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 开始时间：2020-07-02 09:30:00 结束时间：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. |
