Previous Special Year Seminar

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...

In this talk, I will discuss the quadruple junction solutions in the entire three dimensional space to a vector-valued Allen-Cahn equation which models multiple phase separation. The solution is the basic profile of the local structure near a...

Manifolds with geometric structure carry large and useful families of non-standard “subharmonic” functions. For example, any almost complex manifold with hermitian metric carries plurisubharmonic functions. Moreover, it also carries “Lagrangian...