Probability Seminar: Greta Panova, University or Southern California

Algebra meets Probability: random permutations from Schubert and Grothendieck polynomials via 6-vertex models and TASEP. Schubert and Grothendieck polynomials arise from the cohomology and K-theory of the flag variety, but have combinatorial descriptions as partition functions of certain vertex models with long-range interactions or intersecting lattice path configurations known as pipe dreams. In this talk we will start with the open problem of asymptotically counting these configurations and show how the probabilistic perspective leads to new structures, including random permutations (permutons). Based on: Morales, Panova, Petrov, Yeliussizov, "Grothendieck Shenanigans: Permutons from Pipe Dreams via Integrable Probability", Adv. Math 2025. Anderson, Panova, Petrov, "Computations and sampling for Schubert specializations", PNAS 2026 (to appear)