# Selected Publications

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

- Family index for Fredholm extensions of semi-Fredholm operators.

arXiv:2401.16060 (2024), 37 pp. - From graph to Riesz continuity.

arXiv:2202.03337 (2022), 26 pp. - The continuity properties of discrete-spectrum families of Fredholm operators.

arXiv:2201.09869 (2022), 4 pp. - Spaces of unbounded Fredholm operators. I. Homotopy equivalences.

arXiv:2110.14359 (2021), 24 pp. - Spectral Sections.

Israel Journal of Mathematics 259 (2024), 651–700 (pdf)

arXiv:2008.04672. - Self-adjoint local boundary problems on compact surfaces. II. Family index.

Journal of Noncommutative Geometry, 16 (2022), no. 4, 1213-1257.

arXiv:1809.04353. - Self-adjoint local boundary problems on compact surfaces. I. Spectral flow.

Journal of Geometric Analysis, 31 (2021), no. 2, 1510-1554.

arXiv:1703.06105. - The structure of the category of parabolic equations. I.

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

CEUR Workshop Proceedings 1662 (2016), 134-147. - 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) - 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 - 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). - (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] - 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). - 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 70 (1997), no. 5, 744–748. - Self-similar solutions of the Stefan problem.

Journal of Engineering Physics and Thermophysics 63 (1992), no. 4, 1032–1036. - The shape of a growing dendrite.

Journal of Engineering Physics and Thermophysics 70 (1997), no. 5, 744–748.