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)