Riccardo Caniato (University of Warwick) – Topology, Morse Index, and Area of Minimal Surfaces in Three-Manifolds

A foundational and fascinating theme in differential geometry is to understand how geometric quantities constrain topology. In this talk, we will explain how the topological complexity of minimal surfaces in closed three-manifolds can be controlled by their variational instability and area, and how positive Ricci curvature of the ambient manifold leads to stronger bounds depending only on the Morse index. Finally, we will discuss some consequences for the topology of min–max minimal surfaces.