Previous Special Year Seminar
Dual Legendrian Variations in Contact Form Geometry
In 1979, in collaboration with D. Bennequin, we started a
direction of research around the study of periodic trajectories of
the Reeb vector field $\xi$ on a contact manifold $(M^3, \alpha)$.
We will describe in this talk where this direction of...
The Composite Membrane Problem
We address the problem of building a body of specified shape and
of specified mass, out of materials of varying density so as to
minimize the first Dirichlet eigenvalue. It leads to a free
boundary problem and many uniqueness questions, The...
The Global Smooth Effects and Well Posedness for the Derivative Nonlinear Schr\"odinger Equation with Small Rough Data
Baoxiang Wang
Continuity of Optimal Transport Maps Under a Degenerate MTW Condition
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...
Second Order Parabolic and Elliptic Equations With Very Rough Coefficients
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...
Convexity and Partial Convexity of the Solution of Elliptic Partial Equation
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...
Special Lagrangian Equations
Micah Warren
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...
Optimal Transportation and Nonlinear Elliptic PDE
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...
Optimal Transportation and Nonlinear Elliptic PDE
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...
Faddeev Model in Higher Dimensions
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.
