Title: Minimal surfaces in geometry and topology
Abstract: Minimal surfaces are natural objects in geometry arising as critical points of the area functional on the space of surfaces in a Riemannian manifold. In the 80s variational methods were developed to construct minimal surfaces in great generality. A main challenge however is to understand the topological type and Morse index (as a critical point) of the surfaces obtained. I’ll describe some situations where the geometry can be controlled, and some applications to studying the topology of three-manifolds.