Numerous objects in algebraic and enumerative geometry encode discrete structures either in the form of graphs, polytopes, or other polyhedral properties.
I adapt methods from tropical geometry, convex geometry and graph theory to tackle problems related to the topology of (real, or complex) algebraic varieties, polynomial maps, and ramified covers.
Problems that I am interested in are those of relevance to both pure mathematics, and its applications to sciences, engineering and intelligent systems.
- Fewnomial theory
- Topology of polynomial maps
- Tropical geometry
- Real algebraic geometry
- Real Hurwitz numbers
I am working at 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".
I was 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.