Previous Special Year Seminar

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...

This talk is based on joint work with YanYan Li and Eduardo Teixeira. Some geometric problems in conformal geometry lead naturally to the study of singular solutions to certain PDEs that describe "canonical" conformal metrics. A good example is the...

Conditional on the scattering conjecture of the mass-critical nonlinear Schrodinger equation in spatial dimension one, we show that there exists a blow-up solution to the mass-critical generalized Korteweg de Vries equation (gKdV) with the minimal...

In 2005 Ma, Trudinger and Wang introduced a fourth-order differential condition which comes close to be necessary and sufficient for the smoothness of solutions to optimal transport problems with a given cost function. If the cost function is the...

In this talk, I will discuss some characterizations of Sobolev spaces, BV spaces, and present some new inequalities in this context. As a consequence, I can improve classical properties of Sobolev spaces such as Sobolev inequality, Poincare...