Session S33 - Spectral Geometry

Tuesday, July 13, 14:30 ~ 14:50 UTC-3

Polyakov Formulas for conical singularities in two dimensions

Clara Aldana

Universidad del Norte, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In 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. Time permitting, I will mention the variational Polyakov formula for cones and sectors and how in these cases we can obtain closed formulas for the logarithmic derivative of 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.

Joint work with Klaus Kirsten (Baylor University Waco, US) and Julie Rowlett (Chalmers University of Technology and the University of Gothenburg, Sweden).

View abstract PDF