Southeast Geometry Seminar XXI
Sunday December 9, 2012
University of Tennessee, Knoxville
Ayres Hall Room 405
8:30am4pm
Program
(All events, including breakfast, lunch and snacks, in Ayres 405)
7:308:30am
Posters, Registration and Breakfast
8:309:30am
Davi Maximo: "On the blowup of fourdimensional Ricci flow singularities."
9:4510:45am
Ailana Fraser: "Eigenvalue problems and minimal surfaces"
10:4511:15am
Coffee Break
11:15am12:15pm
John Pardon: "Totally disconnected groups (not) acting on threemanifolds."
12:301:45pm
Lunch
1:452:45pm
Christine Breiner: "Gluing constructions for embedded constant mean curvature surfaces."
34pm
Marcelo Disconzi: "On the Einstein equations for relativistic fluids."
46pm
Snacks
Abstracts
Christine Breiner,
Columbia
Marcelo Disconzi,
Vanderbilt
"On the Einstein equations for relativistic fluids."
Abstract: 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 spacetime, as well as from the point of view of the geometry induced on a spacelike three surface. This talk will focus on the former situation. More specifically, we shall discuss relativistic fluids with and without viscosity, and prove a wellposedness 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
"Eigenvalue problems and minimal surfaces"
Abstract: Finding sharp eigenvalue bounds and characterizing the extremals is a basic problem in geometric analysis. We will describe the structure of metrics which are obtained by maximizing the first eigenvalue over all metrics on a surface (either closed or with boundary). It turns out that the extremals are related to minimal surfaces, and in some cases it is possible to use minimal surface theory to characterize the extremal metrics. This is joint work with R. Schoen.
Davi Maximo,
UT Austin
"On the blowup of fourdimensional Ricci flow singularities."
Abstract: In 2002, Feldman, Ilmanen, and Knopf constructed the first
example of a nontrivial (i.e. nonconstant curvature) complete
noncompact shrinking soliton, and conjectured that it models a Ricci flow
singularity forming on a closed fourmanifold. In this talk, we confirm
their conjecture and, as a consequence, show that limits of blowups of
Ricci flow singularities on closed fourdimensional manifolds do not
necessarily have nonnegative Ricci curvature.
John Pardon,
Stanford
