報告題目：Separable Volterra operators and generalized Reynolds algebras
報 告 人：Li Guo, Rutgers University-Newark
所在單位：Rutgers University-Newark
報告時間：2024年8月23日 11:00-13:00
報告地點：吉林大學數學樓第6研讨室
報告摘要: 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.
報告人簡介：郭锂，美國羅格斯大學紐瓦克分校教授。他的數論工作為懷爾斯證明費馬大定理的文章所引用，并将重整化這一物理方法應用于數學研究。他近年來推動Rota-Baxter代數及相關數學和數學物理的研究，應邀為美國數學會在“What Is”欄目中介紹Rota-Baxter代數，并出版這個領域的第一部專著。研究涉及結合代數，李代數，Hopf代數，operad，數論，組合，計算數學，量子場論和可積系統籌廣泛領域。
