报告题目：Enriched and Extended Shuffle Algebras from Multiple Zeta Values

报告人：Li Guo, Rutgers University-Newark

所在单位：Rutgers University-Newark

报告时间：2026年7月19日16:00-17:00

报告地点：成人直播平台 伍卓群楼第5研讨室

报告摘要: The algebra of multiple zeta values (MZVs) is encoded as a shuffle (quasi-shuffle) algebra and a shuffle algebra. The MZV shuffle algebra has a natural Hopf algebra structure which has important applications to MZVs. Recently the MZV shuffle algebra is equipped with a Hopf algebra structure. The needed coproduct is defined by a recursion through a family of weight-increasing linear operators, and can be recovered from a differential locality Hopf algebra on Chen fractions. On the other hand, the MZV shuffle algebra naturally extends to a larger shuffle algebra that corresponds to MZVs with arbitrary arguments, and another Hopf algebra structure is given to the subalgebra for negative arguments. Moreover, the two Hopf algebras are naturally related by a duality. This talk will give a survey of these results, obtained in joint works with Wenchuan Hu, Hongyu Xiang and Bin Zhang.

报告人简介：郭锂，美国罗格斯大学纽瓦克分校教授。他的数论工作为怀尔斯证明费马大定理的文章所引用，并将重整化这一物理方法应用于数学研究。他近年来推动Rota-Baxter代数及相关数学和数学物理的研究，应邀为美国数学会在“What Is”栏目中介绍Rota-Baxter代数，并出版这个领域的第一部专著。研究涉及结合代数，李代数，Hopf代数，operad，数论，组合，计算数学，量子场论和可积系统等广泛领域。