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SUMMARY:Bootstrapping automorphic spectra
DTSTART;VALUE=DATE-TIME:20211111T131500Z
DTEND;VALUE=DATE-TIME:20211111T151500Z
DTSTAMP;VALUE=DATE-TIME:20220123T203200Z
UID:indico-event-31166@indico.desy.de
DESCRIPTION:Speakers: Dalimil Mazac (IAS)\nI will explain how the conforma
l bootstrap can be adapted to place rigorous bounds on the spectra of auto
morphic forms on locally symmetric spaces. A locally symmetric space is a
space of the form H\\G/K\, where G is a non-compact semisimple Lie group\,
K is the maximal compact subgroup of G\, and H is a lattice in G. If we t
ake G = SL(2\,R)\, then spaces of this form are precisely hyperbolic surfa
ces and hyperbolic 2-orbifolds. The bootstrap constraints arise from the a
ssociativity of function multiplication on the space H\\G\, and are very s
imilar to the usual correlator bootstrap equations with G playing the role
of the conformal group. For G=SL(2\,R)\, I will use this method to prove
upper bounds on the lowest positive eigenvalue of the Laplacian on closed
hyperbolic surfaces of a fixed genus. The bounds at genus 2 and genus 3 ar
e very nearly saturated by the Bolza surface and the Klein quartic. This i
s based on work with P. Kravchuk and S. Pal.\nhttps://indico.desy.de/event
/31166/
URL:https://indico.desy.de/event/31166/
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