Trace and Regularized Index of Callias Operators on Hyperbolic SpaceOberseminar Global Analysis and Operator Algebras

by Jilly Kevo (Uni Bonn)

Tuesday Jun 24, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Seminar room 1.008 (Mathezentrum)

We consider Callias operators, i.e. Dirac operators perturbed by an operator valued potential $A$, on odd, $d$-dimensional hyperbolic space. Without imposing invertibility of the potential outside a compact region, the operators are no longer Fredholm so that the Witten index, a type of regularized index defined via trace limits, becomes the natural substitute for the classical notion of index. An explicit trace formula, which leads to a new index formula, has already been found in the Euclidean case, independently by Pushnitski, Gesztesy et al. and others for $d=1$, and recently, by Fürst for $d \geq 3$. Besides employing representation-theoretic arguments, we describe how the current techniques can be modified to incorporate the effects of nonzero curvature and present a partial result.

This talk is the first in a sequence of talks on the topic of my Master's thesis.