報告題目：Operated algebras and derived structures

　　報告人：郭鋰教授（羅格斯大學紐瓦克分校）

　　時間：2025年5月30日 10:00-11:00

　　地點：理學院1號樓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.

　　報告人簡介：郭鋰，美國羅格斯大學紐瓦克分校教授。郭鋰博士于蘭州大學獲學士學位，于武漢大學獲碩士學位，于華盛頓大學獲博士學位，并在俄亥俄州立大學、普林斯頓高等研究院和佐治亞州大學作博士后。郭鋰博士的數(shù)論工作為懷爾斯證明費馬大定理的文章所引用，并將懷爾斯文中的主猜想推廣到高權(quán)模形式上。他近年來將重整化這一物理方法應(yīng)用于數(shù)學研究，推動Rota-Baxter代數(shù)及相關(guān)數(shù)學和理論物理的研究。應(yīng)邀為美國數(shù)學會在“What Is”欄目中介紹Rota-Baxter代數(shù)，并出版這個領(lǐng)域的第一部專著。研究涉及結(jié)合代數(shù)，李代數(shù)，Hopf代數(shù)，operad，數(shù)論，組合，計算數(shù)學，量子場論和可積系統(tǒng)等數(shù)學和理論物理的廣泛領(lǐng)域。在Duke Math. J.、Comm. Math. Phy.、Adv. Math.、 Trans. AMS、IMRN、Math Ann.等國際著名雜志發(fā)表論文140余篇。