Survey on Index Theory on Lorentzian Manifolds

Christian Bär (U of Potsdam)

Jul 12. 2023, 09:00 — 09:50

I will survey the current status of index theory for Dirac-type operators on Lorentzian manifolds. We start with the Lorentzian analog of the Atiyah-Patodi-Singer index theorem due to Bär and Strohmaier and then discuss extensions to Callias operatos by Braverman and to Galois coverings by Damaschke, amonsgst others. As an application, we show how to rigorously compute the chiral anomaly in QFT on curved spacetimes.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)