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.