Investigating Fredholm properties of Lorentzian Dirac operators with boundary conditions

21.03.2024, 16:15  –  Raum 1.22
Forschungsseminar Differentialgeometrie

Lennart Ronge (UP)

Given a Dirac operator on a Lorentzian manifold with timelike boundary, its Fredholm index (and whether it is Fredholm at all) heavily depends on the boundary conditions that one imposes on the operator. This talk will briefly explain how the index is determined by the boundary conditions, before presenting ongoing work towards finding criteria that describe which boundary conditions yield a Fredholm operator. This approach uses the symbol calculus of Fourier integral operators, which will also be briefly sketched.