# Seminars & Events for Special Colloquium

##### Min-max methods, Willmore conjecture and the energy of links

The idea of finding closed geodesics in surfaces by using sweep-outs goes back to the work of Birkhoff in the 1920s. Minimal surfaces in three-manifolds can also be constructed that way. This was the main accomplishment of Almgren and Pitts (1981), using powerful tools of Geometric Measure Theory. In this talk I will describe some unexpected relations between the min-max approach for minimal surfaces and conformally invariant variational problems in Geometry and Topology. More concretely, I will discuss the theory developed In a joint paper with Andre Neves, in which we prove the Willmore conjecture (1965) by