Geometric and Algebraic Approach to Polytopes

多面体的几何和代数方法

• 批准号: RGPIN-2016-05354
• 负责人: Weiss, Asia
• 金额: $ 1.31万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635438
• 关键词: Geometric; Algebraic; Approach; Polytopes

Symmetry, a frequently recurring theme in mathematics, is at core of this proposal. The last three decades have seen a remarkable revival of interest in geometric and combinatorial structures and their symmetry. The general area of the proposed research is in discrete and combinatorial geometry and interaction between geometry and algebra. The questions posed and the methods proposed will capitalize on the recent rapid developments of three areas that have largely developed independently: the study of maps, the theory of geometric and abstract polytopes (combinatorial objects that locally have structure of classical polytopes or tessellations) and thin geometries. My contribution to the proposed research is in the use of classical euclidean and hyperbolic geometry and algebra. Many of the proposed projects will involve junior researchers.

对称性是数学中一个经常出现的主题，也是这个提议的核心。在过去的三十年里，人们对几何结构、组合结构及其对称性的兴趣显著复苏。建议研究的一般领域是在离散和组合几何和几何与代数之间的相互作用。所提出的问题和提出的方法将利用最近的快速发展的三个领域，在很大程度上独立发展：研究地图，理论的几何和抽象多面体（组合对象，局部具有结构的经典多面体或镶嵌）和薄几何。我的贡献，拟议的研究是在使用古典欧几里德和双曲几何和代数。许多拟议的项目将涉及初级研究人员。