Model theory and applications to algebra and geometry

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，主要研究人员将模型理论技术应用于广义线性群的表示理论、紧致复杂流形和微分方程式的代数理论中的问题。模型理论已经在这三个领域做出了实质性的贡献，首席研究者计划进一步扩展这些贡献，并提出新的贡献。模型理论是数理逻辑的一个分支，从形式语言中公式定义的集合的几何角度进行研究。因此，它允许人们处理几何具体的情况，其中几何不明显的其他方面。相反，它允许将逻辑和组合工具应用于几何问题。拟议的项目将把这些技术应用于代数、几何和微分方程式的问题。

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.