# Seminars & Events for Joint Princeton Rutgers Geometric PDEs Seminar

October 4, 2013
3:00pm - 4:00pm
##### TBA - Viaclovsky
###### Joint Princeton Rutgers Geometric PDEs Seminar

THIS IS A JOINT SEMINAR WITH DIFFERENTIAL GEOMETRY & GEOMETRIC ANALYSIS and JOINT PRINCETON-RUTGERS GEOMETRIC PDEs.    I will discuss a gluing procedure designed to obtain canonical metrics on connected sums of Einstein four-manifolds. The main application is an existence result, using two well-known Einstein manifolds as building blocks: the Fubini-Study metric on CP^2, and the product metric on S^2 x S^2. Using these metrics in various gluing configurations, critical metrics are found on connected sums for a specific Riemannian functional, which depends on the global geometry of the factors. This is joint work with Matt Gursky.

Speaker: Jeff Viaclovsky , University of Wisconsin-Madison
Location:
Fine Hall 110
October 4, 2013
4:15pm - 5:15pm
##### TBA - Sesum
###### Joint Princeton Rutgers Geometric PDEs Seminar

THIS IS A JOINT SEMINAR WITH DIFFERENTIAL GEOMETRY & GEOMETRIC ANALYSIS and JOINT PRINCETON-RUTGERS GEOMETRIC PDEs.   We will discuss conformally flat complete Yamabe flow and show
that in some cases we can give the precise description of singularity profiles close to the extinction time of the solution. We will also talk about a construction of new compact ancient solutions to the Yamabe flow. This is a joint work with Daskalopoulos, King and Manuel del Pino.

Speaker: Natasa Sesum, Rutgers University
Location:
Fine Hall 110
December 3, 2013
4:30pm - 5:30pm
##### The logarithmic Minkowski problem
###### Joint Princeton Rutgers Geometric PDEs Seminar

The logarithmic Minkowski problem asks for necessary and sufficient conditions in order that a nonnegative finite Borel measure in (n-1)-dimensional projective space be the cone-volume measure of the unit ball of an n-dimensional Banach space. The solution to this problem is presented. Its relation to conjectured geometric inequalities that are stronger than the classical Brunn-Minkowski inequality will be explained.

Speaker: Gaoyong Zhang , Polytechnic Institute of New York University
Location:
Rutgers - Hill Center, Room 705
December 3, 2013
5:30pm - 6:30pm
##### On the Reality of Black Holes
###### Joint Princeton Rutgers Geometric PDEs Seminar
Speaker: Sergiu Klainerman, Princeton University
Location:
Rutgers - Hill Center, Room 705
March 11, 2014
4:45pm - 5:45pm
##### Talk #1: Long time behavior of forced 2D SQG equations
###### Joint Princeton Rutgers Geometric PDEs Seminar

We prove the absence of anomalous dissipation of energy for the forced critical surface quasi-geostrophic equation (SQG) in {\mathbb {R}}^2  and the existence of a compact finite dimensional golbal attractor in      {\mathbb T}^2. The absence of anomalous dissipation can be proved for rather rough forces, and employs methods that are suitable for situations when uniform bounds for the dissipation are not available. For the        finite dimensionality of the attractor in the space-periodic case, the global regularity of the forced critical SQG equation needs to be revisited, with a new and final proof. We show that the system looses infinite dimensional information, by obtaining strong long time bounds that are independent of initial data. This is joint work with A. Tarfulea and V. Vicol.

Speaker: Peter Constantin, Princeton University
Location:
Rutgers - Hill Center, Room 525
March 11, 2014
5:45pm - 6:45pm
##### The linear stability of the Schwarzschild solution under gravitational perturbations in general relativity
###### Joint Princeton Rutgers Geometric PDEs Seminar

I will discuss joint work with G. Holzegel and I. Rodnianski showing the linear stability of the celebrated Schwarzschild black hole solution in general relativity.

Speaker: Mihalis Dafermos , Princeton University
Location:
Rutgers - Hill Center, Room 525
April 30, 2014
2:00pm - 3:00pm
##### Large N asymptotics of Optimal partitions of Dirichlet eigenvalues
###### Joint Princeton Rutgers Geometric PDEs Seminar

In this talk,  we will discuss the following problem:  Given a bounded domain $\Omega$ in R^n, and a positive energy N, one divides $\Omega$ into N subdomains, $\Omega_j, j= 1, 2,..., N$. We consider the so-called optimal partitions that give the least possible value for the sum of the first Dirichelet eigenvalues on these sumdomains among all admissible partitions of $\Omega$. For given N the problem has been studied by various authors. I shall discuss some recent progress and conjectures on the analysis on asymptotic behavior these optimal partitions as N tends to infinite.

Speaker: Fanghua Lin , NYU
Location: