报告一：Paramanifolds for Green’s generalised quantisation

报告华体会（中国）官方：2024年7月3日下午14:40-15:30

报告地点：翡翠科教楼B1710

报告人：张瑞斌 教授

工作单位：University of Sydney

报告摘要：Herbert S. Greenintroduced a generalised quantisation in 1953, which gave rise to the celebrated parastatistics that included the standard Bose-Fermi statistics as the special case of order 1. In recent years there have been reportsof quantum simulations of para-particles using systems of trapped ions, indicating that some quasi particles observed in condensed matter may indeed be parabosons or parafermions.

Parastatistics has been widely studied mathematically since its inception. However, the following fundamental questions concerningparafermionshave not been addressed systematically:

(1)What are the algebras in which the coordinates of parafermions at the classical level are valued in?

(2)What are the spaces whose functions describe classical parafermionic fields?

It is well known that these questions were answered for order 1 parafermions (i.e., usual fermions) by the theory of supermanifolds built with Grassmann algebras. We generalise the theory to answer the above questions for parafermions of orders greater than 1.

We introduce a class of non-commutative algebras which we callpara-algebras, and use them to develop generalisations of supermanifolds, which are ringed spaces referred to asparamanifolds. We present basic facts on paramanifolds, showing that they admit a viable differential analysis that is readily applicable to model physical problems.

报告人简介：张瑞斌，教授，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，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》，《J. Eur. Math. Soc.》，《Adv. Math》，《Comm. Math. Phys.》，《Proc. Lond. Math. Soc.》在内的多种重要数学刊物上发表了140多篇高水平论文，被国际同行大量引用。

报告二：Mirror construction of cellular algebras

报告华体会（中国）官方：2024年7月3日下午15:35-16:25

报告地点：翡翠科教楼B1710

报告人：方明 研究员

工作单位：中国科学院

报告摘要：Mirror construction of finite dimensional algebras was introduced by Chen-Xi and the author to study Tachikawa's second conjecture. In this talk, we consider the question when the iterated mirror construction of a gendo-symmetric cellular algebra is always cellular.

报告人简介：方明，中国科学院数学与系统科学研究院研究员。研究方向：代数表示论。

报告三：Preprojective algebras, skew group algebras and Morita equivalences

报告华体会（中国）官方：2024年7月3日下午16:40-17:30

报告地点：翡翠科教楼B1710

报告人：陈小伍 教授

工作单位：中国科学技术大学

报告摘要：The folding process is classic in Lie theory and palys a role in the representation theory of quivers.

By the work of Buan-Iyama-Reiten-Scott, Mizuno, and Fu-Geng, there are remarkable bijections between certain ideal monoids of preprojective algebras and Weyl groups. We use the folding process to compare these bijections. This is joint with Ren Wang.

报告人简介：陈小伍，中国科学技术大学教授，博导，德国洪堡学者，曾获得国家杰出青年基金，荣获首届安徽省青年数学奖。主要论文发表在Memoirs ams., Adv. Math., Doc. Math., Math. Z., IMRN以及 J. Algebra 等国际知名期刊，任伦敦数学会BLMS以及JLMS编委。

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