New Kazhdan groups with infinitely many alternating quotients

11-Oct-2022, 13:00-15:00 (18 months ago)

Abstract: 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.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic


Vienna Geometry and Analysis on Groups Seminar

Organizer: Christopher Cashen*
*contact for this listing

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