The Joys of MOIsOberseminar Global Analysis and Operator Algebras

by Eva-Maria Hekkelman (MPIM Bonn)

Tuesday Oct 28, 2025, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

Techniques for manipulating operator integrals in noncommutative 
geometry can be systematised and simplified with the language of 
Multiple Operator Integrals (MOIs). This is relevant for asymptotic  expansions of
the spectral action and the heat trace, and simplifies  proofs of the local index
formula amongst others. This requires adapting  the construction of MOIs to an
abstract pseudodifferential calculus  developed by Connes–Moscovici, Higson and
Guillemin. With this 
machinery, many commonly used expansions in NCG can be boiled down to  combinations
of just two simple MOI identities. Based on joint work with  Edward McDonald and
Teun van Nuland.