Previous Special Year Seminar

Mean curvature flow is the negative gradient flow of the volume functional which decreases the volume of (hyper)surfaces in the steepest way. Starting from any closed surface, the flow exists uniquely for a short period of time, but always develops...

In this talk I would like to explain how methods from symplectic geometry can be used to obtain sharp systolic inequalities. I will focus on two applications. The first is the proof of a conjecture due to Babenko-Balacheff on the local systolic...

Minimal surfaces are critical points of the area functional. In this talk I will discuss classification results for minimal surfaces with index one in 3-manifolds with non-negative Ricci curvature and outline the proof that in spherical space forms...

The lecture will discuss recent joint work with C. Bellettini and O. Chodosh. The work taken together establishes sharp regularity conclusions, compactness and curvature estimates for any family of codimension 1 integral $n$-varifolds satisfying: (i...

Renormalized volume (and more generally W-volume) is a geometric quantity found by volume regularization. In this talk I'll describe its properties for hyperbolic 3-manifolds, as well as discuss techniques to prove optimality results.

In the 90's, Gromov and Schoen introduced the theory of harmonic maps into singular spaces, in particular Euclidean buildings, in order to understand p-adic superrigidity. The study was quickly generalized in a number of directions by a number of...

I will outline the proof of density of minimal hypersurfaces (Irie-Marques-Neves) and equidistribution of minimal hypersurfaces (Marques-Neves-Song).

I will first survey some recent progress on global problems related to scalar curvature and area/volume, focusing in particular on scale breaking phenomena in such problems. I will then discuss the role of the Hawking mass in the resolution of this...

We will discuss the bubbling and neck analysis for degenerating sequences of minimal hypersurfaces which, in particular, lead to qualitative relationships between the variational, topological and geometric properties of these objects. Our aim is to...

Back in the 70s, Gromov started to study the relationship between the Lipschitz constant of a map (also called the dilation) and its topology. The Lipschitz constant describes the local geometric features of the map, and the problem is to understand...