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UID:1650d3b0fb7ab7b76f738d6492e1b6de
CATEGORIES:Joint Princeton-Rutgers Seminar on Geometric PDE's
CREATED:20250314T151609
SUMMARY:Ramon van Handel:  Random covers of hyperbolic surfaces 
LOCATION:Hill 705
DESCRIPTION:<p style="margin-top: 0px; margin-bottom: 0px;">Abstract: &nbsp; It was sho
 wn long ago by Huber that the first nonzero eigenvalue of the&nbsp;<br>Lapl
 acian on a closed hyperbolic surface cannot exceed that of the&nbsp;<br>hyp
 erbolic plane, asymptotically as the genus goes to infinity. Whether&nbsp;<
 br>there exists a sequence of closed hyperbolic surfaces that achieves this
 &nbsp;<br>bound---an old conjecture of Buser---was settled a few years ago 
 by Hide&nbsp;<br>and Magee. This was done by exhibiting a sequence of cover
 ing spaces of a&nbsp;<br>fixed base surface that have good spectral propert
 ies. In this talk, I&nbsp;<br>will discuss joint work with Magee and Puder 
 where we show that this&nbsp;<br>phenomenon is in fact much more prevalent:
  given any closed hyperbolic&nbsp;<br>surface, not only do there exist cove
 ring spaces that have good spectral&nbsp;<br>properties, but this is in fac
 t the case for all but a vanishing fraction&nbsp;<br>of its covering spaces
 . The proof is based on recent developments on the&nbsp;<br>notion of stron
 g convergence, which combines ideas from random matrix&nbsp;<br>theory, rep
 resentation theory, and combinatorial group theory.&nbsp;</p>
CONTACT:Princeton University
DTSTAMP:20260831T083557
DTSTART;TZID=America/New_York:20250502T163000
DTEND;TZID=America/New_York:20250502T173000
SEQUENCE:0
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