Title: Unbounded operator integrals in noncommutative Quantum Field Theory.

 

Abstract: In Noncommutative Geometry (NCG), operator integrals appear all over the place. These do not fit neatly in the existing theories on Multiple Operator Integrals (MOIs), however, since the operator arguments involved can typically be unbounded. In joint work with Edward McDonald and Teun van Nuland, we provide a construction of MOIs which can handle (unbounded) abstract pseudodifferential operators. I'll sketch how this construction can play a role in a noncommutative QFT model based on the spectral action. The latter is based on joint work with Teun van Nuland and Jesse Reimann.

 

About the speaker: Eva-Maria Hakkelman is a postdoctoral researcher at the Max Planck Institute for Mathematics in Bonn, in the research group of Matthias Lesch. In 2025, she completed her PhD at the University of New South Wales, Sydney, under the supervision of Fedor Sukochev, Dmitriy Zanin, and Edward McDonald. Prior to that, she studied at Radboud University in Nijmegen, where she wrote her master’s thesis under the supervision of Walter van Suijlekom. Her research focuses on noncommutative geometry and operator theory, motivated by mathematical physics. Recently, she has been interested in operator integrals and properties of (abstract) pseudodifferential operators.