Alberto Richtsfeld

Doktorand

Kontakt
Raum:
2.09.3.05
Telefon:
+49 331 977-1195
...

Research Interests

  • Differential Geometry
  • Operator Theory
  • Index Theory
  • Spin Geometry

Preprints

2024 | Local index theory for the Rarita-Schwinger operator | Alberto RichtsfeldLink zum Preprint

Local index theory for the Rarita-Schwinger operator

Autoren: Alberto Richtsfeld (2024)

We prove the local index theorem for the Rarita-Schwinger operator and higher Dirac operators using Gilkey's invariance theory. That is, we show that the supertrace of the heat kernel of a given geometric operator converges as time goes to zero, and identifies the limit as the Chern-Weil form of the Atiyah-Singer integrand.

2023 | Boundary Value Problems for Dirac Operators on Graphs | Alberto RichtsfeldLink zum Preprint

Boundary Value Problems for Dirac Operators on Graphs

Autoren: Alberto Richtsfeld (2023)

We carry the index theory for manifolds with boundary of Bär and Ballmann over to first order differential operators on metric graphs. This results in an elegant proof for the index of such operators. Then the self-adjoint extensions and the spectrum of the Dirac operator on the complex line bundle are studied. We also introduce two types of boundary conditions for the Dirac operator, whose spectrum encodes information of the underlying topology of the graph.