Education

1999 — Ph.D. (C.Sc.) in Mathematics and Physics («Mathematical Physics»)
Institution: St. Petersburg State University
Advisor: M.S. Birman

Scientific interests

• Spectral theory of differential operators
• Periodic differential operators
• Maxwell operator
• Partial differential equations

Selected publications

1. N. Filonov. Gaps in the spectrum of the Maxwell operator with periodic coefficients. Communications in Mathematical Physics 240:1–2 (2003), 161–170.
2. N. Filonov. On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator. St. Petersburg Mathematical Journal 16:2 (2005), 413–416.
3. N. Filonov and A. Pushnitski. Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains. Communications in Mathematical Physics 264:3 (2006), 759–772.
4. N. Filonov. Uniqueness of the Leray-Hopf solution for a dyadic model. Transactions of the American Mathematical Society 369:12 (2017), 8663–8684.
5. N. Filonov and I. Kachkovskiy. On the structure of band edges of 2-dimensional periodic elliptic operators, Acta Mathematica 221:1 (2018), 59–80.

Additional Information

filonov@pdmi.ras.ru

Former students: I.V. Kachkovskiy (completed his Ph.D. in 2013 at St. Petersburg Department of Steklov Mathematical Institute).