Lecture announcement

As part of the Advanced Seminar on Analysis and Numerics,

Mr Eric Trébuchon

(University of Freiburg)

THE DIRAC OPERATOR ON CONICAL DOMAINS

Abstract "This talk concerns the self-adjointness and regularity of the Dirac operator with boundary conditions on domains containing singularities. We first review known results for two-dimensional corner domains and for convex domains with MIT boundary conditions. We then extend this theory to higher-dimensional conical domains with generic local boundary conditions

The key idea is to locally transform the Dirac operator under general boundary conditions on a conical domain near the singularities into a perturbed Dirac operator under MIT boundary conditions on the model cones. This process introduces a perturbation that can be dealt with using the Kato–Rellich theorem. In the model case, the theory relies heavily on the separation ansatz and a spectral gap on the link of the cone, which ultimately ensures self-adjointness and regularity."

The lecture will take place on

Thursday, 9 July 2026 at 2.30 pm in Room W01 1-117

Anyone interested is warmly invited to attend.