Research

My research areas are Differential Geometry and Algebraic Topology; in particular so-called higher-categorical structures. I am also interested in the geometry of loop spaces, Lie theory, spin geometry, and homotopy theory. My research is mainly motivated by problems from theoretical physics, mostly in the field of two and three dimensional quantum field theories, and in the field of topological phases in condensed matter systems.

Please consult the following subpages for more information:

Recent work

Real twistings are 2-line bundles
Paper, written together with Tim Lüders, Lynn Otto
February 2025

Internal geometry and functors between sites
Paper, August 2024

String structures and loop spaces
Paper, December 2023
to appear in Encyclopedia of Mathematical Physics (2nd edition)

Upcoming visits and talks

  • Conference "C*-Algebras, Coarse Geometry and Physics"
    Universität Greifswald
    June 23-27, 2025
    Webpage  

  • Workshop "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras"
    Max-Planck-Institut für Mathematik Bonn
    June 30 - July 11, 2025
    Webpage  

  • Workshop "Renormalisation and randomness"
    Mathematisches Forschungsinstitut Oberwolfach
    September 22-26, 2025