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Rota-Baxter Algebras and Quasi-Symmetric Functions
郭锂 教授(美国Rutgers大学)
2020年7月2日10:00-11:00  Zoom房间号:685 9743 2504

报告人:郭锂 教授(美国Rutgers大学)
主持人:谢兵永副教授、周国栋副教授
报告时间:2020年7月2日10:00-11:00
报告平台:Zoom房间号:685 9743 2504 会议密码:164921

报告人介绍:郭锂,美国罗格斯大学纽瓦克分校教授,江西师范大学特聘教授。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,现任罗格斯大学数学与计算机科学系系主任。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。

报告内容摘要: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.