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SUMMARY:Approximate actions and Ulam stability - Oren Becker (University o
 f Cambridge)
DTSTART:20191108T134500Z
DTEND:20191108T144500Z
UID:TALK134194@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Given two permutations A and B in Sym(n) such that AB and BA a
 re almost equal\, are there A' and B' in Sym(n) such that A is close to A'
 \, B is close to B'\, and A'B'=B'A'?\nArzhantseva and Paunescu formalized 
 this question and gave an affirmative answer: "Nearly commuting permutatio
 ns are near commuting permutations". Equivalently\, approximate actions of
  the group Z^2^ on finite sets are close to genuine actions\, i.e.\, Z^2^ 
 is stable (in permutations).\nI will discuss the more general problem: Whi
 ch finitely generated groups are stable?\n\nThis will bring into the pictu
 re notions such as Property (T)\, amenability\, invariant random subgroups
 \, sofic groups and property testing.\n\nThe talk is based on joint works 
 with Alex Lubotzky\, Andreas Thom and Jonathan Mosheiff.
LOCATION:CMS\, MR13
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