Hermann Schulz-Baldes
(Universität Erlangen-Nürnberg)
March 24, 2021
14:00
(CET)
Organized by Europe GNCG Seminar.

## Computational $$K$$-theory via the spectral localizer

Parings of $$K$$-theory with Fredholm modules given by Dirac operators can be computed numerically as the half-signature of a suitable finite dimensional-matrix called the spectral localizer. This allows to access integer-valued pairings, $$\mathbb{Z}_2$$-valued pairing arising in Real $K$-theory as well as semifinite index pairings. Topological insulators constitute a rich field of applications within which the above can be illustrated. (Joint work with Nora Doll, Terry Loring, Tom Stoiber).