Previous Special Year Seminar

“Deep learning” refers to use of neural networks to solve learning problems, including “learning” hidden structures in large and complex data sets. The theory for this field is still in its infancy. Lately physical and biological scientists have...

In this talk I will begin by reviewing classical geometric properties of constant mean curvature surfaces, H>0, in R^3. I will then talk about several more recent results for surfaces embedded in R^3 with constant mean curvature, such as curvature...

I will discuss a proof of the existence of infinitely many solutions for the singular Yamabe problem in spheres using bifurcation theory and the spectral theory of hyperbolic surfaces.

The problem of finding metrics with constant Q-curvature in a prescribed conformal class is an important fourth-order cousin of the Yamabe problem. In this talk, I will explain how certain variational bifurcation techniques used to prove non...

A Riemannian manifold is called Besse, if all of its geodesics are periodic. The goal of this talk is to study the energy functional on the free loop space of a Besse manifold. In particular, we show that this is a perfect Morse-Bott function for...

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...