  I will talk about my recent work with Fernando Marques where we used
Almgren-Pitts Min-max Theory to settle some open questions in Geometry: The
Willmore conjecture, the Freedman-He-Wang conjecture for links (jointly with
Ian Agol), and the existence of infinitely many minimal hypersurfaces in
manifolds of positive Ricci curvature. Some open questions are suggested in the
last section.
