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SUMMARY:Spectral gaps of random hyperbolic surfaces - Will Hide (Oxford)
DTSTART:20251111T140000Z
DTEND:20251111T150000Z
UID:TALK239986@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Based on joint work with Davide Macera and Joe Thomas.\nThe fi
 rst non-zero eigenvalue\, or spectral gap\, of the Laplacian on a closed h
 yperbolic surface encodes important geometric and dynamical information ab
 out the surface.\nWe study the size of the spectral gap for random large g
 enus hyperbolic surfaces sampled according to the Weil-Petersson probabili
 ty measure.\nWe show that there is a c>0 such that a random surface of gen
 us g has spectral gap at least 1/4-O(g^-c) with high probability.\nOur app
 roach adapts the polynomial method for the strong convergence of random ma
 trices\, introduced by Chen\, Garza-Vargas\, Tropp and van Handel\, and it
 s generalization to the strong convergence of surface groups by Magee\, Pu
 der and van Handel\, to the Laplacian on Weil-Petersson random hyperbolic 
 surfaces.
LOCATION:MR12
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