代数与表示论讨论班

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

报告人：Professor Li Guo (郭锂), Rutgers University

时间：2026年6月3日， 14:45-15:45

地点：海纳苑2幢101

摘要：The algebra of multiple zeta values (MZVs) is encoded as both a stuffle (quasi-shuffle) algebra and a shuffle algebra. The MZV stuffle algebra possesses a natural Hopf algebra structure with significant applications to MZVs. Recently, the MZV shuffle algebra has also been equipped with a Hopf algebra structure. The required coproduct is defined recursively via 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 corresponding to MZVs with arbitrary arguments, and another Hopf algebra structure is provided for the subalgebra concerning negative arguments. Furthermore, these two Hopf algebras are naturally related by a duality. This talk will survey these results, obtained in joint work with Wenchuan Hu, Hongyu Xiang, and Bin Zhang.

联系人：李方（fangli@zju.edu.cn）