Polyakov Formulas for conical singularities in two dimensions.

Abstract: In the first part of the talk I will introduce the regularized determinant of the Laplace operator on a Riemannian manifold and will explain the context and the motivation to consider Polyakov's formulas. Then, I will present the formula for surfaces with conical singularities and smooth conformal factors, and for polygonal domains in a Riemannian surface. I will mention how we obtain the so-called variational Polyakov formula for cones and sectors and how in these cases we can obtain closed formulas for the determinant of the Laplacian. The results presented in this talk are joint work with Klaus Kirsten and Julie Rowlett, arxiv.org/abs/2010.02776.

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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