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

by Jilly Kevo (University Bonn)

Tuesday Mar 31, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

This talk continues our study of non-Fredholm Callias operators $D$ on odd-dimensional hyperbolic space, that is, Dirac operators perturbed by operator-valued potentials without any assumption of invertibility at infinity. In this non-Fredholm setting, the classical Fredholm index is replaced by the Witten index, defined through trace limits of the associated heat semigroups.

Building on the analytical framework developed in the first talk, we derive an explicit formula for the iterated trace of the difference of heat semigroups associated with $D^*D$ and $DD^*$. Our approach combines representation-theoretic methods with geometric and analytic heat-kernel techniques in the spirit of Berline and Getzler, adapted to the curved setting of hyperbolic space.

This trace formula extends recent Euclidean results by Pushnitski, Gesztesy, Fürst, and others to a manifold of nonzero curvature. To our knowledge, it constitutes the first explicit formula of this type in the non-Fredholm, curved setting.