Special Colloquium-Model theory and Painlevé equations

Place: Phillips 217

Abstract: The Painlevé equations are six families of nonlinear order two differential equations with complex parameters. Around the start of the last century, the equations were isolated for foundational reasons in analysis, but the equations have since arisen naturally in various mathematical contexts. In this talk, we will discuss how to use model theory, a part of mathematical logic, to answer several open questions about Painlevé equations. We will also describe several other applications of model theory and differential algebraic equations to number theory.