Solvable lattice models originated in mathematical physics (Ising model, square ice). They found numerous applications to combinatorics (enumerative and algebraic - keywords are nonsymmetric Macdonald polynomials and Hecke algebras), representation theory (keyword - quantum groups), and more recently, probability. We will start with classical results, such as the Izergin-Korepin determinant and the entropy of the square ice. We’ll select further topics based on the audience’s interests.
August 29, 2023
Leo Petrov - Introduction
September 5, 2023
Nick Sweeney - The Alternating Sign Matrix conjecture
after Chapter 1 of the book Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture by David M. Bressoud
September 12, 2023
Petch Chueluecha - Dodgson condensation
after Section 3.5 of the book Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture by David M. Bressoud
September 19, 2023
Mikhail Tikhonov - The Yang-Baxter equation and the Izergin-Korepin determinant
after Wheeler-Zinn-Justin 2015 (Section 4.2 with $u=1$) and Petrov 2020 (Yang-Baxter equation is Proposition 2.1; and the determinant is proven in Section 3.4 with $\gamma=1$, $s_0=0$)
September 26, 2023
Leo Petrov - From the Izergin-Korepin determinant to the number of alternating sign matrices
October 10, 2023
Jacob Campbell - Quantim groups and Yang-Baxter equation
October 17, 2023
TBA
October 24, 2023
TBA
October 31, 2023
TBA
November 7, 2023
TBA
November 14, 2023
TBA
November 28, 2023
Zongrui Yang (Columbia) - Probability seminar talk (special day)