups G in the square model have w.o.p. Kazhdan's property (T). The proof proceeds by constructing a triangular group H, which maps onto finite index subgroup of G and verifying that the 呕uk's spectral criterion can be successfully applied to yield Kazhdan's property of H. The verification proceeds by analyzing random walks on the link of H, in the spirit of Broder and Shamir. Joint work with T. Odrzyg贸藕d藕 and P. Przytycki.