M. Sc. Penelope Gehring
Doctoral student
Universität Potsdam
Homepage: https://www.math.uni-potsdam.de/professu…
Project
37Boundary value problems and index theory on Riemannian and Lorentzian manifolds
Publications within SPP2026
Non-local boundary conditions, such as the Atiyah-Patodi-Singer (APS) conditions, for Dirac operators on Riemannian manifolds are well under\-stood while not much is known for such operators on spacetimes with timelike boundary. We define a class of Lorentzian boundary conditions that are local in time and non-local in the spatial directions and show that they lead to a well-posed Cauchy problem for the Dirac operator. This applies in particular to the APS conditions imposed on each level set of a given Cauchy temporal function.
Related project(s):
37Boundary value problems and index theory on Riemannian and Lorentzian manifolds