数学学科2025系列学术报告之九

　　报告题目：Operated algebras and derived structures

　　报告人：郭锂教授（罗格斯大学纽瓦克分校）

　　时间：2025年5月30日 10:00-11:00

　　地点：理学院1号楼1-301

　　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 throughout the history of mathematics, their algebraic studies have been limited, and have been specializes to special cases. Recently the general notion was introduced as operated algebras. Their study have shown promising developments. We discuss some recent developments on the general theory of operated algebras, their important classes and derived structures.

　　报告人简介：郭锂，美国罗格斯大学纽瓦克分校教授。郭锂博士于兰州大学获学士学位，于武汉大学获硕士学位，于华盛顿大学获博士学位，并在俄亥俄州立大学、普林斯顿高等研究院和佐治亚州大学作博士后。郭锂博士的数论工作为怀尔斯证明费马大定理的文章所引用，并将怀尔斯文中的主猜想推广到高权模形式上。他近年来将重整化这一物理方法应用于数学研究，推动Rota-Baxter代数及相关数学和理论物理的研究。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数学和理论物理的广泛领域。在Duke Math. J.、Comm. Math. Phy.、Adv. Math.、 Trans. AMS、IMRN、Math Ann.等国际著名杂志发表论文140余篇。