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

二、报告人：Alexander A. 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 construction of the Thompson sporadic simple group E. As a result, (a) we obtain a conceptual explanation of the dichotomy between Lie and finite 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 subgroups ³D₄(2) : 3, (F₂₁ × L₃(2)) : 2, (G₂(3) × 3) : 2 and U₃(8) : 6; (c) we consider the coset geometry of the above subgroups and identify the corresponding geometric presentation with that by Havas–Soicher–Wilson; (d) this amounts to a geometric construction and uniqueness proof for E (the uniqueness issue for the Thompson group was listed6 as one of just two outstanding in the Classification of Finite Simple 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 by the recent reappearance of E in the Moonshine context.

报告人简介：Alexander A. 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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