The semester runs for five weeks, with four weeks at IMPAN in Warsaw and a final conference in Będlewo.

Week 1 — Introductory school

17–21 May 2027 · IMPAN, Warsaw (room 321)
Mini-courses introducing the core themes of the semester for early-career participants.

Mini-course — Gaëtan Borot (Humboldt University of Berlin): Free probability under the surface

I will explain the notion of all-order free cumulants and freeness and their relevance for unitarily invariant random matrices from several perspectives:

• combinatorics of surfaced permutations, multiplicative functions, Möbius and zeta functions;
• convolution with double Hurwitz numbers;
• fully simple observables in random matrices;
• functional relations and analytic properties;
• symplectic exchange and (un)compatibility with topological recursion.

Mini-course — Greta Panova (University of Southern California): Asymptotic Algebraic Combinatorics

Algebraic Combinatorics studies objects and quantities motivated by or originating from Algebra, Representation Theory, Geometry. Such objects are the standard Young tableaux, enumerated by the celebrated hook-length formula, or the Littlewood–Richardson coefficients which give multiplicities of irreducible GL representations in tensor products and are counted by the combinatorial LR rule. Yet many other quantities which are multiplicities (like Kronecker or plethysm) or dimensions and are inherently nonnegative integers do not enjoy such nice formulas or combinatorial interpretations. Understanding their behavior has applications beyond combinatorics and understanding their asymptotics is the next natural and important step.

At the same time key part of algebraic combinatorics is the theory of symmetric functions, which gives explicit ways to extract multiplicities as coefficients. It is a powerful tool of enumeration applied beyond combinatorics and algebra to statistical mechanics and integrable probability, allowing us to study asymptotics of dimer configurations and vertex models.

In this mini-course we will introduce the basic objects and tools of algebraic combinatorics and symmetric functions, understand some key applications and discuss the open problems in asymptotics.

Mini-course — Bálint Virág (University of Toronto): A brief user’s manual to the directed landscape

The directed landscape is the conjectured scaling limit of first passage percolation in 2 dimensions. But how does one prove theorems about such an object? I will work through several examples from recent results.

Week 2 — Workshop

24–28 May 2027 · IMPAN, Warsaw (room 321)
Research talks bringing together the combinatorics, probability, and topological-recursion communities (40–50 participants).

Weeks 3–4 — Collaboration weeks

31 May – 11 June 2027 · IMPAN, Warsaw (room 403)
Two weeks dedicated to collaborative research, informal seminars, and working groups.

Week 5 — Final conference

14–18 June 2027 · Mathematical Research and Conference Center, Będlewo
A final conference (50–80 participants) presenting results and new directions arising from the semester.

A detailed schedule, speaker list, and abstracts will be posted here closer to the event.