Model theory and applications to algebra and geometry

模型理论及其在代数和几何中的应用

• 批准号: 1001741
• 负责人: Moshe Kamensky
• 金额: $ 10.36万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1001741&HistoricalAwards=false
• 关键词: Model; theory; applications; algebra; geometry

The project consists in applying model theory to questions in other branches of mathematics. More precisely, the principal investigator will apply model theoretic techniques to problems in representation theory of generalised linear groups, compact complex manifolds, and the algebraic theory of differential equations. Model theory has already made substantial contributions in all three areas, and the principal investigator plans to further extend these contributions, and come up with new ones.Model theory is a branch of mathematical logic, which studies sets defined by formulas in a formal language from the point of view of their geometry. As a result, it allows one to treat geometrically concrete situations in which geometry is not apparent otherwise. Conversely, it allows the application of logical and combinatorial tools to geometric questions. The proposed project will apply such techniques to problems in algebra, geometry and differential equations.

该项目包括将模型理论应用于其他数学分支的问题。更确切地说，首席研究员将应用模型理论技术来解决广义线性群的表示理论、紧复流形和微分方程的代数理论等问题。模型理论已经在这三个领域做出了重大贡献，首席研究员计划进一步扩展这些贡献，并提出新的贡献。模型论是数理逻辑的一个分支，它从几何的角度研究用形式语言用公式定义的集合。因此，它允许一个人处理几何的具体情况，其中几何不明显，否则。相反，它允许将逻辑和组合工具应用于几何问题。该计划将把这些技术应用于代数、几何和微分方程的问题。