Model theory and applications to algebra and geometry

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

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.