Speaker: Jang Soo Kim, Professor and Head of the Department of Mathematics at Sungkyunkwan University, South Korea. Prof. Kim received his PhD from KAIST, South Korea, in 2009, and subsequently held postdoctoral positions at Université Paris VII, France, and the University of Minnesota, USA, from 2009 to 2013. His main research field is algebraic combinatorics. He serves on the editorial boards of leading combinatorics journals such as Discrete Mathematics, Combinatorial Theory, and Annals of Combinatorics.

Date: June 3, 2026

Time: 10:00-11:00 am

Location: E119, Huagang East Building, Shandong University Qingdao Campus

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences, Shandong University

Abstract:

Orthogonal polynomials are classical objects arising from the study of continued fractions. Due to the long history of orthogonal polynomials, they have now become important objects of study in many areas: classical analysis and PDE, mathematical physics, probability, random matrix theory, and combinatorics. The combinatorial study of orthogonal polynomials was pioneered by Flajolet and Viennot in the 1980s. In this lecture series, we study fascinating combinatorial properties of orthogonal polynomials. We first study basic properties of univariate orthogonal polynomials including Viennot's combinatorial theory. We will show that moments of multivariate little q-Jacobi polynomials are generating functions for lecture hall tableaux, which are a 2-dimensional generalization of lecture hall partitions. These moments are closely related to q-Selberg integrals. We will also show that such an approach can be generalized to all orthogonal polynomials in the q-Askey scheme. This is based on joint papers with Sylvie Corteel, Bhargavi Jonnadula, Jon Keating.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/212634.htm