Serguei Denissov

My area of research is Analysis. I work mainly in two classical areas: Approximation theory and Scattering theory. Recently, I have been also working on some projects related to two-dimensional fluid motion. The Approximation theory is a classical area in Analysis with links to almost any other branch of Mathematics. I am mostly interested in the behavior of polynomials orthogonal on the unit circle/real line and the relation between the orthogonality measure and the recursion parameters. These questions are very interesting per se but they also are well motivated by some problems in mathematical physics.

In the scattering theory, I am studying the problems that describe the propagation of electromagnetic or acoustic wave through the medium. This process is described by the Schrodinger or the wave equations, respectively. One of the key problems is to understand what are the minimal assumptions of the medium that allow the wave to propagate and how exactly it propagates. This gives rise to very hard problems that can be addressed using methods of the analytic function theory and harmonic analysis.

The dynamics of fluids is a classical and perhaps one of the most difficult branches in the subject of Partial Differential Equations. My research was focused on one very particular problem which seems to hold a key to understanding even harder questions. The motion of the two-dimensional incompressible fluid is governed by the well-known Euler equation. It was proved long time ago that once the initial velocity is regular, the motion is regular forever. However, very little was known whether this motion can become singular at infinity. Mathematically, this problem is conventionally described in terms of the size of the Sobolev norms which measure the ``singularity" of the fluid at any given time. By do they grow at all and, if yes, how fast? What is the intrinsic mechanism of the singularity formation? These are the problems I am mostly interested in.

For more details on my research, check my blog or my website.

Moscow State University
Associate Professor
Research Interests: 
Analysis, Mathematical Physics
Sergeui Denissov
denissov at math dot wisc dot edu