Zoom Details:

Zoom Link: https://unm.zoom.us/j/93557022920

Meeting ID: 935 5702 2920

Passcode: 868713

Title: Spectral flow for unitaries and Levinson's theorem

Abstract: The celebrated theorem of Levinson relates the number of bound states of the Schrödinger system $-\Delta+V$ to the scattering matrix $S(\lambda)$ of the pair $(-\Delta, -\Delta+V)$. By considering $S(\cdot)$ as a path of unitaries, we show that the Levinson theorem can be stated as an analytic spectral flow formula for the path of scattering matrices $S(\cdot)$. This perspective provides a unified and analytic framework that works in all dimensions and remains valid both in the presence and absence of resonances.

About Speaker: Galina Levitina is a Senior Lecturer at the Mathematical Sciences Institute, Australian National University. Her research interests are functional analysis, operator theory, scattering theory, and noncommutative geometry.