报告题目：Cluster structures on quantum groups and the full Berenstein-Zelevinsky conjecture
中文标题：量子群的簇结构和Berenstein-Zelevinsky 猜想
报告人 (Speaker)： Milen Yakimov 教授（ Northeastern University）
报告时间 (Time)：2026年 1月28日（周三）11：00 am
报告地点 (Place)：宝山校区F309
邀请人(Inviter)：黄红娣
报告摘要：Cluster Algebras were invented by Fomin and Zelevinsky in the early 2000s and quickly turned into an indispensable tool in many areas of mathematics. In this talk, we will provide a gentle introduction to the subject. From the early days of the theory of cluster algebras, one of the desired constructions was to turn the quantized coordinate rings of complex simple Lie groups into quantum cluster algebras. This remained elusive. We will present a resolution of it and of the Berenstein-Zelevinsky conjecture on cluster structures on quantum double Bruhat cells, a special case of which was proved in an earlier work with Ken Goodearl. This is a joint work with Fan Qin and Hironori Oya.