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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Stability of homomorphisms into symmetric groups -
Oren Becker (Cambridge)
DTSTART;TZID=Europe/London:20200122T134500
DTEND;TZID=Europe/London:20200122T144500
UID:TALK137737AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/137737
DESCRIPTION:Ulam stability asks whether approximate homomorphi
sms are close to homomorphisms. It is much studied
in the context of homomorphisms into groups of li
near operators.\nWe shall discuss it in the contex
t of maps from a finitely generated group G to Sym
(n)\, as n tends to infinity\, using the normalize
d Hamming metric d_n on Sym(n).\nMore precisely\,
we fix a group G\, and ask whether for any given s
equence {f_n} of maps f_n : G -> Sym(n)\, such tha
t d_n(f_n(xy)\,f_n(x)f_n(y)) -> 0 for all x\,y in
G\, there 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 ver
sion and a uniform version\, and we will discuss b
oth. In any case\, the answer depends on the group
G.\n\nThe study of stability involves notions suc
h as amenability\, invariant random subgroups\, pr
operty (T)\, sofic groups and basis reduction theo
ry. We shall survey known results and the connecti
ons to property testing and to approximability in
group theory.\n\nThe talk is based on joint works
with Alex Lubotzky\, Andreas Thom\, Jonathan Moseh
iff and Michael Chapman.\n\nMore details will be g
iven in the course Approximate Group Actions and U
lam Stability\, given on Mondays and Wednesdays th
roughout Lent term.\n
LOCATION:MR4\, CMS
CONTACT:Peter Varju
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