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SUMMARY:Tsachik Gelander (Weizmann Institute of Science)
DTSTART:20200520T111000Z
DTEND:20200520T123000Z
DTSTAMP:20260404T131151Z
UID:GDS/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/GDS/4
 /">Convergence of normalized Betti numbers in nonpositive curvature</a>\nb
 y Tsachik Gelander (Weizmann Institute of Science) as part of Geometry and
  Dynamics seminar\n\n\nAbstract\nI will show that if X is any symmetric sp
 ace other than 3-dimensional \nhyperbolic space and M is any finite volume
  manifold that is a quotient \nof X\, then the normalized Betti numbers of
  M are "testable"\, i.e. one \ncan guess their values by sampling the mani
 fold at random places. This \nis joint with Abert\, Biringer and Bergeron\
 , and extends some of our \nolder work with Nikolov\, Raimbault and Samet.
  The content of the recent \npaper involves a random discretization proces
 s that converts the "thick \npart" of M into a simplicial complex\, togeth
 er with analysis of the \n"thin parts" of M. As a corollary\, we obtain th
 at whenever X is a higher \nrank irreducible symmetric space and M_i is an
 y sequence of distinct \nfinite volume quotients of X\, the normalized Bet
 ti numbers of the M_i \nconverge to the "L^2-Betti numbers" of X.\n
LOCATION:https://stable.researchseminars.org/talk/GDS/4/
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