Previous Special Year Seminar

In recent years, fully nonlinear versions of the Yamabe problem have received much attention. In particular, for manifolds with boundary, $C^1$ and $C^2$a priori estimates have been proved for a large class of data. To get an existence result, it is...

In pioneering work Tian/Viaclovsky initiated the study of the moduli space of Bach-flat metrics. They showed C^0-orbifold regularity and, equivalently, ALE order zero of noncompact finite-energy solutions. By use of Kato inequalities, the full...

I shall explain how to obtain Strichartz estimates with no loss for Schrodinger equation in some cases where the geodesic flow has some trapped trajectories, but the flow is hyperbolic. (This is joint work with Burq and Hassell.)

The first aim of Fefferman-Graham ambient metric construction was to write down all scalar invariants of conformal structures. For odd dimensions, the aim was achieved with the aid of the parabolic invariant theory by Bailey, Eastwood and Graham. In...

I shall discuss two related local regularity results for asymptotically hyperbolic (or complex hyperbolic) Einstein metrics, near a point at infinity: local polyhomogeneity and unique continuation.

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...

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...