Stochastic symplectic ice: a stochastic vertex model with U-turn boundary

mathematical physicscombinatoricsnumber theoryprobabilityquantum algebrarepresentation theory

Audience: advanced learners

Solvable Lattice Models Seminar

Series comments: Seminar website: naprienko.com/lattice-seminar

Solvable lattice models are statistical mechanical systems that can be studied exactly by a method of Baxter, based on the Yang-Baxter equation. This can be understood in terms of quantum groups. Recently particular examples showing symmetry with respect to the Lie quantum super group U_q(\widehat{\mathfrak{gl}}(r|n) arose in two very different contexts: the representation theory of p-adic groups, where such models were used by Brubaker, Buciumas, Bump and Gustafsson to study Iwahori Whittaker functions on metaplectic groups; and in integrable probability, in work recent of Aggarwal, Borodin and Wheeler. We will introduce the topic starting with Baxter's work on six vertex model, then look at more recent work explaining some of the ideas.

The seminar serves both learning and research purposes. We explore applications of solvable lattice models in different areas of mathematics. First we give "learning" talks with history and first results in the area. After that we give several "research" talks on the recent results. Thus, the seminar is friendly for both students and researchers. Feel free to join every new "topic" even if you got lost last time because we start over with introductory talks.