The geometry of semiclassical limits on regular Dirichlet spaces

15.12.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12
Forschungsseminar Differentialgeometrie

Batu Güneysu

In this talk, I will first explain how one can reformulate the known semiclassical limit results for the heat trace of Schrödinger operators on Riemannian manifolds and infinite weighted graphs in a form which makes sense for abstract Schrödinger type operators on locally compact spaces. Then I will give a probabilistic proof of this reformulation in case the "free operator" stems from a regular Dirichlet form which satisfies a principle of not feeling the boundary. This abstract result leads to completely new results for Schrödinger operators on arbitrary complete Riemannian manifolds, and allows to recover the known results for weighted infinite graphs.