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SUMMARY:Uniform stability of high-rank Arithmetic groups - Alex Lubotzky (
 Weizmann Institute of Science)
DTSTART:20251126T114500Z
DTEND:20251126T124500Z
UID:TALK240430@talks.cam.ac.uk
DESCRIPTION:Lattices in high-rank semisimple groups enjoy several special 
 properties like super-rigidity\, quasi-isometric rigidity\, first-order ri
 gidity\, and more.\nIn this talk\, we will add another one: uniform ( a.k.
 a. Ulam) stability. Namely\,&nbsp\; it will be shown that (most)\nsuch lat
 tices D satisfy: every finite-dimensional unitary&nbsp\; "almost-represent
 ation" of D ( almost w.r.t. to a sub-multiplicative norm on the complex ma
 trices)&nbsp\;is a small deformation of a true unitary representation.&nbs
 p\;\nThis extends a result of Kazhdan (1982)&nbsp\; for amenable groups an
 d Burger-Ozawa-Thom (2013) for SL(n\,Z)\, n>2.&nbsp\;\nThe main technical 
 tool is a new cohomology theory ("asymptotic cohomology") that is related 
 to bounded cohomology in a similar way to the connection of the last one w
 ith ordinary cohomology. The vanishing of H^2 w.r.t. to a suitable module 
 implies the above stability.\nThe talk is based on joint work with L. Gleb
 sky\, N. Monod\, and B. Rangarajan (to appear in Memoirs of the EMS).&nbsp
 \;
LOCATION:Seminar Room 1\, Newton Institute
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