Research interests

I love to link different fields of mathematics and to developing algebraic techniques to solve problems arising in the sciences. My research addresses Algebraic Analysis, Applied Algebraic Geometry, and Topological Data Analysis.

Algebraic Analysis investigates systems of linear partial differential equations by algebraic methods. It elegantly combines methods from Algebraic Geometry, Algebraic Topology, Category Theory, and Complex Analysis. Many special functions in the sciences are encoded by a holonomic annihilating ideal in the Weyl algebra D and can be investigated by means of D-modules. In this area, I focus on computational aspects and applications - among others, the maximum likelihood estimation of discrete statistical models for the inference of data. At my (virtual) office door, you can have a look at my poster about Algebraic Analysis and Applications.

Topological Data Analysis analyzes the shape of data by topological methods. It has concrete applications in the medical sciences and machine learning, for instance. One main tool is persistent homology. It associates persistence modules and so called barcodes to data, from which one easily reads topological features. Behind the scenes, algebraic invariants keep the machinery running. My emphasis in this area lies on the development of stable invariants for multipersistence modules.