Lukas Müller
I am a postdoc at the Perimeter Institute for Theoretical Physics funded by the Simons Collaboration on Global Categorical Symmetries. Before that, I was a postdoc at the Max Planck Institute for Mathematics in Bonn and a PhD-student at the Heriot-Watt university in Edinburgh under the supervision of Richard J. Szabo.
My research interest lies at the intersection of higher category theory, geometry and mathematical physics. I am particularly interested in connections between different fields of mathematics inspired by physics. More concretely, I work on the following:
Higher geometry: Smooth functorial field theories, Constructions from index theory, Higher quantization and gerbes, Applications to string theory and non-associative quantum mechanics.
Topology: Equivariant field theories, State sum constructions, Connections to algebra through operads and topological field theories, Factorization homology.
Algebra: Non-semisimple representation categories, Grothendieck-Verdier categories, Hochschild homology.
Mathematical Physics: Anomalies and relative field theories, Topological phases of matter, Mathematical foundations of quantum field theory.
Recorded Talks:
Topological defects form higher dagger categories, February 2024, Slides and recording
Reflection positivity for extended topological field theories, Ocotober 2023, Perimeter Institute, Recording
Reflection positivity for extended topological field theories, August 2023, Higher Structures in Functorial Field Theory, Slides, Recording
Deformation quantization and categorical factorization homology, March 2023, Geometry, Topology, and Physics Seminar, NYU Abu Dhabi, Recording
Anomalies, higher geometry, and functorial field theories, November 2021 Generalized Cohomology and Physics, Recording
Rigidity results for topological field theories and modular functors, July 2021, Higher Structures in QFT and String Theory, Recording
Symmetry defects in 2D Yang-Mills theory, twisted bundles and quantization, January2021, Prague mathematical physics seminar, Recording
Organization:
Higher categorical tools for quantum phases of matter, 18-22 March 2024, Perimeter Insitute
Categorical Symmetries in Quantum Field Theory (Conference and School), 27 August-8 September 2023, Les Diablerets
GCS Postdoc and Student Colloquium, 2022-2023, online
Teaching:
In 2023 I taught a course on topological quantum field theories. A recording of the lectures can be found at: https://pirsa.org/c23048
You can reach me at: lmueller "at" perimeterinstitute "dot" ca