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SUMMARY:Michael Magee (Durham University)
DTSTART:20211104T213000Z
DTEND:20211104T223000Z
DTSTAMP:20260423T022836Z
UID:JNTS/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/28/">Th
 e maximal spectral gap of a hyperbolic surface</a>\nby Michael Magee (Durh
 am University) as part of Columbia CUNY NYU number theory seminar\n\n\nAbs
 tract\nA hyperbolic surface is a surface with metric of constant curvature
  -1. The spectral gap between the first two eigenvalues of the Laplacian o
 n a closed hyperbolic surface contains a good deal of information about th
 e surface\, including its connectivity\, dynamical properties of its geode
 sic flow\, and error terms in geodesic counting problems. For arithmetic h
 yperbolic surfaces the spectral gap is also the subject of one of the bigg
 est open problems in automorphic forms: Selberg’s eigenvalue conjecture.
 \n\nIt was an open problem from the 1970s whether there exist a sequence o
 f closed hyperbolic surfaces with genera tending to infinity and spectral 
 gap tending to 1/4. (The value 1/4 here is the asymptotically optimal one.
 ) Recently we proved that this is indeed possible. I’ll discuss the very
  interesting background of this problem in detail as well as some ideas of
  the proof.\n\nThis is joint work with Will Hide.\n
LOCATION:https://researchseminars.org/talk/JNTS/28/
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