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UID:20250913T032822EDT-5451zF1L8G@132.216.98.100
DTSTAMP:20250913T072822Z
DESCRIPTION:Title: Groups' approximation\, stability and high dimensional e
 xpanders\n\nAbstract: Several well-known open questions (such as: are all 
 groups sofic or hyperlinear?) have a common form: can all groups be approx
 imated by asymptotic homomorphisms into the symmetric groups Sym(n) (in th
 e sofic case) or the  unitary groups U(n) (in the hyperlinear case)?  In t
 he case of U(n)\, the question can be asked with respect to different metr
 ics and norms. We answer\, for the first time\, some of these versions\, s
 howing that there exist finitely presented groups which are not approximat
 ed by U(n) with respect to the Frobenius (=L_2)norm.   The strategy is via
  the notion of 'stability': some higher dimensional  cohomology vanishing 
 phenomena is proven to imply stability  and using   higher dimensional exp
 anders\, it is shown that some non-residually finite groups (central exten
 sions of some lattices in p-adic Lie groups)  are Frobenious stable and he
 nce cannot be Frobenius approximated. \n	\n	All notions will be explained.  
 Based on joint works with M\, De Chiffre\, L. Glebsky and A. Thom and with
  I. Oppenheim. \n
DTSTART:20190920T200000Z
DTEND:20190920T210000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Alex Lubotzky\, The Hebrew University of Jerusalem
URL:/mathstat/channels/event/alex-lubotzky-hebrew-univ
 ersity-jerusalem-300754
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