Algebraic Topology

代数拓扑

• 批准号: 1000225825-2011
• 负责人: Adem, Alejandro
• 金额: $ 14.57万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 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=642751
• 关键词: Algebraic; Topology

Symmetry plays a key role in mathematics and the natural sciences. Groups are the basic mathematical objects which encode this information, and they are used to model physical systems such as crystals, elementary particles and energy levels in atoms. Understanding their structure and content is a central problem in modern mathematics. This research program proposes to develop extensive theoretical tools to analyze these symmetries, construct new ones and relate them to deep mathematical invariants. This will involve applying topological methods to help understand basic objects such as spaces of representations, which have many applications in geometry and physics.

对称性在数学和自然科学中起关键作用。组是编码此信息的基本数学对象，它们用于建模物理系统，例如原子中的晶体，基本颗粒和能级。了解它们的结构和内容是现代数学中的一个核心问题。该研究计划建议开发广泛的理论工具来分析这些对称性，构建新的工具并将其与深度数学不变性相关联。这将涉及应用拓扑方法来帮助理解基本对象，例如代表空间，这些对象在几何和物理学中具有许多应用。