Operator algebras and mathematical physics

In operator algebras we are particularly interested in $\mathsf{C}^*$-algebra theory and its connections to other areas such as dynamical systems, group theory, topology, non-commutative geometry, and mathematical logic.

One focus lies in translating dynamical properties into $\mathsf{C}^*$-algebraic properties and, conversely, interpreting $\mathsf{C}^*$-algebraic concepts within the context of dynamics. Another central topic is the structure and classification theory of nuclear $\mathsf{C}^*$-algebras.

In mathematical physics we focus on rigorous constructions of quantum field theory models by employing methods from topological recursion, non-commutative geometry and renormalisation theory. We explore connections to the moduli space of curves and to integrable hierarchies.