Over the past decades, much attention has been devoted to the
detection of small inhomogeneities in materials or tissues, using
non-invasive techniques, primarily electromagnetic wave-fields. The
characterization of the signature of small inclusions...
The NLSE is relevant for the explorations of Bose-Einstein
Condensates and for Nonlinear Classical Optics. In presence of a
random potential it can be used to study the competition between
Anderson localization, that is characteristic of linear...
Band matrices are a class of random operators with rows and
columns indexed by elements of the d-dimensional lattice, and
random entries H(u, v) which are small when the distance between u
and v on the lattice is...
Deift--Simon and Poltoratskii--Remling proved upper bounds on
the measure of the absolutely continuous spectrum of Jacobi
matrices. Using methods of classical approximation theory, we give
a new proof of their results, and generalize them in several...
As originally proposed by Anderson (1958), a quantum system of
many local degrees of freedom with short-range interactions and
static disorder may fail to thermally equilibrate, even with strong
interactions and...
I will discuss the problem of determining the number of
infinite-volume ground states in the Edwards-Anderson (nearest
neighbor) spin glass model on $Z^D$ for $D \geq 2$. There are no
complete results for this problem even in $D=2$. I will focus
on...
In this talk I will describe a real-variable method to extract
long-time asymptotics for solutions of many nonlinear equations
(including the Schrodinger and mKdV equations). The method has many
resemblances to the classical stationary phase method...
Concentration phenomena for Laplacian eigenfunctions can be
studied by obtaining estimates for their $L^{p}$ growth. By
considering eigenfunctions as quasimodes (approximate
eigenfunctions) within the...
The Gaussian central limit theorem says that for a wide class of
stochastic systems, the bell curve (Gaussian distribution)
describes the statistics for random fluctuations of important
observables. In this...
For many elegant mathematical examples, one can 1) find theories
behind them, 2) understand why they exist in the first place, 3)
explore the consequences in math and physics. If one takes the
Euler number as...
Using the spectral multiplicities of the standard torus, we
endow the Laplace eigenspace with Gaussian probability measure.
This induces a notion of a random Gaussian Laplace eigenfunctions
on the torus. We...
The Coulomb Gas is a model of Statistical Mechanics with a
special type of phase transition. In the first part of the talk I
will review the expected features conjectured by physicists and the
few mathematical results so far obtained. The second...
We explain an exact solution of the one-dimensional
Kardar-Parisi-Zhang equation with sharp wedge initial data.
Physically this solution describes the shape fluctuations of a thin
film droplet formed by the stable phase expanding into the...
