Combinatorics Seminar - Sean Eberhard

16:00-18:00

Speaker: Sean Eberhard

Title: Diameter of high-rank classical groups with random generators

Abstract: Babai's conjecture asserts that the diameter of the Cayley graph of any finite simple group G is bounded by (log |G|)^O(1). This conjecture has been resolved for groups of bounded rank, but for groups of unbounded rank such as SL_n(2) it is wide open. Even for random generators, only the case of alternating groups is resolved. I will talk about some recent work with Urban Jezernik in which we resolve the case of G = SL_n(p), p = O(1), with at least *three* random generators, and other classical groups with a few more random generators.