Скачать или смотреть Victor Kalvin : Determinants of Laplacians on compact surfaces with conical singularities

Due to a technical error, the sound is missing for the first few minutes. Audio begins at 5.38.

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.