Colloque des sciences mathématiques du Québec

11 avril 2014 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Flat surfaces and determinants of Laplaciancs

Colloque par Alexey Kobotov (Concordia University)

In 2008 D. Korotkin and the author found an explicit formula for the determinant of the Friedrichs Laplacian on a compact 2d surface of genus g >1 provided with flat conical metric with trivial holonomy. This formula can be considered as a higher genus version of the classical Ray-Singer formula for the determinant of the Laplace operator on an elliptic curve provided with (smooth) flat conformal metric. We will discuss further generalizations of this result for 1) General polyhedral metrics on compact surfaces. 2) Other (i.e. non Friedrichs) self-adjoint extensions of conical Laplacians. 3) Noncompact flat surfaces with cylindrical and Euclidean ends. The talk is based on the joint works with L. Hillairet and V. Kalvin.


CRM, Université de Montréal, pavillon André-Aisenstadt, 2920 chemin de la Tour, salle 6214