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Mathematical Physics and Probability Reading seminar

(Covering topics related to random matrices, representation theory, integrable systems and interacting stochastic particle systems)

Seminars are held on Tuesdays at 12:00, B3.02

Term 1

2 October. No seminar

9 October. Leonid Petrov (Virginia). Cauchy identities, Yang-Baxter equation, and their randomization.

Abstract. Cauchy type summation identities for various families of symmetric polynomials (with Schur polynomials as the first example) are crucial in bringing exact solvability to various stochastic particle systems in the Kardar-Parisi-Zhang universality class. First breakthroughs in this direction about 20 years ago employed Robinson-Schensted-Knuth correspondences to study asymptotic fluctuations of longest increasing subsequences and TASEP (totally asymmetric simple exclusion process). Deforming the Schur structure, one can connect Cauchy identities to the Yang-Baxter equation for the six vertex model, and use this to exactly solve more general models such as ASEP. I will discuss how the structure of RSK correspondences should be adapted in connection with these deformations, providing a "bijective" point of view on the Yang-Baxter equation.

16 October. Jon Warren (Warwick). A first look at the Gaussian Free Field. 

Abstract. I will try to give some intuition for why this is a fundamental process, starting with a discrete version, emphasizing the Markov property, and concluding with a quick look at an example of an interesting model in which the GFF arises.

23 October

30 October

6 November

13 November

20 November

27 November

4 December

Reading List

N. Berestycki, Introduction to the Gaussian Free Field and Liouville Quantum Gravity

W. Werner, Topics on the two-dimensional Gaussian Free Field

O. Zeitouni,Gaussian Fields

Marek Biskup, Extrema of 2D Discrete Gaussian Free Field