Department of Mathematics - Master Calendar

Notions of curvature are so ubiquitous in differential geometry that the whole field may as well be called “the study of curvature”. In essence, a curvature describes deviation from a notion of flatness. I will try to give a historical account of curvature, going from circles approximating curves in the plane to curvature of connections. I will also explore some relations with topology, physics, and PDEs. Finally, I will talk about intrinsic curvature of geometric structures, and how it relates to formal solvability of certain PDEs.