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SUMMARY:Volume\, Complexity and Torsion - Raz Slutsky (University of Oxfor
 d)
DTSTART:20250715T143000Z
DTEND:20250715T150000Z
UID:TALK234034@talks.cam.ac.uk
DESCRIPTION:In many non-positively curved settings\, the volume of a manif
 old controls its complexity in various ways. Many of these results are bas
 ed on geometric methods and thus do not apply in the case of orbifolds\, o
 r equivalently\, in the presence of torsion in the corresponding group. In
  this talk\, I will discuss two results which try to overcome this issue. 
 The first is a quantitative version of Selberg's lemma\, relating the co-v
 olume of an arithmetic lattice to the minimal index of a torsion-free subg
 roup. The second is a bound on the Betti numbers over finite fields of neg
 atively curved orbifolds in terms of their volume. This extends a result b
 y Gromov. These are joint works with Tsachik Gelander and Guy Kapon.
LOCATION:Seminar Room 1\, Newton Institute
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