BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20281105T010000 RDATE:20290311T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20240501T163000 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20280312T030000 RDATE:20281105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT 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:Abstract:   It was shown long ago by Huber that the first nonzero eigenvalu e of the \nLaplacian on a closed hyperbolic surface cannot exceed that of t he \nhyperbolic plane, asymptotically as the genus goes to infinity. Whethe r \nthere exists a sequence of closed hyperbolic surfaces that achieves thi s \nbound---an old conjecture of Buser---was settled a few years ago by Hid e \nand Magee. This was done by exhibiting a sequence of covering spaces of a \nfixed base surface that have good spectral properties. In this talk, I  \nwill discuss joint work with Magee and Puder where we show that this \np henomenon is in fact much more prevalent: given any closed hyperbolic \nsur face, not only do there exist covering spaces that have good spectral \npro perties, but this is in fact the case for all but a vanishing fraction \nof its covering spaces. The proof is based on recent developments on the \nno tion of strong convergence, which combines ideas from random matrix \ntheor y, representation theory, and combinatorial group theory. \n X-ALT-DESC;FMTTYPE=text/html:

Abstract:   It was sho wn long ago by Huber that the first nonzero eigenvalue of the 
Lapl acian on a closed hyperbolic surface cannot exceed that of the 
hyp erbolic plane, asymptotically as the genus goes to infinity. Whether < br>there exists a sequence of closed hyperbolic surfaces that achieves this  
bound---an old conjecture of Buser---was settled a few years ago by Hide 
and Magee. This was done by exhibiting a sequence of cover ing spaces of a 
fixed base surface that have good spectral propert ies. In this talk, I 
will discuss joint work with Magee and Puder where we show that this 
phenomenon is in fact much more prevalent: given any closed hyperbolic 
surface, not only do there exist cove ring spaces that have good spectral 
properties, but this is in fac t the case for all but a vanishing fraction 
of its covering spaces . The proof is based on recent developments on the 
notion of stron g convergence, which combines ideas from random matrix 
theory, rep resentation theory, and combinatorial group theory. 

CONTACT:Princeton University DTSTAMP:20260831T111730 DTSTART;TZID=America/New_York:20250502T163000 DTEND;TZID=America/New_York:20250502T173000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR