Report Title：Enriched and Extended Shuffle Algebras from Multiple Zeta Values
Reporter：Li Guo, Rutgers University-Newark
Affiliation: Rutgers University-Newark
Report Time: July 19, 2026
Report Location: Fifth Seminar Room, Wu Zhuoqun Building
Abstract:
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.
Bio:
Li Guo is a professor at Rutgers University–Newark, USA. His work in number theory was cited in Andrew Wiles’s paper proving Fermat’s Last Theorem, and he has applied renormalization, a method originating in physics, to mathematical research. In recent years, he has advanced the study of Rota–Baxter algebras and related areas of mathematics and mathematical physics. At the invitation of the American Mathematical Society, he contributed an introduction to Rota–Baxter algebras to its “What Is” column and authored the first monograph in the field. His research spans associative algebras, Lie algebras, Hopf algebras, operads, number theory, combinatorics, computational mathematics, quantum field theory, and integrable systems.
