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UID:20250709T181746EDT-2368mcJK7v@132.216.98.100
DTSTAMP:20250709T221746Z
DESCRIPTION:Title: The spectral gap of a random hyperbolic surface\n	Abstrac
 t: On a compact hyperbolic surface\, the Laplacian has a spectral gap betw
 een 0 and the next smallest eigenvalue if and only if the surface is conne
 cted. The size of the spectral gap measures both how highly connected the 
 surface is\, and the rate of exponential mixing of the geodesic flow on th
 e surface. There is an analogous concept of spectral gap for graphs\, with
  analogous connections to connectivity and dynamics. Motivated by theorems
  about the spectral gap of random regular graphs\, we proved that for any 
 $\epsilon > 0$\, a random cover of a fixed compact connected hyperbolic su
 rface has no new eigenvalues below 3/16 - $\epsilon$\, with probability te
 nding to 1 as the covering degree tends to infinity. The number 3/16 is\, 
 mysteriously\, the same spectral gap that Selberg obtained for congruence 
 modular curves. The talk is intended to be accessible to graduate students
  and is based on joint works with Frédéric Naud and Doron Puder.\n\n \n\nF
 or zoom link for the meeting please contact dmitry.jakobson [at] mcgill.ca
 \n
DTSTART:20200715T150000Z
DTEND:20200715T160000Z
SUMMARY:Michael Magee (Durham University)
URL:/mathstat/channels/event/michael-magee-durham-univ
 ersity-323238
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