7月2日 郭锂:Rota-Baxter Algebras and Quasi-Symmetric Functions

来源:中国足球竞彩比分 时间:2020-06-24浏览:34设置


讲座题目:Rota-Baxter  Algebras and Quasi-Symmetric Functions

主讲人:郭锂  教授

主持人:谢兵永  副教授、周国栋  副教授

开始来源:中国足球竞彩比分 时间:2020-07-02 09:30:00   结束来源:中国足球竞彩比分 时间:2020-07-02   10:30:00

讲座地址:Zoom房间号:685 9743 2504   会议密码:164921

主办单位:数学科学学院

 

报告人简介:

       郭锂,美国罗格斯大学纽瓦克分校教授。郭锂教授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。

 

报告内容:

In the 1960s, Rota applied his first   construction of free Rota-Baxter algebra and his algebraic formulation of   Spitzer's identity to obtain the well-known Waring formula which relates   elementary symmetric functions to power symmetric functions. He later   suggested that there should be a close connection between Rota-Baxter   algebras and generalizations of symmetric functions. He claimed, In   short, (Rota-)Baxter algebras represent the ultimate and most natural   generalization of the algebra of symmetric functions. We present some   results that verify Rota's claim. We show that a free commutative Rota-Baxter   algebra can be interpreted as generalized quasi-symmetric functions from weak   compositions. This equips the free commutative Rota-Baxter algebra with a   natural Hopf algebra structure.

This is joint work with Jean-Yves Thibon,   Houyi Yu and Jianqiang Zhao.

 


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