报告题目：A proof of the multi-component $q$-Baker--Forrester conjecture

报告时间：4月16日，腾讯会议：667-150-369

报告摘要：The Selberg integral, an $n$-dimensional generalization of the Euler beta integral, plays a central role in random matrix theory, Calogero--Sutherland quantum many body systems, Knizhnik--Zamolodchikov equations, and multivariable orthogonal polynomial theory. The Selberg integral is known to be equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a $(p+1)$-component generalization of the $q$-Morris identity. It in turn yields a generalization of the Selberg integral. The $p=1$ case of Baker and Forrester's conjecture was proved by K\'{a}rolyi, Nagy, Petrov and Volkov in 2015.

In this talk, we present our proof of the $(p+1)$-component $q$-Baker--Forrester conjecture, thereby settling this 27-year-old conjecture.

个人简介：周岳，中南大学数学与统计学院博士生导师、教授。研究方向为代数组合学，主要研 究常数项等式及对称函数。在 Advances in Mathematics、Transactions of the American Mathematical Society、Journal of Combinatorial Theory,Series A、Advances in Applied Mathematics、Proceedings of the American Mathematical Society 等国际重要期刊上发表多篇论文。现主持国家自然科学基金面上项目一项。曾主持国家自然科学基金及省部级项目多项。