### Research

As a mathematical physicist, I work on conceptual and mathematical problems arising in quantum field theory. I am particularly interested in new approaches to the problem of rigorously constructing quantum field theory models. A novel line of research addresses this question via operator-algebraic deformations of quantum field theories, a topic also connected to non-commutative geometry and quantum field theory on non-commutative spaces.

A further interest are integrable models in quantum field theory and related structures, such as the Yang-Baxter equation, braid group representations and link invariants.

Some recent research of mine is:

**Yang-Baxter Representations **(with Ulrich Pennig and Simon Wood)

The Yang-Baxter equation appears in a remarkable number of different fields, such as statistical mechanics, knot theory, quantum groups. quantum field theory, quantum mechanics, quantum information theory, subfactors, … . This equation is very hard to solve directly, and the structure of the set of its solutions is insufficiently understood. We considered the case of *involutive* solutions $R$, i.e. satisfying $R^2=1$. In this case, we found a complete classification of all solutions up to a natural equivalence suggested by applications in quantum field theory.

**Quantum-mechanical Backflow** (with Henning Bostelmann and Daniela Cadamuro)

One incarnation of the uncertainty relation is the so-called *backflow* effect: A quantum-mechanical particle in one spatial dimension that has *positive* momentum (with probability 1) may still have *negative* probability flux, i.e. the probability can flow in the direction opposite to the momentum. We investigated the backflow effect for interacting systems governed by an arbitrary short-range potential. It turns out that backflow is a universal effect that exists in any such system, and its magnitude can be estimated by analytic methods.

**Constructive Algebraic Quantum Field Theory
**In 2015, I wrote a book chapter reviewing the status of constructive algebraic quantum field theory.

For more details about my research, you can have a look at my publications and talks: