Selected Publications

My papers on Google Scholar       My papers on arXiv

  1. Family index for Fredholm extensions of semi-Fredholm operators.
    arXiv:2401.16060 (2024), 37 pp.
  2. From graph to Riesz continuity.
    arXiv:2202.03337 (2022), 26 pp.
  3. The continuity properties of discrete-spectrum families of Fredholm operators.
    arXiv:2201.09869 (2022), 4 pp.
  4. Spaces of unbounded Fredholm operators. I. Homotopy equivalences.
    arXiv:2110.14359 (2021), 24 pp.
  5. Spectral Sections.
    Israel Journal of Mathematics 259 (2024), 651–700 (pdf) 
    arXiv:2008.04672.
  6. Self-adjoint local boundary problems on compact surfaces. II. Family index.
    Journal of Noncommutative Geometry, 16 (2022), no. 4, 1213-1257.
    arXiv:1809.04353.
  7. Self-adjoint local boundary problems on compact surfaces. I. Spectral flow.
    Journal of Geometric Analysis, 31 (2021), no. 2, 1510-1554.
    arXiv:1703.06105.
  8. The structure of the category of parabolic equations. I.
    CEUR Workshop Proceedings 1662 (2016), 121-133.
  9. The structure of the category of parabolic equations. II.
    CEUR Workshop Proceedings 1662 (2016), 134-147.
  10. Factorization of the Reaction-Diffusion Equation, the Wave Equation, and Other Equations.
    Proceedings of the Steklov Institute of Mathematics 287 (2014), Suppl. 1, S156-S166.
    (text in English, text in Russian)
  11. The spectral flow for Dirac operators on compact planar domains with local boundary conditions.
    Communications in Mathematical Physics 322 (2013), no.2, 385-414.
    arXiv:1108.0806
  12. Homeomorphism criteria for the theory of grid generation.
    Zh. Vychisl. Mat. i Mat. Fiz. 52 (2012), no.5, 878–882 (in Russian);
    arXiv:1504.01087 (in English).
  13. (with M.I. Katsnelson)
    Zero-energy states in corrugated bilayer graphene.
    Physical Review B 77 (2008), no.20.
    arXiv:0802.1409 [cond-mat.mes-hall]
  14. Homeomorphism problems arising in the theory of grid generation.
    Proceedings of the Steklov Institute of Mathematics 261 (2008), Suppl.1, S165-S182.
    (see also text in Russian).
  15. On the existence of factor sets by external equivalence relations in IST.
    Siberian Mathematical Journal 43 (2002), no. 4, 708-713
    (see also text in Russian).
  16. External sets properties in IST. The Bulletin of Symbolic Logic 8 (2002), Issue 1, 155-156.
  17. Heat equation on Riemann manifolds: morphisms and factorization to smaller dimension.
    Proceedings of Institute of Mathematics of NAS of Ukraine 43 (2002), 194–200.
  18. On relative near-standardness in IST.
    Siberian Mathematical Journal 39 (1998), no. 3, 518-521
    (see also text in Russian).
  19. Modeling of solutions of the heat equation and of the Stefan problem with dimension decrease.
    Russian Acad. Sci. Docl. Math. 58 (1998), no.1, 88-90.
  20. (with L.D. Zabezhinskii, V.V. Prokhorov, M.N. Mil'shtein, S.G. Stakheev)
    Statement and personal-computer-aided realization of the conjugate problem of heat transfer in a power-technological boiler with a moving bed of dispersed heat-transfer agent.
    Journal of Engineering Physics and Thermophysics 70 (1997), no. 5, 744–748.
  21. Self-similar solutions of the Stefan problem.
    Journal of Engineering Physics and Thermophysics 63 (1992), no. 4, 1032–1036.
  22. The shape of a growing dendrite.
    Journal of Engineering Physics and Thermophysics 70 (1997), no. 5, 744–748.