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: 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=635376
• 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.

对称是一个重要的数学概念：自然界中的所有对象都有对称性。我将几何技术应用于对对称组（称为谎言组）的研究，这是基本粒子结构的基础。几何形状使我们能够在说谎组的表示理论中理解新结构，称为分类。我的作品构成了几何兰兰兹计划的一部分，这是数学的新分支，有些人称之为“数学统一理论”，因为它汇集了数字理论，自动形式，代数曲线，表示理论和量子场理论。