Heat and resolvent expansions in the noncommutative case

03.07.2025, 16:15  –  Raum 1.22
Forschungsseminar Differentialgeometrie

Matthias Lesch (Bonn)

Heat and resolvent expansions are a fundamental tool in spectral geometry and index theory. In the noncommutative world (á la Connes) such expansions exhibit fundamentally new structures. I will recast the corresponding results for vector bundles over noncommutative tori due to Connes, Moscovici, and myself. In the second part of my talk, I will discuss more technical aspects and their relations to divided differences and multivariate holomorphic functional calculus.

The talk is based on joint work with Henri Moscovici and, more recently, with Gihyun Lee and Luiz Hartmann.