|Date: Tuesday, February 13, 2018
Title: Gromov, Yau, and existence of minimal surfaces
Abstract: Minimal surfaces are ubiquitous in Geometry but they are quite hard to find. For instance, Yau in 1982 conjectured that any 3-manifold admits infinitely many closed minimal surfaces but the best one knows is the existence of at least two.
In a different direction, Gromov conjectured a Weyl Law for the volume spectrum that was proven last year by Liokumovich, Marques, and myself.
I talk about my recent work with Irie, Marques, and Song where we combined Gromovâ€™s Weyl Law with the Min-max theory Marques and I have been developing over the last years to prove that, for generic metrics, not only there are infinitely many minimal hypersurfaces but they are also dense and equidistributed .
I will cover the history of the problem and try address the main ideas without being technical.
Speaker: Andre Neves
Institution: University of Chicago