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
Victor Ivrii' Rumblings and Musings
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 L0201 section
There is another section L0101, 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 L0101 section
There is another section L5101, taught by a different instructor (I know his name but I am not going to announce it 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 L5101 (night section)
There are two other sections L0101 and L0201, taught by two 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.