Previous Special Year Seminar

I will present a series of results concerning the interplay between two different curvature conditions, in the special case when these are given by pointwise inequalities on the scalar curvature of a manifold, and the mean curvature of its boundary...

In recent works with N. Wickramasekera we develop a regularity and compactness theory for stable hypersurfaces (technically, integral varifolds) whose generalized mean curvature is prescribed by a (smooth enough) function on the ambient Riemannian...

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, we will be concerned with the existence of a third embedded minimal hypersurface spanning a closed submanifold B contained in the boundary of a compact Riemannian manifold with convex boundary, when it is known a priori the existence...

In a famous paper, Sacks and Uhlenbeck introduced a perturbation of the Dirichlet energy, the so-called $\alpha$-energy $E_\alpha$, $\alpha > 1$, to construct non-trivial harmonic maps of the two-sphere in manifolds with a non-contractible universal...

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...