Research
Our research group works on the intersection of mathematical physics, algebraic topology, and higher structures. That is, we apply homotopical, categorical, and topological tools to understand quantum field theory, as well as develop the foundational knowledge necessary for these applications.
Our research is heavily concerned with functorial field theories, which use a higher-categorical framework to provide one rigorous formulation of locality in quantum field theory. Such functorial field theories also provide invariants of manifolds valued in higher categories, and as such, our work also uses and develops tools from derived geometry and higher category theory. One particular focus is factorization homology, which builds a functorial field theory on framed manifolds by gluing together local algebraic data.
The research group receives support from the DFG via the SFB/CRC 1624 Higher Structures, moduli spaces and integrability and the SFB/CRC 1085 Higher Invariants, as well as from the Simons Foundation via the Simons Collaboration on Global Categorical Symmetries.