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SUMMARY:Pierre-Emmanuel Caprace (UC Louvain)
DTSTART:20221011T130000Z
DTEND:20221011T150000Z
DTSTAMP:20260423T041749Z
UID:WienGAGT/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WienGAGT/24/
 ">New Kazhdan groups with infinitely many alternating quotients</a>\nby Pi
 erre-Emmanuel Caprace (UC Louvain) as part of Vienna Geometry and Analysis
  on Groups Seminar\n\n\nAbstract\nIntroductory talk: "Generating the alter
 nating groups"\n\nAbstract: The goal of this talk is to provide an overvie
 w of results and methods allowing one to build generating sets for the fin
 ite alternating groups. Some of those rely on the Classification of the Fi
 nite Simple Groups\, others don't. This theme will be motivated by open pr
 oblems concerning the construction of finite quotients of certain families
  of finitely generated infinite groups. \n\nResearch talk: "New Kazhdan gr
 oups with infinitely many alternating quotients"\n\nAbstract: I will intro
 duce a new class of infinite groups enjoying Kazhdan's property (T) and ad
 mitting alternating group quotients of arbitrarily large degree. Those gro
 ups are constructed as automorphism groups of the ring of polynomials in n
  indeterminates with coefficients in the finite field of order p\, generat
 ed by a suitable finite set of polynomial transvections. As an application
 \, we obtain the first examples of hyperbolic Kazdhan groups with infinite
 ly many alternating group quotients. We also obtain expander Cayley graphs
  of degree 4 for an infinite family of alternating groups. The talk is bas
 ed on joint work with Martin Kassabov.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/24/
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