Monday, December 5, 2022 — 5:00 pm — aula M1.4, edificio Matematica
Min-max methods: on the existence of closed geodesics on Riemannian manifolds
Abstract: In this talk, we will introduce the theory of min-max methods for minimal surfaces.
Starting from the prototype example of Birkhoff’s theorem on the existence of one closed geodesic on $\mathbb{S}^2$, we will build up the relation between the topology of the space of closed curves and the existence of closed geodesics.
If time permits, we will also sketch the idea behind the proof of Lusternik–Schnirelmann’s three geodesics theorem, and we will briefly talk about how a generalization of these ideas, namely Almgren-Pitts min-max theory, led to incredibly general results on the existence of minimal surfaces.