Speaker: Eva-Maria Hekkelmann (University of New South Wales)
Title: Unbounded operator integrals in noncommutative geometry
Abstract:
Operator integrals appear in various contexts of noncommutative geometry. Proofs of the local index formula, expansions of the spectral action and asymptotics of the heat trace are just a few examples. Thankfully, a Soviet school of mathematics cooked up a theory of Multiple Operator Integrals (MOIs) which provides a big toolbox for handling complicated integrals of bounded operators. This is still an active field of research. In joint work with Ed McDonald and Teun van Nuland we adapted the theory of MOIs to the framework of abstract pseudodifferential operators Connes–Moscovici/Higson style, which makes MOI theory usable in NCG. We hope this greatly reduces the time noncommutative geometers have to spend fiddling with operator integral analysis.