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SUMMARY:Stability of homomorphisms into symmetric groups - Oren Becker (Ca
 mbridge)
DTSTART:20200122T134500Z
DTEND:20200122T144500Z
UID:TALK137737@talks.cam.ac.uk
CONTACT:Peter Varju
DESCRIPTION:Ulam stability asks whether approximate homomorphisms are clos
 e to homomorphisms. It is much studied in the context of homomorphisms int
 o groups of linear operators.\nWe shall discuss it in the context of maps 
 from a finitely generated group G to Sym(n)\, as n tends to infinity\, usi
 ng the normalized Hamming metric d_n on Sym(n).\nMore precisely\, we fix a
  group G\, and ask whether for any given sequence {f_n} of maps f_n : G ->
  Sym(n)\, such that d_n(f_n(xy)\,f_n(x)f_n(y)) -> 0 for all x\,y in G\, th
 ere is a sequence {h_n} of homomorphisms h_n : G -> Sym(n) such that d_n(f
 _n(x)\,h_n(x)) -> 0 for all x in G.\nThis question has a pointwise version
  and a uniform version\, and we will discuss both. In any case\, the answe
 r depends on the group G.\n\nThe study of stability involves notions such 
 as amenability\, invariant random subgroups\, property (T)\, sofic groups 
 and basis reduction theory. We shall survey known results and the connecti
 ons to property testing and to approximability in group theory.\n\nThe tal
 k is based on joint works with Alex Lubotzky\, Andreas Thom\, Jonathan Mos
 ehiff and Michael Chapman.\n\nMore details will be given in the course App
 roximate Group Actions and Ulam Stability\, given on Mondays and Wednesday
 s throughout Lent term.\n
LOCATION:MR4\, CMS
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