Scalar Curvature, Minimal Surfaces, and the Shape of Manifolds
Davi Maximo, UPenn
Abstract: Scalar curvature is a fundamental invariant in Riemannian geometry, capturing how volumes and distances deviate from those of flat space at infinitesimal scales. While comparison geometry has long used curvature bounds to derive strong geometric and topological consequences, scalar curvature has historically been more subtle and resistant to such techniques.
In this talk, I will give an introductory overview of how minimal surface methods can be used to extract global geometric and topological information from scalar curvature assumptions. After reviewing the basic ideas behind scalar curvature and minimal surfaces, I will explain how their interaction leads to restrictions on the topology and geometry of manifolds with positive scalar curvature.
The talk will emphasize ideas, examples, and geometric intuition rather than technical details, and is intended to offer non-experts a glimpse into the subject.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
