Speaker: Gioacchino Antonelli,

Room: Keller 302

TITLE: Isoperimetric problems in curved spaces and applications

ABSTRACT: The isoperimetric problem is one of the oldest and fundamental challenges in mathematics, offering a classic example of an optimization problem. Over the last forty years, research has increasingly focused on the connection between the isoperimetric properties of a space and its geometry. In this talk, I will explain how ideas developed to study the relationship between lower curvature bounds and the isoperimetric problem have been applied to resolve a longstanding question in the theory of minimal surfaces: proving that stable minimal hypersurfaces in R^n are flat when n<=6.