Christine Breiner, Columbia

"Gluing constructions for embedded constant mean curvature surfaces."

Constant mean curvature (CMC) surfaces are critical points to the area functional with an enclosed volume constraint. Classic examples include the round sphere and a one parameter family of rotationally invariant surfaces discovered by Delaunay. In this talk I outline the gluing method we develop that produces a large class of new examples of embedded CMC surfaces of finite topology. We refine the method first developed by Kapouleas in 1990, that produced immersed examples, using fundamental ideas he later introduced to construct a larger class of immersed examples. I will explain the essential aspects of our proof and outline some of the new examples we can produce. Finally, I will mention aspects of the proof we must alter to adapt the method to higher dimensions. This work is joint with Nicos Kapouleas.

Marcelo Disconzi, Vanderbilt

"On the Einstein equations for relativistic fluids."

The Einstein equations have been a source of many interesting problems in Physics, Analysis and Geometry. Despite the great deal of work which has been devoted to them, with many success stories, several important questions remain open. One of the them is a satisfactory theory of isolated systems, such as stars, both from a perspective of the time development of the space-time, as well as from the point of view of the geometry induced on a space-like three surface. This talk will focus on the former situation. More specifically, we shall discuss relativistic fluids with and without viscosity, and prove a well-posedness result for the Cauchy problem. The viscous case, in particular, is of significant interest in light of recent developments in Astrophysics.

Ailana Fraser, University of British Columbia

TBA

Davi Maximo, UT Austin

"On the blow-up of four-dimensional Ricci flow singularities." 

In 2002, Feldman, Ilmanen, and Knopf constructed the first example of a non-trivial (i.e. non-constant curvature) complete non-compact shrinking soliton, and conjectured that it models a Ricci flow singularity forming on a closed four-manifold. In this talk, we confirm their conjecture and, as a consequence, show that limits of blow-ups of Ricci flow singularities on closed four-dimensional manifolds do not necessarily have non-negative Ricci curvature.

John Pardon, Stanford