Analysis and Mathematical Physics

The question of asbolute continuity, with respect to the reference measure, of the harmonic measure on a domain with rough boundary has been the object of many important results. Here we ask about the similar question, but where the Dirichlet...

I will describe the duality of incompressible Navier-Stokes fluid dynamics in three dimensions, leading to its reformulation in terms of a one-dimensional momentum loop equation.

The decaying turbulence is a solution of this equation equivalent to a...

In this talk, we will explore recent developments in the study of coherent structures evolving by incompressible flows. Our focus will be on the behavior of fluid interfaces and vortex filaments. We include the dynamics of gravity Stokes interfaces...

The classical Serrin’s overdetermined theorem states that a C^2 bounded domain, which admits a function with constant Laplacian that satisfies both constant Dirichlet and Neumann boundary conditions, must necessarily be a ball. While extensions of...

Fourier Quasicrystals (FQ) are defined as crystalline measures

μ=∑λ∈Λaλδλ,μ̂ =∑s∈Sbsδs, so that not only μ (and hence μ̂ ) are tempered distributions, but also |μ|:=∑λ∈Λ|aλ|δλand|μ̂ |:=∑s∈S|bs|δs,

are tempered.

One-dimensional FQs with positive...

An inertial manifold is a positively invariant smooth finite-dimensional manifold which contains the global attractor and which attracts the trajectories at a uniform exponential rate. It follows that the infinite-dimensional dynamical system is...

We discuss an application of the SUSY approach to the analysis of spectral characteristics of hermitian and non hermitian random band matrices. In 1D case the obtained integral representations for correlation functions of characteristic polynomials...

Let G be a compact Lie group acting on a closed manifold M. Partially motivated by work of Uhlenbeck (1976), we explore the generic properties of Laplace eigenfunctions associated to G-invariant metrics on M. We find that, in the case where 𝕋 is a...

What happens to an Lp function when one truncates its Fourier transform to a domain? This question is now rather well understood, thanks to famous results by Marcel Riesz and Charles Fefferman, and the answer depends on the domain: if it is a...

Interaction models discussed here are the (asymmetric) quantum Rabi model (QRM), which describes the interaction between a photon and two-level atoms, and the non-commutative harmonic oscillator (NCHO). The latter can be considered as a covering...