Special Year 2018-19: Variational Methods in Geometry - Seminar

I will present a proof with some substantial details of the Multiplicity One Conjecture in Min-max theory, raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal...

In this talk I want to discuss two related questions about the variational structure of the Yang-Mills functional in dimension four. The first is the question of 'gap' estimates; i.e., determining an energy threshold below which any solution must be...

A decades-old application of the second variation formula proves that if the scalar curvature of a closed 3--manifold is bounded below by that of the product of the hyperbolic plane with the line, then every 2--sided stable minimal surface has area...

Abstract: Uryson k-width of a metric space X measures how close X is to being k-dimensional. Several years ago Larry Guth proved that if M is a closed n-dimensional manifold, and the volume of each ball of radius 1 in M does not exceed a certain...

We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds, including the mean curvature flow. As an application, we show that an ancient (arbitrarycodimension) mean curvature flow in $S^n$ with low area must...

Geodesic nets on Riemannian manifolds is a natural generalization of geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean plane or the round 2-sphere.

In...

It has been conjectured that a simply-connected complete Kahler manifold of negatively pinched sectional curvature is biholomorphic to a bounded domain in complex Euclidean space. One evidence is that the manifold is Stein, which is, in particular...

Anisotropic surface energies are a natural generalization of the perimeter functional that arise in models in crystallography and in scaling limits for certain probabilistic models on lattices. This talk focuses on two results concerning...