Boundary value problems for Dirac Operators on graphs

15.11.2021, 16:15  –  2.09.0.12
Forschungsseminar Differentialgeometrie

Alberto Richtsfeld

In this talk, I will present the results of my master’s thesis concerning the index and the spectrum of Dirac operators on metric digraphs, which are subject to general boundary conditions. Relying on the work of Bär and Ballmann, we deduce an index theorem and some basic properties of the spectrum. We will discuss two types of boundary conditions: one given by permutations of the edges which lead to decompositions of the digraph into directed trails and the other given by an edge-to-edge incidence matrix whose spectrum is determined by the cycles appearing in the digraph.