My Research Monograph
Microlocal Analysis, Sharp Spectral Asymptotics and Applications
Updated! Added article
Complete semiclassical spectral asymptotics for periodic and almost periodic perturbations of constant operators
Like it or hate it—I don't care
My Research Monograph
Microlocal Analysis, Sharp Spectral Asymptotics and Applications
Updated! Added article
Complete semiclassical spectral asymptotics for periodic and almost periodic perturbations of constant operators
I am teaching LEC 0201 section of APM 346 Partial Differential Equations
There is another section LEC 0101, taught by a different instructor (I know his name but I am not going to announce it until it appears on the official timetable).
Details about this course will be provided on the class official page in the due time.
I am teaching LEC 0101 section of MAT 334 Complex Variables
There are another sections LEC 0201 and LEC 5101, taught by different instructors (I know their names but I am not going to announce them until it appears on the official timetable).
I am the class coordinator. The content, tests and exam for all sections are exactly the same.
Details about this course are provided on the class official page.
I am teaching LEC 5101 section of MAT 334 Introduction to Ordinary Differential Equations
There are three other sections LEC 0101, LEC 0201 and LEC 5201, taught by three other instructors. I am the class coordinator. The content, tests and exam for all sections are exactly the same.
Textbook:
We support both editions but 11th is preferable.
Details about this course are provided on the class official page.
Conference on Partial Differential Equations and Applications
in Memory of Professor B.Yu. Sternin
November 6–9, 2018, Moscow, Russia
10th St. Petersburg Conference in Spectral Theory
dedicated to the memory of M. Sh. Birman
9 – 12 June, 2018 Euler Institute, St. Petersburg, Russia
Spectral asymptotic for Steklov’s problem in domains with edges (work in progress)
We derive sharp eigenvalue asymptotics for Dirichlet-to-Neumann operator in the domain with edges and discuss obstacles for deriving a sharper (two-term) asymptotics
My Research Monograph is almost ready (in January I plan to edit Introduction, Preface and add some references, after which I pronounce it “Done” and I am not going to add any new material, at least for several years).
Meanwhile I started several new topics:
Asymptotics of the ground state energy for relativistic heavy atoms and molecules
We discuss sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, without magnetic field or with the self-generated magnetic field, and, in particular, relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. In particular, we conclude that the Thomas-Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.