Explore the connections between symmetric functions and vertex models in this 50-minute lecture from the Asymptotic Algebraic Combinatorics 2020 conference. Delve into Konstantin Matveev's research on classifying homomorphisms with positive values on Macdonald symmetric functions and the unexpected positivity in stochastic six-vertex models. Discover the relationship between these two areas and their connection to the Robinson-Schensted-Knuth (RSK) algorithm. Gain insights into advanced topics in algebraic combinatorics and statistical mechanics as presented by Matveev from Rutgers University at the Institute for Pure and Applied Mathematics, UCLA.