Special Year 2018-19: Variational Methods in Geometry

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...

The (Simon-Smith) min-max width of a Riemannian three dimensional sphere is a geometric invariant that measures the tightest way, in terms of area, of sweeping out the three-sphere by two-spheres. In this talk, we will explore the properties of this...

In the 60's Almgren initiated a program for developing Morse theory on the space of flat cycles. I will discuss some simplifications, generalizations and quantitative versions of Almgren's results about the topology of the space of flat cycles and...

We will present the project of using the Willmore elastic energy as a quasi-Morse function to explore the topology of immersions of the 2-sphere into Euclidean spaces and explain how this relates to the classical theory of complete minimal surfaces...

A translator for mean curvature flow is a hypersurface $M$ with the property that translation is a mean curvature flow. That is, if the translation is $t\rightarrow M+t\vec{v}$, then the normal component of the velocity vector $\vec{v}$ is equal to...

Abstract: I will go over some recent work that I have been involved in on surface geometry in complete locally homogeneous 3-manifolds X. In joint work with Mira, Perez and Ros, we have been able to finish a long term project related to the Hopf...

Abstract: We will discuss a new family of free boundary minimal Möbius bands in $B^4$ that are critical for higher Steklov eigenvalues among $S^1$-invariant metrics.

Abstract: We will explain how to prove properness of a complete embedded minimal surface in Euclidean three-space, provided that the surface has finite genus and countably many limit ends (and possibly compact boundary). This is joint work with...