Video Lectures

We discuss various Gaussian ensembles for real homogeneous polynomials in several variables and the question of the distribution of the topologies of the connected components of the zero sets of a typical such random real hypersurface. For the "real...

The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. In this talk, I will explain the ideas of the proof and discuss our recent simplifications. One of the main ingredients in the proof is a...

I will review some aspects of many-body Anderson localization. Many-body localized systems have a type of integrable Hamiltonian, with an extensive set of operators that are localized in real-space that each commute with the Hamiltonian. The...

We introduce a new family of robust semiparametric methods for analyzing large, complex, and noisy datasets. Our method is based on the transelliptical distribution family which assumes that the variables follow an elliptical distribution after a...

When a 2D many-particle system with a repulsive interaction is subject to a sufficiently strong magnetic field, that can also be produced by rapid rotation, strongly correlated many-body states in the lowest Landau level LLL may emerge. In the talk...

The systems of elasticity in 2D are wave-type equations with two different propagation speeds at a linear level. Due to the incompressibility, the system is nonlocal and is not Lorentz invariant, but it is inherently linear degenerate. We talk about...

We compute new families of time-periodic and quasi-periodic solutions of the free-surface Euler equations involving extreme standing waves and collisions of traveling waves of various types. A Floquet analysis shows that many of the new solutions...