Reading seminar on solvable lattice models in Fall 2023

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Tuesdays, 11:00am - 12:10pm, Kerchof 111

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.

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Schedule of meetings

1. August 29, 2023

   Leo Petrov - Introduction

2. 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

3. 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

4. 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 $\gamma=1$, $s_0=0$)

5. September 26, 2023

   Leo Petrov - From the Izergin-Korepin determinant to the number of alternating sign matrices

6. October 10, 2023

   Jacob Campbell - Quantim groups and Yang-Baxter equation

7. October 17, 2023

   TBA

8. October 24, 2023

   TBA

9. October 31, 2023

   TBA

10. November 7, 2023

    TBA

11. November 14, 2023

    TBA

12. November 28, 2023

    Zongrui Yang (Columbia) - Probability seminar talk (special day)

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