Geometric representation theory and categorification

几何表示理论与分类

• 批准号: 355574-2013
• 负责人: Kamnitzer, Joel
• 金额: $ 3.21万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=595697
• 关键词: Geometric; representation; theory; categorification

Symmetry is an important mathematical concept: all objects in nature have symmetries. I apply geometric techniques to the study of the groups of symmetries, called Lie groups, that underlie the structure of elementary particles. Geometry allows us to understand new structure, known as categorification, in the representation theory of Lie groups. My work forms part of the geometric Langlands program, a new branch of mathematics which some call a "Grand Unified Theory of Mathematics", because it brings together number theory, automorphic forms, algebraic curves, representation theory and quantum field theory.

对称性是一个重要的数学概念：自然界中的所有物体都具有对称性。我应用几何技术来研究对称群，称为李群，它是基本粒子结构的基础。几何学使我们能够理解李群表示论中的新结构，称为范畴化。我的工作是几何朗兰兹纲领的一部分，这是数学的一个新的分支，有人称之为“数学的大统一理论”，因为它汇集了数论、自守形式、代数曲线、表示论和量子场论。