Analysis Seminar

I will describe joint work with Boris Solomyak, in which we show that the stationary (Furstenberg) measure on the projective line associated to 2x2 random matrix products has the "correct" dimension (entropy / Lyapunov exponent) provided that the...

An important question in hydrodynamic turbulence concerns the scaling proprties in the inertial range. Many years of experimental and computational work suggests---some would say, convincingly shows---that anomalous scaling prevails. If so, this...

I will discuss random field Ising model on $Z^2$ where the external field is given by i.i.d. Gaussian variables with mean zero and positive variance. I will present a recent result that at zero temperature the effect of boundary conditions on the...

In this talk, I will give an overview of some of what is known about solutions to the thin obstacle problem, and then move on to a discussion of a higher regularity result on the singular part of the free boundary. This is joint work with Xavier...

We consider a reaction-diffusion equation with a nonlocal reaction term. This PDE arises as a model in evolutionary ecology. We study the regularity properties and asymptotic behavior of its solutions.

We consider a system of two interacting one-dimensional quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$. The fact that particle frequencies are identical, implies a new effect compared to generic 2D potentials: the presence of large...

I will discuss some new results for gradient field models with uniformly convex potentials. A connection between the scaling limit of the field and elliptic homogenization was introduced more than twenty years ago by Naddaf and Spencer. In joint...

In this talk we discuss the cubic wave equation in three dimensions. In three dimensions the critical Sobolev exponent is 1/2. There is no known conserved quantity that controls this norm. We prove unconditional global well-posedness for radial...

We introduce a length scale in Plateau’s problem by modeling soap films as liquid with small volume rather than as surfaces, and study the relaxed problem and its relation to minimal surfaces. This is based on joint works with Antonello Scardicchio...