A relative trace formula in obstacle scattering

Professor Alexander Strohmaier (University of Leeds) will present his research in Analysis.

I will briefly remind the audience about trace formulae in spectral geometry of compact domains and will then explain the changes in the non-compact setting and I will define the scattering matrix in the context of the Dirichlet Laplacian of a non-compact domain. I will then review the Birman-Krein formula: a classical theorem that relates the trace of the difference of two operators to the scattering matrix.

The main result will be that a relative trace formula that allows for a much larger class of test functions than the original Birman-Krein formula. If time permits I will explain an application of this formula in physics. (Joint work with F. Hanisch and A. Waters)

Virtual Open Days
Be Curious 2020