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SUMMARY:&quot\;Almost&quot\; Representations and Group Stability - Bharatr
 am Rangarajan\, Hebrew University of Jerusalem
DTSTART:20240531T124500Z
DTEND:20240531T134500Z
UID:TALK212323@talks.cam.ac.uk
CONTACT:Francesco Fournier-Facio
DESCRIPTION:The notion of group stability\, which asks if an "almost" homo
 rmorphism is "close" to a homomorphism\, was introduced in Dogon's talk la
 st week\, and studied in the setting of pointwise Hilbert-Schmidt stabilit
 y.\nIn this talk\, we will explore the question in the context of uniform 
 distance with respect to the operator norm. This is a more natural questio
 n that goes all the way back to Turing and Ulam\, with subsequent developm
 ents by Kazhdan\, et al. The main tool we use is a non-standard asymptotic
  variant of bounded cohomology of groups\, devised so that the vanishing o
 f this cohomology implies stability in this setting. We will then sketch h
 ow\, apart from unifying earlier stability results\, this theory can help 
 prove stability for a large class of groups\, including high-rank lattices
  and lamplighters.\nBased on joint works with Glebsky\, Lubotzky\, Monod\,
  and Fournier-Facio.
LOCATION:MR11
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