Mathematics Colloquia and Seminars

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Second order differential 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, such as Dirac operators, are still not as well-understood, specially on spacetimes with boundary.

In this talk, I will focus on the spin Dirac operator on spacetimes with timelike boundary and discuss initial boundary value problems with respect to certain classes of boundary conditions. After giving a brief introduction to non-local boundary conditons for Dirac operators on Riemannian manifolds, I will define a class of Lorentzian boundary conditions that are local in time and non-local in the spatial direction and show that they lead to a well-posed initial boundary value problem for the Dirac operator. If time permits, I will then give some more comments on Green’s operators and finite propagation speed of the corresponding solutions.