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SUMMARY:Piotr Nowak (Polish Academy of Sciences\, Poland)
DTSTART:20200929T140000Z
DTEND:20200929T150000Z
DTSTAMP:20260423T024741Z
UID:CRM-CAMP/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/19/
 ">A computer-assisted proof of Kazhdan’s property (T) for automorphism g
 roups of free groups</a>\nby Piotr Nowak (Polish Academy of Sciences\, Pol
 and) as part of CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlin
 ear Analysis\n\n\nAbstract\nProperty (T) was introduced in 1967 by Kazhdan
  and is an important rigidity property of groups. The most elementary way 
 to define it is through a fixed point property: a group G has property (T)
  if every action of G by affine isometries on a Hilbert space has a fixed 
 point. Property (T) has numerous applications in the form of rigidity of a
 ctions and operator algebras associated to the group\, constructions of ex
 pander graphs or constructions of counterexamples to Baum-Connes-type conj
 ectures. \n\nIn this talk I will give a brief introduction to property (T)
  and explain the necessary group-theoretic background in order to present 
 a computer-assisted approach to proving property (T) by showing that the L
 aplacian on the group has a spectral gap. This approach allowed us show th
 at Aut(F_n)\, the group of automorphisms of the free group F_n on n genera
 tors\, has property (T) when n is at least 5: the case n=5 is joint work w
 ith Marek Kaluba and Narutaka Ozawa\, and the case of n at least 6 is join
 t work with Kaluba and Dawid Kielak. Important aspects of our methods incl
 ude passing from a computational result to a rigorous proof and later obta
 ining the result for an infinite family of groups using a single computati
 on. I will present an overview of these arguments.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/19/
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