Here you will find some information about my research interests, our research group and their activities.

Research

Most of my research is on algebraic and enumerative aspects of combinatorics. I am particularly interested in interactions between combinatorics and other fields of mathematics such as representation theory, probability, mathematical physics and enumerative geometry. I like it when combinatorial objects can be used to give an explicit meaning to complicated and abstract structures in mathematics. There are two types of combinatorial objects that I personally have found to be fascinating, as they seem to connect various areas of mathematics. These objects are Young diagrams, and combinatorial maps, which can be interpreted as discrete surfaces.

A large part of my research is supported by the NCN grant project “One-parameter deformations in symmetric functions theory”. The overall goal is to extend our understanding of classical Schur-related discrete models to the realm of their one-parameter deformations. We intend to use combinatorial methods to explain many mysterious phenomenas in a uniform way. Here are some key words that appear in my research:

  • Young diagrams
  • combinatorial maps aka ribbon graphs
  • asymptotic representation theory
  • integrable probability
  • Jack and Macdonald polynomials
  • topological recursion
  • Hurwitz theory

Research group at IM PAN Kraków

I work in the Kraków branch of IM PAN, where we have a group working on combinatorics and interactions (mathematical physics, probability, representation theory). The group is financially supported by different grants, largely by the NCN grant “One-parameter deformations in symmetric functions theory”.

Postdocs:

Students:

  • Maciej Kowalski (2018–2024)
  • Andrey Naradzetski (2023–now)

Activities

Jointly with Jacinta Torres we organize the Combinatorics and Interactions seminar. We usually meet on (every other) Tuesday at 14:00 at the Kraków branch of IM PAN.