Past Events

I'll give an introduction to rational homotopy theory. The plan is to describe the basic ideas of the theory, and hopefully to comment on some connections to differential and symplectic geometry.

Let X be a Hirzebruch surface.  Moduli spaces of semistable sheaves on X with fixed numerical invariants are always irreducible by a theorem of Walter.  On the other hand, many other basic properties of sheaves on Hirzebruch surfaces are unknown.  I will discuss two different…

The Gagliardo-Nirenberg inequality allows an interpolation of L^p-based Sobolev spaces by combining L^p estimates of higher-order derivatives for p small and L^p estimates of lower-order derivatives for p large to give an L^p estimate of intermediate derivatives for p intermediate. Such…

One of the goals of harmonic analysis is to study singular integrals. These are ubiquitous in PDEs and mathematical physics and, as it transpired recently, play an important role in geometric measure theory. The simplest ones are called Calderón--Zygmund operators. Their theory was…

There is a classical connection between toric varieties and combinatorics, and tools from algebraic geometry can be used to prove facts about combinatorics. For example, one can give a proof of Euler's formula for the Euler characteristic of a convex polyhedron using the cohomology of complex…

We consider the problem of imaging sparse scenes from a few noisy data using an l1-minimization approach.
This problem can be cast as a linear system of the form Ax=b. The dimension of the unknown sparse vector x is much larger than the dimension of the data vector b. The l1-minimization…

The Hitchin-Simpson equations defined over a K\"ahler manifold are first order, non-linear equations for a pair of connection on a Hermitian vector bundle and a 1-form with values in the endomorphism bundle. We will describe the behavior of solutions to the Hitchin-Simpson…