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SUMMARY:Geometry and spectrum of random hyperbolic surfaces - Laura Monk (
 Bristol)
DTSTART:20220504T150000Z
DTEND:20220504T160000Z
UID:TALK171989@talks.cam.ac.uk
CONTACT:Henry Wilton
DESCRIPTION:The aim of this talk is to present recent progress in the spec
 tral theory of hyperbolic surfaces\, which was achieved by bringing a new 
 probabilistic viewpoint to this classic field. Studying random hyperbolic 
 surfaces allows to prove statements true for most surfaces rather than eve
 ry single one of them\, and hence to exclude some known pathological examp
 les. I will present estimates on the density of eigenvalues and the spectr
 al gap of typical surfaces in the Weil--Petersson random setting. These re
 sults are proven using the Selberg trace formula\, together with geometric
  information on closed geodesics on random surfaces.
LOCATION:MR13
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