Theta functions in differential and arithmetic geometry

微分几何和算术几何中的 Theta 函数

• 批准号: RGPIN-2017-04959
• 负责人: Sankaran, Siddarth
• 金额: $ 1.53万
• 依托单位: University of Manitoba
• 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=635476
• 关键词: Theta; functions; differential; arithmetic; geometry

My research lies in the field of arithmetic geometry, at the interface of two mathematical subfields: number theory and geometry. Number theory is the study of integers, which are essentially discrete and rigid in nature. On the other hand, geometry deals with objects that are continuous, that can be stretched and pulled and deformed in a fluid manner. Arithmetic geometry marries these two points of view, applying tools and intuitions from the world of geometry to gain greater insight into number theoretic phenomena, and vice versa.

我的研究领域是算术几何，是数论和几何这两个数学子领域的交汇处。数论是对整数的研究，它本质上是离散的和刚性的。另一方面，几何处理的对象是连续的，可以以流体的方式拉伸、拉伸和变形。算术几何结合了这两种观点，应用几何世界的工具和直觉来更深入地了解数论现象，反之亦然。