Seminar on Global Analysis

Index theory goes back to Atiyah and Singer and deals with elliptic operators on Riemannian manifolds. It has numerous applications in geometry, topology, mathematical physics and other fields. On a Lorentzian manifold, naturally associated operators such as the Dirac operator are hyperbolic and not Fredholm in general. Nonetheless, it turns out that there is a Lorentzian analogue to the Atiyah-Patodi-Singer index theorem for manifolds with boundary.

The result looks formally very similar to its Riemannian counterpart but the underlying analysis is quite different. If time permits, I will also describe an application to the chiral anomaly in quantum field theory.

This is joint work with Alexander Strohmaier (Leeds).

https://www.math.uni-potsdam.de/en/professuren/geometry/team/prof-dr-christian-baer