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SUMMARY:Hilbert-Schmidt stability\, character theory and approximation pro
 perties of groups - Alon Dogon\, Weizmann Institute of Science
DTSTART:20240524T124500Z
DTEND:20240524T134500Z
UID:TALK212320@talks.cam.ac.uk
CONTACT:Francesco Fournier-Facio
DESCRIPTION:In recent years there has been a considerable interest in ques
 tions regarding approximate homomorphisms between groups\, going under the
  name of group stability. For our setting\, a group G is said to be HS-sta
 ble if any (pointwise) approximate finite dimensional unitary representati
 on of G is (pointwise) close to a true unitary representation of G\, where
  proximity is measured by the normalized Hilbert-Schmidt norm. \nIn this t
 alk we will introduce and connect stability to other important questions i
 n approximation theory and representation theory of infinite discrete grou
 ps. In the situation of amenable groups\, stability can be translated to a
  question regarding character theory of the group\, yielding a useful crit
 erion for giving examples. In particular\, it can be utilized to prove exi
 stence of uncountably many such groups (joint work with Vigdorovich and Le
 vit).\nIn the opposite case of property (T) groups\, such as lattices in s
 imple higher rank Lie groups and Gromov random groups\, stability is a pot
 entially rare property. Indeed\, we showed that in many cases\, weakenings
  of stability would imply the existence of a non-sofic group.
LOCATION:MR13
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