Manifolds and Groups

流形和组

• 批准号: RGPIN-2017-03750
• 负责人: Rolfsen, Dale
• 金额: $ 1.02万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675413
• 关键词: Manifolds; Groups

Three-dimensional manifolds model the universe we inhabit. They also arise in the study of dynamical systems, solutions of several-variable equations and other applications in mathematics, physics and engineering. My research program will focus on a better understanding of 3-manifolds, to contribute to their classification and investigate their structures, by the use of algebraic and geometric techniques, both old and new. A related research direction is the algebraic theory of groups and their orderings, as well as geometric group theory, in which algebraic structures are viewed geometrically. **

三维流形模拟了我们居住的宇宙。 它们也出现在动力系统的研究中，多变量方程的解以及数学，物理和工程中的其他应用。 我的研究计划将集中在更好地理解3-流形，有助于他们的分类和调查他们的结构，通过使用代数和几何技术，无论是旧的还是新的。 一个相关的研究方向是群的代数理论及其排序，以及几何群论，其中代数结构被几何地看待。**