Research Staff

Saburova Natalia

Academic title:  Assistant professor
Degree:  Candidate of science (PhD degree in Phys. & Math.)
Post:  Head of the Department of Mathematical Analysis, Algebra and Geometry
Phone:  (8182) 21-61-00 (add. 1926)
Research interests: 
  • Spectral theory of differential and difference operators on periodic graphs

Selected research projects: 
  • Investigation of actual problems of mathematical physics (RSF, 2015-2017); 
  • Investigation of mathematical models of periodic structures (RFBR, 2016-2017); 
  • Study of spectral properties of differential operators on periodic graphs (Federal target program "Scientific and scientific-pedagogical personnel of innovative Russia", 2009 – 2013)

PhD\DSc thesis:  Construction of quasi-periodic solutions in the two rigid bodies problem
Current Research Achievements:  We consider Schrödinger operators with periodic potentials on periodic discrete graphs. The spectrum of the Schrödinger operator consists of an absolutely continuous part (a union of a finite number of non-degenerated bands) and a finite number of flat bands, i.e., eigenvalues of infinite multiplicity. We obtain estimates of the Lebesgue measure of the spectrum in terms of geometric parameters of the graph and show that they become identities for some class of graphs. We describe a localization of spectral bands in terms of eigenvalues of Dirichlet and Neumann operators on a fundamental domain of the periodic graph. We estimate effective masses associated with the ends of each spectral band in terms of geometric parameters of the graphs. We estimate a variation of the spectrum of the Schrödinger operators under a perturbation by a magnetic field in terms of magnetic fluxes.
Priority research areas:  Information Technologies
Selected Publications: 
  1. Korotyaev E., Saburova N. Schrödinger operators on periodic discrete graphs. Journal of Mathematical Analysis and Applications. 420 (2014), no. 1, 576-611. 
  2.  Korotyaev E., Saburova N. Spectral band localization for Schrödinger operators on periodic graphs. Proc. Amer. Math. Soc. 143 (2015), no. 9, 3951-3967. 
  3. Korotyaev E., Saburova N. Effective masses for Laplacians on periodic graphs. Journal of Mathematical Analysis and Applications. 436 (2016), no. 1, 104-130. 
  4.  Korotyaev E., Saburova N. Estimates of bands for Laplacians on periodic equilateral metric graphs, Proc. Amer. Math. Soc. 144 (2016), 1605-1617. 
  5. Korotyaev E., Saburova N. Magnetic Schrödinger operators on periodic discrete graphs, Journal of Functional Analysis. 272 (2017), 1625-1660.

Scopus\WebOfScience\ResearchGate profile:
Professional memberships:  a reviewer for Mathematical Reviews
Teaching activity:  Differential and Difference Equations, Functional Analysis, Theory of Functions of a Complex Variable, Discrete Mathematics, Applied Mathematics, Mathematical Logic

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Updated 17.09.2018