Homogeneous structures and their automorphism groups

齐次结构及其自同构群

• 批准号: 1834495
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1834495
• 关键词: Homogeneous; structures; their; automorphism; groups

Infinite homogeneous structures arise as canonical 'limits' of certain classes of finite structures. There is a rich and surprising interplay between the combinatorics of the finite structures in the class and the automorphism group (that is, the symmetries) of the homogeneous structure obtained as its limit. The project will focus on various aspects of this interplay, such as subgroup structure of the automorphism group and actions of the automorphism group on various topological spaces. The project will involve a mixture of ideas from different parts of Mathematics, including combinatorics, group theory, topology and model theory. The research is aligned with the EPSRC research areas Logic and Combinatorics and Algebra within Mathematics.

无限齐次结构作为某些有限结构类别的规范“极限”而出现。该类中有限结构的组合与作为其极限获得的齐次结构的自同构群（即对称性）之间存在着丰富且令人惊讶的相互作用。该项目将重点关注这种相互作用的各个方面，例如自同构群的子群结构以及自同构群在各种拓扑空间上的作用。该项目将混合数学不同部分的思想，包括组合学、群论、拓扑和模型论。该研究与 EPSRC 研究领域逻辑、组合学以及数学中的代数相一致。