时间：2021年12月8日（星期三）  18：30-19：30；悉尼时间：21：30-22：30

地点：腾讯会议号：298284191

报告题目：Diagram Algebras in Knot Theory and Invariant Theory
报告专家：张瑞斌教授

报告摘要：This is an elementary introduction to diagram algebras and their applications in invariant theory and topology of knots. We will assume no prior knowledge of any of these topics, and explain everything from scratch.

A remarkable success of classical invariant theory in recent decades is the construction of topological invariants of knots from the study of quantum group actions. Many interesting new algebras presented in terms of tangle-like diagrams emerged in the process, which play important roles in representation theory.

We first analyse the Jones polynomial of knots to uncover the underlying algebraic structure, the Templey-Lieb algebra, then extend the analysis to other knot invariants to treat their underlying diagram algebras in a uniform manner, and finally explain the construction of such knot invariants as an aspect of the first fundamental theorem of invariant theory for quantum groups. At the end of the talk, we discuss some results on affine Templey-Lieb algebras in the invariant theory of a class of infinite dimensional representations of quantum SL(2).

个人简介: 张瑞斌教授是澳大利亚悉尼大学数学与统计学院教授。在量子超群、李超代数、低维拓扑、非交换几何、不变量理论以及量子物理等方面取得了一系列有重要国际影响的研究成果，很多重要研究成果发表于《Annals of Mathematics》(数学年刊)、《Advances in Mathematics》(数学进展)、《Transactions of American Mathematical Society》(美国数学学会会报)等国际数学顶尖期刊上。约发表了140余篇研究论文，论文被他人引用高达1000余次。曾获得澳大利亚研究委员会伊丽莎白二世奖学金(ARC Queen Elizabeth II Fellow)、澳大利亚研究委员会教授奖(ARC Australian Professorial Fellow)等诸多荣誉。

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数学科学学院