短课程：q-Whittaker functions and affine crystals

：Travis Scrimshaw（ 日本北海道大学 ）
：2026-03-12 ——2026-03-17
：海韵园实验楼S207

国家天元数学东南中心拟于2026年3月12日至3月17日开设“q-Whittaker functions and affine crystals”短课程，相关安排如下：

一、短课程介绍

1. 主讲人：

  Travis Scrimshaw works in an area known as combinatorial representation theory, with a focus on the interactions between mathematical physics and probability theory. By transferring problems and theorems from one area to another, not only do new tools become available, even further (and unexpected) connections are often made.

2. 课程简介：

This mini-course will give an introduction to an important class of symmetric functions and discuss their connections with representation theory by using the combinatorics of Kashiwara's theory of crystal bases (focusing on semistandard tableaux). We will generally only assume a basic knowledge of linear algebra.

Lecture 1: We will give an overview of the ring of symmetric functions in some of their classical bases (homogeneous, elementary, powersum, and Schur functions) and their associated combinatorics. We will briefly sketch the relationship with the representation theory. From there, we will abstractly define Macdonald polynomials and study their specializations, with an emphasis on q-Whittaker functions.

Lecture 2: We will begin this lecture by defining the Kashiwara crystal on semistandard tableaux and connect it with Schur functions. From there, we will construct the corresponding affine crystals, discuss the relationship with q-Whittaker functions, and conclude with applications to probability theory.

二、课程日期安排

2026年3月12日报到，3月13日-16日上课，3月17日离会。

授课日期	授课时间	教学内容纲要
3月13日	9:00--12:00	Lecture 1: Symmetric function and representation theory
3月16日	9:00--12:00	Lecture 2: Kashiwara crystals and Schur functions
3月16日	16:30--18:30	Lecture 3: affine crystals, q-Whittaker functions and probability theory

 

三、短课程地点

1. 上课地点：厦门大学海韵园实验楼S207

四、联系人

 马老师（tymath3@xmu.edu.cn）