Topology in quantum systems

Adam Rennie
Wollongong and Sydney

Abstract

The machinery underpinning the Atiyah-Singer index theorem applies in much more general situations. I will give some examples from geometry and dynamics before describing two applications in quantum physics: topological insulators and scattering systems. I will not get into the technical weeds in this talk, focussing on how stable homotopy invariants arise.

As an overview talk, this relies on many prior works and many coauthors. I will try to indicate these as I go along.