Algebraic or geometric objects, such as ideals or varieties, that are combinatorially constructed capture many examples seen in applications. On the other hand, they are amenable to combinatorial techniques. When an object is constructed using only combinatorial data, one expects to have a combinatorial description of its properties. An attempt to achieve this description often leads to surprisingly deep combinatorial questions. White’s conjecture about the toric ideal of a matroid is an example. I work on problems of the above type, as well as other areas of combinatorics: matroids, graphs, extremal combinatorics, probabilistic and topological methods in combinatorics, convex and discrete geometry, polytopes.

"Kombinatoryka oraz Geometria Matroidów i Wielościanów" projekt NCN Sonata Bis 2020-2025

"Combinatorics and Geometry of Matroids and Polytopes" NCN project Sonata Bis 2020-2025