Lorentzian spectral geometry and the fermionic signature operator
Felix Finster (Regensburg)
For the motivation, I begin with the classical "can one hear the shape of a
drum?" problem for elliptic operators and explain how a related problem
can be formulated for hyperbolic operators defined on subsets of two-dimensional
Minkowski space. I mention a few results for the resulting "Lorentzian spectral
geometry" for surfaces. Generalizing the concepts to the Dirac operator in globally
hyperbolic space-times leads to the fermionic signature operator, which will be defined.
I explain a few general results and outline applications in quantum field theory.
This is joint work mainly with Olaf Mueller and Moritz Reintjes.