BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Magee DTSTART:20220323T160000Z DTEND:20220323T170000Z DTSTAMP:20260418T065506Z UID:LNTS/66 DESCRIPTION:Title: Th e maximal spectral gap of a hyperbolic surface\nby Michael Magee as pa rt of London number theory seminar\n\n\nAbstract\nA hyperbolic surface is a surface with metric of constant curvature -1. The spectral gap between\n the first two eigenvalues of the Laplacian on a closed hyperbolic surface contains a good deal of\ninformation about the surface\, including its con nectivity\, dynamical properties of its geodesic flow\,\nand error terms i n geodesic counting problems. For arithmetic hyperbolic surfaces the spect ral gap\nis also the subject of one of the biggest open problems in automo rphic forms: Selberg’s eigenvalue\nconjecture.\nIt was an open problem f rom the 1970s whether there exist a sequence of closed hyperbolic sur-\nfa ces with genera tending to infinity and spectral gap tending to 1/4. (The value 1/4 here is the\nasymptotically optimal one.) Recently we proved tha t this is indeed possible. I’ll discuss the very\ninteresting background of this problem in detail as well as some ideas of the proof. This is joi nt work\nwith Will Hide.\n LOCATION:https://researchseminars.org/talk/LNTS/66/ END:VEVENT END:VCALENDAR