The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

Inverse transport consists of reconstructing the optical properties of a domain from
measurements performed at the domain's boundary. This review concerns several types of …

We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear
Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that …

We study a new method-called Schrodingerisation introduced in [**, Liu, Yu, arxiv:
2212.13969]-for solving general linear partial differential equations with quantum simulation …

We prove rigorously that the one-particle density matrix of three dimensional interacting
Bose systems with a short-scale repulsive pair interaction converges to the solution of the …

We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …

This is a study of the universality of spectral statistics for large random matrices. Considered
are symmetric, Hermitian, or quaternion self-dual random matrices with independent …

Waves generated by opportunistic or ambient noise sources and recorded by passive
sensor arrays can be used to image the medium through which they travel. Spectacular …

The nonlinear Schrödinger equation in the weakly nonlinear regime with random Gaussian
fields as initial data is considered. The problem is set on the torus in any dimension greater …

In a series of previous works (arxiv: 2104.11204, arxiv: 2110.04565, arxiv: 2301.07063), we
gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small …