Continuity properties of the spectral shift function for massless Dirac operators and an application to the Witten index

Math Physics Seminar
Thursday, March 16, 2023 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 005
Fritz Gesztesy – Baylor University –
Michael Loss

 We report on recent results regarding the limiting absorption principle for multi-dimensional, massless Dirac-type operators (implying absence of singularly continuous spectrum) and continuity properties of the associated spectral shift function.

We will motivate our interest in this circle of ideas by briefly describing the connection to the notion of the Witten index for a certain class of non-Fredholm operators.

This is based on various joint work with A. Carey, J. Kaad, G. Levitina, R. Nichols, D. Potapov, F. Sukochev, and D. Zanin.