With this talk I would like to introduce myself and my research to the group in Discrete Mathematics which I have recently joined. In particular, I will give an introductory overview of my research on solvable lattice models. My original motivation for this research was to construct lattice models whose partition functions compute special functions in representation theory. However, as a by-product they also produce special functions (polynomials) of interest in algebraic combinatorics such as Schur polynomials, Hall-Littlewood polynomials and Macdonald polynomials, and this angle will be the starting-point of the talk.
The lattice models can then be used to give (alternative) proofs of a multitude of interesting combinatorial properties, including branching rules, Pieri- and Cauchy-type identities, and functional equations which I will explain diagrammatically.
Based on joint work with Ben Brubaker, Valentin Buciumas and Daniel Bump.
To receive the Zoom link, please contact Maryam Sharifzadeh.
