Explore the intersection of integrable probability and algebraic combinatorics through this comprehensive workshop featuring 25 expert presentations from leading researchers in the field. Delve into recent advances in colored vertex models and interacting particle systems using symmetric functions, including Schur and Macdonald polynomials and their generalizations. Examine various exclusion processes such as TASEP and their steady states where polynomials of algebro-combinatorial significance emerge, including Schubert polynomials. Investigate the emergence of dimer models and electrical networks from the algebra of the positive Grassmannian. Study how probability and statistical physics tools apply to algebraic combinatorics problems, particularly in analyzing asymptotics of structure constants like Kostka, Littlewood-Richardson, and Kronecker coefficients. Discover symmetries of polynomials and rational functions arising from Yang-Baxter equations. Learn about spectrum analysis of random-to-random shuffling in Hecke algebras, compact formulas for symmetric Macdonald polynomials via ASEP and TAZRP, and construction of interpolation symmetric functions from q-Hahn integrable models. Explore logarithmic singularities in density functions of 2-dimensional percolation, hypergeometric matrix models, Schubert to Grothendieck transformations via ice models, and symplectic Schur processes. Examine Andrews-Gordon partition identities, limit shapes for random Young tableaux via determinantal point processes, inhomogeneous multispecies PushTASEP, and MacNeille completions of type B Bruhat posets. Investigate log-concave polynomials in lattice point counting, concentration of hives, correlation decay of eigengaps, move-reduced graphs on tori, and correlation inequalities for Schur functions. Study toric promotion with reflections, global asymptotics of Jack-deformed random Young diagrams, Jack characters as series of bipartite maps, random partitions and Hurwitz numbers, complexity of log-concave poset inequalities, SL_2 double-dimer models, off-diagonally symmetric domino tilings, sums of weighted lattice points of polytopes, rotation-invariant web bases, and unifying lattices through hourglass plabic graphs.

Syllabus

Sarah Brauner - Spectrum of random-to-random shuffling in the Hecke algebra - IPAM at UCLA
Olya Mandelshtam - compact formula for the symmetric Macdonald polynomials via the ASEP and TAZRP
Sergei Korotkikh - Construction of interpolation symmetric functions from q-Hahn integrable models
Yu Feng - Logarithmic singularity in density 4-point function of 2-dimensional percolation in bulk
Jonathan Novak - Hypergeometric Matrix Models and their Duals - IPAM at UCLA
Anna Weigandt - Schubert to Grothendieck via Ice - IPAM at UCLA
Cesar Cuenca - The Symplectic Schur Process - IPAM at UCLA
Jehanne Dousse - The Andrews-Gordon partition identities and commutative algebra - IPAM at UCLA
Jacopo Borga - Limit shapes for random Young tableaux via determinantal point processes
Arvind Ayyer - The inhomogeneous multispecies PushTASEP - IPAM at UCLA
Paul Zinn Justin - The MacNeille completion of the type B Bruhat poset - IPAM at UCLA
Jonathan Leake - Log-concave polynomials, lattice point counting, and traveling salesperson problem
Hariharan Narayanan - Sums of GUE matrices, concentration of hives, correlation decay of eigengaps
Pavel Galashin - Move-reduced graphs on a torus vs positroid Catalan numbers - IPAM at UCLA
Igor Pak - Correlation inequalities for Schur functions and Young tableaux - IPAM at UCLA
Lauren Williams - inhomogeneous multispecies t-PushTASEP and Macdonald polynomials - IPAM at UCLA
Colin Defant - Toric Promotion with Reflections and Refractions - IPAM at UCLA
Maciej Dolega - Global asymptotics of Jack-deformed random Young diagrams via Lukasiewicz paths
Houcine Ben Dali - Jack characters as series of bipartite maps and proof of Lassalle’s conjecture
Harriet Walsh - Random partitions, Hurwitz number and counting high genus surfaces - IPAM at UCLA
Swee Hong Chan - Complexity of log-concave poset inequalities - IPAM at UCLA
Benjamin Young - The squish map and the SL_2 double-dimer model - IPAM at UCLA
Yi-Lin Lee - Further exploration of off-diagonally symmetric domino tilings of the Aztec diamond
Laura Escobar - Sums of weighted lattice points of polytopes - IPAM at UCLA
Jessica Striker - Rotation-invariant web bases, hourglass plabic graphs, symmetrized 6-vertex config
Joshua Swanson - Unifying lattices through hourglass plabic graphs - IPAM at UCLA