Title: Separable Volterra Operators and Generalized Reynolds Algebras
Speaker: Li Guo
Institution: Rutgers University-Newark
Date & Time: August 23, 2024, 11:00–13:00
Location: Seminar Room 6, Mathematics Building, Jilin University
The Reynolds operator traces its origins to Reynolds’ seminal work on fluid mechanics in the late 19th century. A classical example of a Reynolds operator is embodied in a specific Volterra integral operator, first investigated by Reynolds and Rota. In this study, we delve into the rich algebraic structures arising from other Volterra integral operators with
separable kernels. Such operators satisfy a generalized Reynolds identity, termed the
D-differential Reynolds identity. To construct the corresponding free objects, we develop a completion theory for topological operated algebras and define a completion of the shuffle product. This framework provides an algebraic foundation for defining and analyzing Volterra integral equations with separable kernels. Joint work with Richard Gustavson and Yunnan Li.
Li Guo is a Professor at Rutgers University-Newark, USA. His work in number theory has been cited in Andrew Wiles’ proof of Fermat’s Last Theorem. He pioneered the application of renormalization—a key technique in physics—to mathematical research. In recent years, he has been a leading figure in advancing the study of Rota-Baxter algebras and their connections to mathematical physics, having been invited by the American Mathematical Society to introduce Rota-Baxter algebras in its
What Is series and publishing the first monograph in this field. His research spans a broad spectrum of disciplines, including associative algebras, Lie algebras, Hopf algebras, operads, number theory, combinatorics, computational mathematics, quantum field theory, and integrable systems.
