Coxeter groups and related structures

考克塞特群及相关结构

• 批准号: 355458-2013
• 负责人: Hohlweg, Christophe
• 金额: $ 1.38万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=595668
• 关键词: Coxeter; groups; related; structures

My primary area of research is algebraic combinatorics. It is a highly active area of mathematics, with many connections to algebraic geometry, convex geometry, representation theory, topology, mathematical physics and statistical mechanics, among many others. I am more precisely interested on the combinatorial and geometrical aspects of the study of Coxeter (mirror reflection) groups and their related structures. Coxeter groups appear in very many domains of mathematics, for instance, as symmetry groups of regular polytopes, as Weyl groups of semi-simple Lie algebras and Kac-Moody algebras, and as triangle groups in geometry (Euclidean and hyperbolic). Properties of these groups are often key to the understanding of related structures.

我的主要研究领域是代数组合学。它是一个高度活跃的数学领域，与代数几何、凸几何、表示论、拓扑学、数学物理和统计力学等许多学科有许多联系。我更感兴趣的组合和几何方面的研究考克斯特（镜面反射）集团及其相关结构。考克斯特群出现在数学的许多领域，例如，作为正则多面体的对称群，作为半单李代数和卡茨-穆迪代数的外尔群，以及作为几何中的三角群（欧几里得和双曲）。这些基团的性质通常是理解相关结构的关键。