Centre for Geometric Analysis Seminar Series

Operators of Fuchs type, conical singularities, and asymptotic methods

This is an overview talk a variant of which I delivered earlier this year at a conference celebrating the 75th birthday of Bert-Wolfgang Schulze. 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. I will also hint at recent results obtained jointly with Luiz Hartmann and Boris Verman.