Analysis Seminar

In 1975 Szemeredi proved that every subset of the integers with positive density contains arbitrarily long arithmetic progressions. Bergelson and Leibman showed in 1996 that the common difference of the arithmetic progression can be a square, a cube...

In this talk I will consider actions of non-abelian groups on n-dimensional tori, explain the notions of stiffness and stationary measures, and show how under fairly general assumptions stationary measures can be classified. A key ingredient is a...

Let p_1,...,p_k be integer polynomials of one or several variables. There is a relation between the density of polynomial configurations a+p_1(n),...,a+p_k(n) in sets of integers and the form of the closure of the diagonal of X^k under the...

Maps in W^{1,1} from the sphere S^2 into the circle S^1 can have, at most, countably many topological singularities. I will present some techniques which allow us to localize and quantify those "defects". Joint work with H. Brezis and P. Mironescu.

I will talk about some recent joint work with Carlos Kenig on a certain type of uniqueness property for solutions of nonlinear Schrödinger equations on $R^d\times R$.

We will describe a result which extends the classical Coifman-Meyer theorem to the multi-parameter setting of polydiscs. This is based on work recently completed jointly with Jill Pipher, Terry Tao and Christoph Thiele.