Student Study Seminar on Probability Theory and Related Fields
During this seminar, we are planning to study the some topics related to probability, including Hall algebra and Hecke algebra, random matrix theory, KPZ equation, six vertex model. Please email js6157@columbia.edu if you would like to join.
The seminar takes place in room 622 in the mathematics building, from 4pm to 5pm every Monday.
A tentative schedule for the seminar will be as follows (adjustments might be made according to actual progress):
Date
Speaker
Title and Abstract
09/16/2024
Jiahe Shen
Hall algebra
09/23/2024
Jiahe Shen
Hecke algebra and its connections with Hall algebra and symmtric functions
09/30/2024
Jiahe Shen
Spherical functions
10/07/2024
Jiahe Shen
p-adic random matrices
02/19/2024
Xinyi Zhang
The Hall-Littlewood polynomials P_λ, q_λ, Q_λ
02/26/2024
Xinyi Zhang
Orthogonality, six vertex model and Hall-Littlewood Process, Yang Baxter equation
03/04/2024
Xinyi Zhang
Further discussion of six vertex model and connect HL in Macdonald's book
03/18/2024
Jiahe Shen
The Macdonald polynomial: Introduction and Orthogonality
03/25/2024
Jiyue Zeng
The differential operator D_n^r
04/01/2024
Jiyue Zeng
Difference operator and construction of Macdonald polynomials
04/08/2024
Jiyue Zeng
Schur Process
04/15/2024
Xinyi Zhang
Colored linear ensembles
References
[1]I.G.Macdonald, Symmetric Functions and Hall Polynomials (second edition), Oxford Science Publications, 1998.