学 术 报 告

报告题目：Rota-Baxter Algebras and Quasi-Symmetric Functions

报告人：郭锂 教授（罗格斯大学纽瓦克分校, 江西师范大学）

报告时间：2018年7月13日（星期五） 9:00-11:00

报告地点：星际电子在线学术报告厅（25教14楼）

参加人员：教师、研究生、本科生

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 Warning 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.

个人简介：郭锂，美国罗格斯大学纽瓦克分校教授，江西师范大学国家""特聘教授。郭锂于华盛顿大学获博士学位，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数学和理论物理的广泛领域。