【和山数学论坛第403期】美英国帝国理工学院/三峡大学Alexander A.lvanov教授学术报告

一、报告题目：THE THOMPSON GROUP: OPENING A PATH TO MODERN GROUPTHEORY

二、报告人：AlexanderA.lvanov教授

三、时间：2024年3月28日(周四)14:30-15:10

四、地点：闻理园A4-216

报告摘要：We enhance the Thompson–Smith constructionof the Thompson sporadic simple groupE. As a result, (a) we obtain a conceptual explanation of the dichotomy between Lie andfinite cases in terms of representations on an (L₂(8) : 3)-subgroup; (b) along with 2⁵· L₅(2)and 2₊¹⁺⁸· A₉, we construct in E subgroups³D₄(2) : 3, (F₂₁× L₃(2)) : 2, (G₂(3) × 3) : 2and U₃(8) : 6; (c) we consider the coset geometry of the above subgroups and identifythe corresponding geometric presentation with that by Havas–Soicher–Wilson; (d) thisamounts to a geometric construction and uniqueness proof for E (the uniqueness issue forthe Thompson group was listed6 as one of just two outstanding in the Classification of FiniteSimple Groups); (e) we deliver an elementary self-contained construction of the Dempwolff–Thompson orthogonal decomposition on the E₈-Lie algebra, along with the stabiliser 2⁵⁺¹⁰·L₅(2) of this decomposition in the Lie group E₈(C). The work was further stimulated bythe recent reappearance of E in the Moonshine context.

报告人简介：AlexanderA.Ivanov，英国帝国理工学院教授、三峡大学特聘研究员，博士毕业于莫斯科物理技术学院，1990年国际数学家大会45分钟报告人。主要从事群论、代数组合和代数图论方面的研究工作，撰写了零散群几何学方面的经典专著《Geometry of Sporadic Groups I，II》在Invent.Math、J.London Math.Soc.、Trans. Amer. Math.Soc.、Israel J. Math.、J.Algebra等期刊发表学术论文100余篇。

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