Applied and Industrial Mathematics

Coming from an engineering school, I'm very interested in using a broad variety of mathematical tools in real world applications. I have worked together with engineers from different fields from both academia as well as the industry. For example, I helped the textile engineers from ITA RWTH Aachen to improve a pattern for sliver laying in cans and together with the German railway company DB we investigated data inconsistencies.

Calculus of Variations and PDE

During my postdoc I investigated the metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one away from the so-called slow manifold. In other projects we derived optimal relaxation rates for this equation and explore the energy landscape of the Cahn-Hilliard energy.

Geometric Knot Theory and Discrete Geometry

Geometric knot theory is concerned with analytic properties of knots such as the existence and regularity of minimizers of knot energies. The most prominent of these knot energies are the thickness, integral Menger curvature, and the Möbius energy. Discrete differential geometry adapts notions from classic differential geometry to discrete objects like polygons and meshes.

I'm especially interested in topics at the intersection of these two fields: For example in developing discrete counterparts for knot energies that have similar features as the original energies and that are designed to provide a geometrically pleasing and consistent discrete theory. Moreover, the discrete energies should approximate the smooth energies as their underlying objects refine.