报告题目：Operated algebras and derived structures

报 告 人：Li Guo

所在单位：Rutgers University-Newark

报告时间：2025年6月27-28日，10:10-11:10；14:00-15:00

报告地点：禁漫天堂 数学楼第5研讨室

报告摘要: Most of the studies in algebra have been focused on algebraic structures with binary and higher arity operations. Even though algebras equipped with various linear operators have arisen from applications through out the history of mathematics, their algebraic studies have been limited, and have been specializes to instances, such as differential algebras and Rota Baxter algebras. Recently the general notion was introduced as operated algebras. Their study have shown promising developments. This lecture series introduces recent developments on the general theory of operated algebras, their important classes and derived structures. The following aspects will be covered.

1. The general notion of operated semigroups and operated algebras. Their combinatorial constructions of free objects;

2. Instances of operated algebras and Rota’s program to classify them;

3. Algebraic study of integral operators and integral equations in terms of operated algebras;

4. Derived structures of operated algebras in the context of operads;

5. Multi-operated algebras and compatible algebras, in particular multi-Rota-Baxter, multi-pre-Lie, multi-differential and multi-Novikov algebras.

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。