real algebraic curves; decomposable curves; topological classification; isotopy classification.
Subject:
The problem of the classification of arrangements of decomposable algebraic 6-th degree curves of general position in real projective plane was solved. Now the topology classification of decomposable 7-th degree curves under some natural maximality conditions is concluded.
Biography
Graduated from Faculty of Computer Mathematics and Cybernatics of N. I.Lobachevsky Nizhny Novgorod State University (NNGU) in 1970. A list of my works contains more than 80 titles.
1995 — present I am the scientific secretary of the Nizhny Novgorod Mathematical Society (NNMS).
Main publications:
Polotovskii G. M. On the classification of decomposable 7-th degree curves // Contemp. Math., 2000, v. 253, 219–234.
G. M. Polotovskiy, “Essay of history of topological education in Nizhny Novgorod”, Chebyshevskii Sb., 22:1 (2021), 447–459
2020
2.
I. M. Borisov, G. M. Polotovsky, “On the topology of planar real decomposable curves of degree 8”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 176 (2020), 3–18
A. B. Korchagin, G. M. Polotovskii, “On positions of a real plane quintic relative to a couple of lines”, Algebra i Analiz, 21:2 (2009), 92–112; St. Petersburg Math. J., 21:2 (2010), 231–244
M. A. Gushchin, A. N. Korobeinikov, G. M. Polotovsky, “Construction of arrangements of a cubic and a quartic by patchworking”, Zap. Nauchn. Sem. POMI, 267 (2000), 119–132; J. Math. Sci. (N. Y.), 113:6 (2003), 795–803
S. Yu. Orevkov, G. M. Polotovsky, “Projective $M$-cubics and $M$-quartics in general position with a maximally intersecting pair of ovals”, Algebra i Analiz, 11:5 (1999), 166–184; St. Petersburg Math. J., 11:5 (2000), 837–852
G. M. Polotovsky, “Connection between the rigid isotopy class of a fifth-order nonsingular curve in $\mathbb{R}P^2$ and its disposition with respect to a line”, Funktsional. Anal. i Prilozhen., 20:4 (1986), 87–88; Funct. Anal. Appl., 20:4 (1986), 330–332
O. V. Anashkin, P. M. Akhmet'ev, D. V. Balandin, M. K. Barinova, I. V. Boykov, A. N. Bezdenezhnyh, V. N. Belykh, P. A. Vel'misov, I. Yu. Vlasenko, O. E. Galkin, S. Yu. Galkina, V. K. Gorbunov, S. D. Glyzin, S. V. Gonchenko, A. S. Gorodetski, E. V. Gubina, E. Ya. Gurevich, A. A. Davydov, L. S. Efremova, R. V. Zhalnin, A. Yu. Zhirov, E. V. Zhuzhoma, N. I. Zhukova, S. Kh. Zinina, Yu. S. Ilyashenko, N. V. Isaenkova, A. O. Kazakov, A. V. Klimenko, S. A. Komech, Yu. A. Kordyukov, V. E. Kruglov, E. V. Kruglov, E. B. Kuznetsov, S. K. Lando, Yu. A. Levchenko, L. M. Lerman, S. I. Maksimenko, M. I. Malkin, D. S. Malyshev, V. K. Mamaev, T. Ph. Mamedova, V. S. Medvedev, T. V. Medvedev, D. I. Mints, T. M. Mitryakova, A. D. Morozov, A. I. Morozov, E. V. Nozdrinova, E. N. Pelinovsky, Ya. B. Pesin, A. S. Pikovsky, S. Yu. Pilyugin, G. M. Polotovsky, O. V. Pochinka, I. D. Remizov, P. E. Ryabov, A. S. Skripchenko, A. V. Slunyaev, S. V. Sokolov, L. A. Sukharev, E. A. Talanova, V. A. Timorin, S. B. Tikhomirov, V. F. Tishkin, D. V. Treschev, D. V. Turaev, N. G. Chebochko, E. E. Chilina, P. A. Shamanaev, D. D. Shubin, E. I. Yakovlev, “To the 75th anniversary of Vyacheslav Zigmundovich Grines”, Zhurnal SVMO, 23:4 (2021), 472–476
2020
10.
G. M. Polotovskiy, “V. A. Rokhlin and D. A. Gudkov against the background of Hilbert's 16th problem (according to their correspondence in 1971–1982)”, Zap. Nauchn. Sem. POMI, 498 (2020), 157–167
2012
11.
G. M. Polotovskiy, “V. V. Morozov, D. A. Gudkov and the first part of the $16$th Hilbert problem”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 154:2 (2012), 31–43
1992
12.
V. I. Arnol'd, A. M. Vershik, O. Ya. Viro, A. B. Korchagin, E. A. Leontovich-Andronova, S. P. Novikov, O. A. Oleinik, G. M. Polotovsky, G. A. Utkin, E. I. Shustin, “Dmitrii Andreevich Gudkov (obituary)”, Uspekhi Mat. Nauk, 47:6(288) (1992), 195–198; Russian Math. Surveys, 47:6 (1992), 193–197
V. I. Arnol'd, O. Ya. Viro, E. A. Leontovich-Andronova, V. V. Nikulin, S. P. Novikov, O. A. Oleinik, G. M. Polotovsky, V. M. Kharlamov, “Dmitrii Andreevich Gudkov (on his seventieth birthday)”, Uspekhi Mat. Nauk, 44:1(265) (1989), 223–225; Russian Math. Surveys, 44:1 (1989), 271–273
G. M. Polotovsky, “Поправки к статье "Каталог $M$-распадающихся кривых $6$-го порядка" (ДАН, т. 236, № 3, 1977 г.)”, Dokl. Akad. Nauk SSSR, 240:6 (1978), 1272
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