Previous Special Year Seminar

We discuss the local properties of the boundaries of sets whose indicator function is a local minimizer of a Sobolev norm of exponent strictly less than 1/2. It turns out that one devise a regularity that parallels very much that of de Giorgi for...

We will discuss diffusion limits for linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion...

When we look at a differential equation in a very irregular media (composite material, mixed solutions, etc.) from very close, we may see a very complicated problem. However, if we look from far away we may not see the details and the problem may...

When we look at a differential equation in a very irregular media (composite material, mixed solutions, etc.) from very close, we may see a very complicated problem. However, if we look from far away we may not see the details and the problem may...

If a solution (M,g(t)) of Ricci flow develops a local singularity at a finite time T , then there is a proper subset S of M on which the curvature becomes infinite as time approaches T . Existing approaches to Ricci-flow-with-surgery, due to...

In this talk, I will describe the blow-up profile for Q-curvature equations and related work.

Given two differential equations it is often useful to know invariants which guarantee that there exists a transformation of variables (independent, dependent or both) that transforms one of the equations into the other. Recently it has been...

In this talk we describe some recent result as well as the work in progress on the neck pinching of surfaces under under mean curvature flow.

In this talk, we prove existence and uniqueness of vortexless solutions for Chern-Simons-Higgs equation in nonselfdual case.

The de Rham complex is a prototype for a large class of sequences of differential operators often called (generalized) Bernstein-Gelfand-Gelfand BGG sequences. Conformal manifolds admit such sequences and on locally conformally flat manifolds the...