Determinants of Laplacians on compact surfaces with conical singularities
Viktor Kalvin (Dawson College and Concordia Univ.)
Abstract: In this talk I will discuss new anomaly formulae for the zeta regularized spectral determinants of Laplacians on compact Riemann surfaces. These formulae are valid for the metrics with conical singularities and, in particular, show how the determinants of Laplacians depend on the orders (angles) of conical singularities. With a simple example I will show that the extremal properties of the determinants of Laplacians on singular metrics are very different from the classical results of Osgood, Phillips, and Sarnak for the smooth metrics. If time permits, I will also discuss how this is related to Kaehler potentials of metrics on moduli spaces, the famous accessory parameters, and the celebrated DOZZ formula from the Liouville conformal field theory. The talk is based on a series of recent papers of mine.
algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry
Audience: researchers in the topic
CRM - Séminaire du CIRGET / Géométrie et Topologie
Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html
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The livestream is on Zoom at : uqam.zoom.us/j/98999725241 (no password is needed).
The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA
Organizers: | Julien Keller*, Duncan McCoy |
*contact for this listing |