## Translators for Mean Curvature Flow

$t\rightarrow M+t\vec{v}$, then the normal component of the velocity vector $\vec{v}$ is equal to the mean curvature $\vec{ H}$. I will discuss recent joint work with Tom Ilmanen, Francisco Martin and Brian White, specifically our classification of the the complete translators in $R^3$ that are graphical, and the construction of new families of complete translators that are not graphical.

## Morse-Theoretic Aspects of the Willmore Energy

the topology of immersions of the 2-sphere into Euclidean spaces and explain how this relates to the

classical theory of complete minimal surfaces with finite total curvature.

This is partially a joint work in collaboration with Tristan Rivière.

## Distinguishing fillings via dynamics of Fukaya categories

## Progress in the theory of CMC surfaces in locally homgeneous 3-manifolds X

## Jerusalem in Biblical Times: Comments on the Archaeology and History ca. 1350—100 B.C.E.

## Locating Minimal Surfaces in Geometrostatic Manifolds

## Generic uniqueness of expanders with vanishing relative entropy

Abstract: We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same smooth cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that generically expanders with vanishing relative entropy are unique. This also implies that generically locally entropy minimizing expanders are unique. This is joint work with A. Deruelle.

## The embedded Calabi-Yau problem for minimal surfaces of finite genus

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 William H. Meeks and Antonio Ros.

## Progress on existence of minimal surfaces

Abstract: I will survey the recent progress on the existence problem for minimal hypersurfaces and then point for some new directions. This is joint work with Fernando Marques.