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UID:20250714T203733EDT-2655LrEsB3@132.216.98.100
DTSTAMP:20250715T003733Z
DESCRIPTION:Title: Flat conical Laplacian in the square of the canonical bu
 ndle and its regularized determinants\n\nAbstract: We discuss two natural 
 definitions of the determinant of the Dolbeault Laplacian acting in the sq
 uare of the canonical bundle over a compact Riemann surface equipped with 
 flat conical metric given by the modulus of a holomorphic quadratic differ
 ential with simple zeroes. The first one uses the zeta-function of some sp
 ecial self-adjoint extension of the Laplacian (initially defined on smooth
  sections vanishing near the zeroes of the quadratic differential)\, the s
 econd one is an analog of Eskin-Kontsevich-Zorich (EKZ) regularization of 
 the determinant of the conical Laplacian acting in the trivial bundle. In 
 contrast to the situation of operators acting in the trivial bundle\, thes
 e two regularizations turn out to be essentially different. Considering th
 e regularized determinant of the Laplacian as a functional on the moduli s
 pace of quadratic differentials with simple zeroes on compact Riemann surf
 aces of a given genus\, we derive explicit expressions for this functional
  for the both regularizations. The expression for the EKZ regularization i
 s closely related to the well-known explicit expressions for the Mumford m
 easure on the moduli space of compact Riemann surfaces.\n\n \n
DTSTART:20200131T183000Z
DTEND:20200131T193000Z
LOCATION:Room LB 921-4 \, CA\, QC\, Montreal\, H3G 1M8\, Concordia\, Librar
 y building\, 1400 Maisonneuve Blvd W\,
SUMMARY:Alexey Kokotov (Concordia University)
URL:/mathstat/channels/event/alexey-kokotov-concordia-
 university-312176
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