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Mathematics Colloquium


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 Gromov’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


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