### Polyakov Formulas for conical singularities in two dimensions

Analysis and Geometry Seminar

14th January 2021, 3:15 pm – 4:15 pm

Online, (contact organisers for details)

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.

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