Shuffle Algebras, Lattice Paths and Macdonald Functions

Explore a conference talk on the intersection of algebra, combinatorics, and mathematical physics presented by Sasha Garbali from the University of Melbourne at IPAM's Vertex Models workshop. Delve into the computation of skew Macdonald functions as vertex model partition functions, examining the connection between Macdonald functions and the Feign—Odesskii shuffle algebra. Discover a novel construction of shuffle algebra elements using vertex model partition functions. Gain insights into the algebraic and probabilistic aspects of universality in vertex models through this 44-minute presentation recorded on May 21, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.