BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Laura Monk (Bristol) DTSTART:20241210T131500Z DTEND:20241210T140000Z DTSTAMP:20260423T021146Z UID:MAS-MP/85 DESCRIPTION:Title: Typical hyperbolic surfaces have an optimal spectral gap\nby Laura Mon k (Bristol) as part of Munich-Copenhagen-Santiago Mathematical Physics sem inar\n\n\nAbstract\nThe first non-zero Laplace eigenvalue of a hyperbolic surface\, or its spectral gap\, measures how well-connected the surface is : surfaces with a large spectral gap are hard to cut in pieces\, have a sm all diameter and fast mixing times. For large hyperbolic surfaces (of larg e area or large genus g\, equivalently)\, we know that the spectral gap is asymptotically bounded above by 1/4. The aim of this talk is to present a n upcoming article\, joint with Nalini Anantharaman\, where we prove that most hyperbolic surfaces have a near-optimal spectral gap. That is to say\ , we prove that\, for any ε>0\, the Weil-Petersson probability for a hype rbolic surface of genus g to have a spectral gap greater than 1/4-ε goes to one as g goes to infinity. This statement is analogous to Alon’s 1986 conjecture for regular graphs\, proven by Friedman in 2003. I will presen t our approach\, which shares many similarities with Friedman’s work\, a nd introduce new tools and ideas that we have developed in order to tackle this problem.\n LOCATION:https://researchseminars.org/talk/MAS-MP/85/ END:VEVENT END:VCALENDAR