Hebrew University
 
Amitsur Algebra Seminar
*****************************
 
Time: Thursday, May 5, at 12:00.
Place: room 209, Mathematics building
 
Speaker: Tsachik Gelander (HUJI)
 
Title: On the growth of Betti numbers of arithmetic groups and manifolds.
 
Abstract:
We study  the asymptotic behaviour of the Betti numbers of higher rank
locally symmetric manifolds as their volumes
tend to infinity. Our main theorem is a uniform version of the Luck
Approximation Theorem, which is much stronger than the linear upper
bounds on Betti numbers given by Gromov.
 The basic idea is to adapt the theory of local convergence,
originally introduced for sequences of graphs of bounded degree by
Benjamimi and Schramm, to sequences of Riemannian manifolds. Using
rigidity theory we are able to show that when the volume tends to
infinity, the manifolds locally converge to the universal cover in a
sufficiently strong manner that allows us to derive the convergence of
the normalized Betti numbers.
 
Joint work with M. Abert, N. Bergeron, I. Biringer, N. Nikolov, J.
Raimbault and I. Samet.
 
You are cordially invited!
 
 <http://math.huji.ac.il/amitsur.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>