I use, and develop combinatorial tools such as polyhedral geometry, and graphs on surfaces to answer questions about the topology of (real, or complex) algebraic varieties, polynomial maps, and ramified covers.
One focal point is to exploit the structure and geometry of objects in question for the sake of efficient algorithmic implimentations.
Problems that I am interested in are those of relevance to both pure mathematics, and its applications to sciences, and engineering.
- Fewnomial theory
- Topology of polynomial maps
- Tropical geometry
- Real algebraic geometry
- Real Hurwitz numbers
As of May 2021, I will be working in the Institute of Analysis and Algebra at TU Braunschweig as part of my Walter Benjaminn Programme grant EL 1092/1-1, titled "Classifying polynomial maps by means of polyhedral geometry".
Currently, I am a postdoc at the Symbolic Computation group in the Johann Radon Institute for Computational and Applied Mathematics, Linz, working with Niels Lubbes as part of his FWF grant tiltled "Trajectories of motions".
I was a postdoc (Dec. 2018 - Apr. 2020) at the Institute of Mathematics Polish Academy of Sciences.
I was a visiting researcher (Dec. 2017 - Nov. 2018) at the Max Planck Institute für Mathematik, Bonn.