Introductory talk: "Generating the alternating groups"

Abstract: The goal of this talk is to provide an overview of results and methods allowing one to build generating sets for the finite alternating groups. Some of those rely on the Classification of the Finite Simple Groups, others don't. This theme will be motivated by open problems concerning the construction of finite quotients of certain families of finitely generated infinite groups. 

Research talk: "New Kazhdan groups with infinitely many alternating quotients"

Abstract: I will introduce a new class of infinite groups enjoying Kazhdan's property (T) and admitting alternating group quotients of arbitrarily large degree. Those groups are constructed as automorphism groups of the ring of polynomials in n indeterminates with coefficients in the finite field of order p, generated by a suitable finite set of polynomial transvections. As an application, we obtain the first examples of hyperbolic Kazdhan groups with infinitely many alternating group quotients. We also obtain expander Cayley graphs of degree 4 for an infinite family of alternating groups. The talk is based on joint work with Martin Kassabov. 

Join Zoom meeting ID 613 8691 2732 or via the link below.

Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)