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SUMMARY:Alex Lubotzky (The Hebrew University of Jerusalem)
DTSTART:20211005T150000Z
DTEND:20211005T163000Z
DTSTAMP:20260423T005852Z
UID:Vinberg/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Vinberg/1/">
 Stability and testability of permutations' equations</a>\nby Alex Lubotzky
  (The Hebrew University of Jerusalem) as part of The Vinberg Lecture Serie
 s\n\n\nAbstract\nLet $A$ and $B$ be two permutations in $\\text{Sym}(n)$ t
 hat ``almost commute'' -- are they a small deformation of permutations tha
 t truly commute? More generally\, if $R$ is a system of words-equations in
  variables $X = \\{x_1\, \\ldots \,x_d\\}$ and $A_1\, \\ldots \,A_d$ are p
 ermutations that are nearly solutions\; are they near true solutions? \n\n
 It turns out that the answer to this question depends only on the group pr
 esented by the generators $X$ and relations $R$. This leads to the notions
  of ``stable groups'' and ``testable groups''. \n\nWe will present a few r
 esults and methods which were developed in recent years to check whether a
  group is stable or testable. We will also describe the connection of this
  subject with property testing in computer science\, with the long-standin
 g problem of whether every group is sofic\, and with invariant random subg
 roups.\n
LOCATION:https://researchseminars.org/talk/Vinberg/1/
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