The classical Dirac operator on spacetimes with timelike boundary

01.02.2022, 12:15-13:45  –  Room 2.09.2.22 Campus Golm, C9A03 Tübingen
Geometric Analysis, Differential Geometry and Relativity

Penelope Gehring

Second order operators, such as wave operators, are some of the most studied objects in mathematics as well as in physics. On the other hand, the properties of first order operators are still not as well-understood, specially on spacetimes with boundary. In this talk, I will give an introduction to non-local boundary conditions for elliptic first order differential operators on Riemannian manifolds with boundary and will point out the difference to hyperbolic operators on Lorentzian manifolds. Then, I will discuss Cauchy problems of the classical Dirac operator on spacetimes with timelike boundary, where we use elliptic theory to study boundary conditions.