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张瑞斌: Diagram algebras in invariant theory
发布日期:2018-12-10  字号:   【打印

报告时间:2018年12月10日(星期一)15:30-16:30

报告地点:翡翠湖校区科教楼B座1710

  张瑞斌 教授

工作单位悉尼大学 山东师范大学

举办单位:数学学院

报告人简介

张瑞斌教授是澳大利亚悉尼大学数学与统计学院教授, 澳大利亚数学会副主席,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。张瑞斌教授主要从事李理论及其在量子物理中的应用方面的研究,是这一研究方向上的国际领导人之一。张瑞斌教授在量子超群、李超代数、低维拓扑、非交换几何、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,他在包括国际数学顶尖期刊《Annals of Mathematics》在内的多种重要数学刊物上发表了百余篇研究论文,他的论文被国际同行大量引用。

报告简介

A remarkable success of 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 are of central importance in representation theory and are in the focus of current research. This talk is an elementary introduction to diagram algebras and the important role which they play in invariant theory. We will first analyse the Jones polynomial of knots to uncover the underlying algebraic structure, the Templey-Lieb algebra. Then we generalise the analysis to other knot invariants to treat their underlying diagram algebras in a uniform manner. Finally, we discuss the representations of the diagram algebras used in the construction of knot invariants, and explain the construction as an aspect of the first fundamental theorem of invariant theory for quantum groups. At the end of the talk, we will allude to some very recent work on affine Templey-Lieb algebras.

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