# Selected Publications

**My papers on Google Scholar** **My papers on arXiv**

- Spectral Sections.

arXiv:2008.04672 [math.SP], 36 pp. - Self-adjoint local boundary problems on compact surfaces. II. Family index.

To appear in the Journal of Noncommutative Geometry.

arXiv:1809.04353 [math-ph], 46 pp. - Self-adjoint local boundary problems on compact surfaces. I. Spectral flow.

Journal of Geometric Analysis (2019).

arXiv:1703.06105 [math.AP], 46 pp. - The structure of the category of parabolic equations. I.

CEUR Workshop Proceedings, 2016, Vol-1662, 121-133. - The structure of the category of parabolic equations. II.

CEUR Workshop Proceedings, 2016, Vol-1662, 134-147. - Factorization of the Reaction-Diffusion Equation, the Wave Equation, and Other Equations.

Proceedings of the Steklov Institute of Mathematics, 2014, Vol.287, Suppl. 1, S156-S166.

(text in English, text in Russian) - The spectral flow for Dirac operators on compact planar domains with local boundary conditions.

Communications in Mathematical Physics, 2013, Vol.322(2), 385-414.

arXiv:1108.0806 [math-ph] - Homeomorphism criteria for the theory of grid generation.

Zh. Vychisl. Mat. i Mat. Fiz., 52:5 (2012), 878–882 (in Russian);

arXiv:1504.01087 [math.GT] (in English). - (with M.I. Katsnelson)

Zero-energy states in corrugated bilayer graphene.

Physical Review B, 2008, Vol.77, No.20.

arXiv:0802.1409 [cond-mat.mes-hall] - Homeomorphism problems arising in the theory of grid generation.

Proceedings of the Steklov Institute of Mathematics, 2008, Suppl.1, S165-S182.

(see also text in Russian). - 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). - External sets properties in IST. The Bulletin of Symbolic Logic.
**8**(2002), Issue 1, 155-156. - Heat equation on Riemann manifolds: morphisms and factorization to smaller dimension.

Proceedings of Institute of Mathematics of NAS of Ukraine, 43 (2002), 194–200. - On relative near-standardness in IST.

Siberian Mathematical Journal 39 (1998), no. 3, 518-521

(see also text in Russian). - 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. - (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 (1997) 70: 744. - Self-similar solutions of the Stefan problem.

Journal of Engineering Physics and Thermophysics (1992) 63: 1032. - The shape of a growing dendrite.

Journal of Engineering Physics and Thermophysics (1991) 61: 1394.