報告時間：2024年07月03日（星期三）14:40
報告地點：翡翠湖校區科教樓B座1710室
報 告 人：Ruibin Zhang 教授
工作單位：University of Sydney
舉辦單位：數學學院
報告簡介：
Herbert S. Green introduced 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 reports of 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 concerning parafermions have 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.
報告人簡介：
Ruibin Zhang，澳大利亞悉尼大學數學與統計學院教授，澳大利亞數學會副主席。曾獲得澳大利亞研究委員會伊麗莎白二世獎學金，澳大利亞研究委員會教授獎等諸多榮譽。研究主要集中在李理論及其在量子物理中的應用，涉及量子（超）群、李超代數、低維拓撲、非交換幾何等領域。特別地，在量子代數的結構和表示理論等方面取得了一系列有重要國際影響的研究成果，在包括國際數學頂尖期刊Annals of Mathematics, J.Eur.Math.Soc., Adv.Math, Comm.Math.Phys, Proc.Lond.Math.Soc等重要國際數學刊物上發表140多篇高水平論文，并被國際同行大量引用。
