Academic Report of School of Mathematical Sciences [2026] No. 051

(Series Report for High-Level University Construction No. 1310)

Title：Quantum vertex algebras, modules, and ϕ-coordinated modules

Speaker：Haisheng Li (Rutgers University–Kenton)

Time：14:30-15:30, June. 3, 2026

Location：Huiwen Building Room 1425, Yuehai Campus

Abstract：In this talk, we introduce certain developments in the field of quantum vertex algebras along the main line to associate vertex algebralike objects to various (quantum) algebras. More specifically, we introduce the theory of (weak) quantum vertex algebras and modules, including a conceptual construction. We shall explain how to use this construction to connect algebras like double Yangians to quantum vertex algebras. We also introduce the theory of ϕ-coordinated modules for (weak) quantum vertex algebras and a conceptual construction. We shall explain how to use this construction to connect algebras like quantum affine algebras to quantum vertex algebras via ϕ-coordinated modules.

Speaker Profile：Haisheng Li, a tenured professor at Rutgers University–Kenton, is a renowned Chinese mathematician and one of the founders of vertex operator algebras. For many years, he has been engaged in research on important representation and structural theories of infinite-dimensional Lie algebras, vertex algebras, and vertex operator algebras. He has published high-quality academic papers in prestigious journals such as Duke Math. J., Adv. Math., Math. Ann., Comm. Math. Phys., Trans. , Israel J. Math., Math. Z., Selecta Math. (N.S.), J. Algebra, and J. Pure Appl. Algebra. He has been cited by peers over 3,000 times and serves on the editorial board of the Electronic Research Archive. He has led multiple grants from the U.S. National Science Foundation and one grant from the National Natural Science Foundation of China (an overseas collaboration project).

Faculty and students are welcome to attend!

Invited by: Jinkui Wan

School of Mathematical Sciences

June 1, 2026