报告题目：Renormalization of quasisymmetric functions

报 告 人：Li Guo (Rutgers University-Newark)

报告时间：2021年10月15日 09:00

报告地点：Zoom会议 ID： 862 062 0549，会议密码： 2021

会议网址：https://us02web.zoom.us/j/8620620549?pwd=NUhCMWpuTG9Od1RMNjhEdkdwTzlsUT09

报告摘要：The Hopf algebra of quasisymmetric functions (QSym) has played a central role in algebraic combinatorics and has broad applications. A natural linear basis of QSym is the set of monomial quasisymmetric functions defined by compositions, that is, vectors of positive integers. Extending such a definition for weak compositions, that is, vectors of nonnegative integers, leads to divergent expressions. This difficulty was addressed by a formal regularization in a previous work with Jean-Yves Thibon and Houyi Yu. Here we apply the method of renormalization in the spirit of Connes and Kreimer and realize weak composition quasisymmetric functions as power series. The resulting Hopf algebra has the Hopf algebra of quasisymmetric functions as both a Hopf subalgebra and a Hopf quotient algebra. It also gives a realization of free commutative Rota-Baxter algebra on one generator by weak quasisymmetric functions and thus addresses a question raise by Rota many years ago. This is a joint work with Houyi Yu and Bin Zhang.

报告人简介：郭锂，美国罗格斯大学纽瓦克分校教授。郭锂博士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广泛领域。