The resolvent expansion of geometric operators on singular spaces

Matthias Lesch (University of Bonn)

Abstract

In this overview talk I will review the “direct” approach to the resolvent expansion of Laplace type operators on certain singular spaces. The paradigm is that on the model singularity one has a second order Sturm-Liouville operator with operator valued coefficients. This point of view has the advantage of being very elementary, microlocal analysis is only needed in the smooth interior. This is an ongoing projectwith Boris Vertman and Luiz Hartmann.