报告题目：Separable Volterra operators and generalized Reynolds algebras
报 告 人：Li Guo, Rutgers University-Newark
所在单位：Rutgers University-Newark
报告时间：2024年8月23日 11:00-13:00
报告地点：金沙集团1862cc数学楼第6研讨室
报告摘要: The Reynolds operator originated from the well-known work of Reynolds on fluid mechanics in the late 19th century. The classical example of a Reynolds operator is given by a specific Volterra integral operator, first studied by Reynolds and Rota. In this study, we explore the rich algebraic structures from other Volterra integral operators, when the kernel of the operator is separable. The operator satisfies a generalized Reynolds identity, called the D-differential Reynolds identity. To construct the corresponding free objects, we develop a completion for topological operated algebras and define a completion of the shuffle product. The construction provides an algebraic framework to define and study Volterra integral equations with separable kernels. This is a joint work with Richard Gustavson and Yunnan Li.
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。
