Analysis and Mathematical Physics

In this overview talk we will explore a variational approach to the problem of Spectral Minimal Partitions (SMPs).  The problem is to partition a domain or a manifold into k subdomains so that the first Dirichlet eigenvalue on each subdomain is as...

In this talk, I will present several a priori interior and boundary trace estimates for the 3D incompressible Navier–Stokes equation, which recover and extend the current picture of higher derivative estimates in the mixed norm. Then we discuss the...

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...