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Explore a lecture from the Workshop on Combinatorics of Enumerative Geometry where Greta Panova delves into the intersection of algebra and integrable probability through Grothendieck polynomials. Starting with Richard Stanley's 2018 paper "Some Schubert shenanigans" and its open question about Schubert polynomial asymptotic behavior, discover how the generalization to Grothendieck polynomials reveals statistical mechanical structures and new permutons. Learn about pipe dreams as tiling models and their interpretation as lattice walk ensembles with interaction constraints. Examine typical Grothendieck permutations through the Totally Asymmetric Simple Exclusion Process (TASEP) theory, analyzed using Schur functions. Investigate connections between free fermion 6 vertex models and Aztec diamond domino tilings to understand extreme cases and identify permutations that maximize Grothendieck polynomial principle specialization at β=1. The research presented represents collaborative work with A. H. Morales, L. Petrov, and D. Yeliussizov.
