Previous Special Year Seminar

In optimal transport theory, one wants to understand the phenomena arising when mass is transported in a cheapest way. This variational problem is governed by the structure of the transportation cost function defined on the product of the source and...

A well-known example by N. N. Ural'tseva suggests that for fixed p > 2 there is no unique $W^2_p$-solvability of elliptic equations under p > the condition that the leading coefficients are measurable in two spatial variables. We will present a...

In this talk, we shall review the convexity of solutions of elliptic partial differential equations; we concentrate on the constant rank theorem for the hessian of the convex solution. As for the interesting from geometry problems, recently we have...

The special Lagrangian equations define calibrated minimal Lagrangian surfaces in complex space. These fully nonlinear Hessian equations can also be written in terms of symmetric polynomials of the Hessian, giving a minimal surface interpretation to...

In these lectures we will describe the relationship between optimal transportation and nonlinear elliptic PDE of Monge-Ampere type, focusing on recent advances in characterizing costs and domains for which the Monge-Kantorovich problem has smooth...

In these lectures we will describe the relationship between optimal transportation and nonlinear elliptic PDE of Monge-Ampere type, focusing on recent advances in characterizing costs and domains for which the Monge-Kantorovich problem has smooth...

We will discuss topological information carried by weakly differentiable maps and its applications in an existence theory for absolute minimizers of the Faddeev knot energies in higher dimensions.

I will discuss how some questions in conformal geometry can be answered using twistor theory. One such application is to the classification of locally conformally flat Hermitian surfaces. Another application is to determining the conformal...

We consider the problem of finding complete conformal metrics determined by a symmetric function of Ricci tensor in a negative convex cone on compact manifolds. A consequence of our main results is that any smooth bounded domain in Euclidean space...

After recalling the definition of $Q$-curvature and some applications, we will address the question of prescribing it through a conformal deformation of the metric. We will address some compactness issues, treated via blow-up analysis, and then...