# Analysis/Mathematical Physics Seminar

### Date

### Affiliation

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 Nonlinear Schroedinger Equation (NLSE) with a Random Potential: Effective Noise and Scaling Theory

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...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

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...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

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...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

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...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

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...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

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...

ANALYSIS AND MATHEMATICAL PHYSICS SEMINAR

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...