Student Study Seminar on I.G.Macdonald's book, "Symmetric Functions and Hall Polynomials"
During this seminar, we are planning the study I.G.Macdonald's book, "Symmetric Functions and Hall Polynomials", which provides techniques that are wildely involved in representation theory, integrable probability, and number theory. No background knowledge is required. Please email js6157@columbia.edu if you would like to join.
The seminar takes place in room 528 in the mathematics building, from 4:30pm to 5:30pm every Monday. See the notes for Chapter 1,2,5.

A tentative schedule for the seminar will be as follows (adjustments might be made according to actual progress):
1. Chapter 1 (4 weeks)
2. Chapter 3 (3 weeks)
3. Chapter 6 (3 weeks)
4. Chapters 2 and 5 (2 weeks)

      

 

Date Speaker Title and Abstract
01/22/2024 Jiahe Shen Partitions, ring of symmetric functions
01/29/2024 Jiahe Shen Four basis for the ring of symmetric functions, also the Schur symmetric functions
02/05/2024 Jiahe Shen Orthogonality, skew symmetric functions
02/12/2024 Xinyi Zhang LPP and RSK correspondence, the symmetric polynomials R_λ
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.