Algebraic Geometry and Geometric Representation Theory

代数几何与几何表示论

• 批准号: 1000229452-2013
• 负责人: Cautis, Sabin
• 金额: $ 7.29万
• 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=642740
• 关键词: Algebraic; Geometry; Geometric; Representation; Theory

Categorification is a philosophy in mathematics that suggests that much of the theory developed so far in a variety of areas is just a shadow of something deeper and more complex. In my research over the last few years I have been following this line of thinking to study several closely related fields: algebraic geometry (which is the study of polynomials), representation theory (roughly, the study of matrices) and topology (the study of surfaces, knots and other more complicated shapes). By thinking one level higher this philosophy has found surprising applications in the fields mentioned above. A shadow gives you only a rough (and possibly wrong) depiction of the real nature of things. Discovering the actual object can reveal amazing and unexpected detail. In the same way, categorification has revealed new, remarkable, deep structures in mathematics.

分类是一种数学哲学，它表明，迄今为止在各个领域发展起来的许多理论只是更深层次、更复杂事物的影子。在我过去几年的研究中，我一直遵循这一思路来研究几个密切相关的领域：代数几何（即多项式的研究），表示理论（粗略地说，是对矩阵的研究）和拓扑学（对表面，结和其他更复杂形状的研究）。