Penelope Gehring (UP)
Boundary value problems for elliptic first order differential operators on Riemannian manifolds are rather well understood. Recently, Bär-Strohmaier introduced APS-conditions for the Dirac operator on spacetimes with spacelike boundary and proved a Lorentzian index theorem. This, as well as the increasing relevance of the anti-de Sitter spacetime in theoretical physics, motivates to also take a look at boundary value problems on spacetimes with timelike boundary. In this talk, I will give a brief introduction to globally hyperbolic manifolds with timelike boundary and differential operators on these manifolds. Then, I will give an overview of some recent developments on local boundary conditions and some ongoing work on global boundary conditions in this setting.
Zoom access data are available at this moodle.