Previous Special Year Seminar

We formulate several new boundary value problems for the 2D Navier-Stokes system. In all cases, we obtain quantitative decay estimates of the Fourier modes for both the vorticity and the velocity. In some special cases we found that the Fourier...

In this talk, I will first give an overview of recent progress on the scattering conjecture and rigidity conjecture for mass critical NLS. Then I will describe our recent results concerning both conjectures for L_2 initial data. I will also discuss...

We construct new solutions to the $\sigma_k$-Yamabe problem on compact manifolds by considering the connected sum of two nondegenerate solutions $(M^n_1,g_1)$ and $(M^n_2,g_2)$, for any $2 \leq 2k < n$.

Dislocations are line defects in crystals, and can be modeled using non-local operators. In this talk we will consider a related reaction-diffusion equation with a half-Laplacian. We show that the limit dynamics is characterized by a system of ODEs...

We study a class of fully nonlinear metric flow on K\"ahler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for the long time convergence of the flow, generalizing the result of Song-Weinkove...

The talk is devoted to the homogenization of a stochastic evolution problem with non Lipschitz forcing. The problem is considered in a sequence of perforated cylindrical domains obtained from the removal of tiny cylinders from a fixed one (the...

The location of blowup points is often related to critical points of Green function. In fact, Green function plays a important role to understand the solutions structure of mean field equations. We will show how to use the elliptic function and the...

A three dimensional strongly pseudoconvex Cauchy Riemann manifold can be considered as a contact manifold with a conformal structure on the hyperplane distribution. In this talk, we will discuss CR structures near the standard one on S^3 , the...

The "sigma_k Yamabe problem" is a fully nonlinear generalization of the Yamabe problem, in which one attempts to find a conformal multiple of a given metric to make constant the k-th elementary symmetric function of the eigenvalues of the Schouten...