Analysis Seminar

If we deform a submanifold along its mean curvature vector, which is called mean curvature flow (MCF), the area will decrease most rapidly. Being Lagrangian is preserved along MCF in Kahler-Einstein manifolds. We can thus try to construct special...

We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z^2 actions. Our techniques combine novel one and a half dimensional phase-space analysis with more...

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 $R^d\times R$.