Diophantine equations,
algorithms in number theory,
combinatorial group theory,
combinatorics.
Subject:
It was proved that there exists an infinite set of primes which coincides with the set of positive values of a polynomial in 8 integer-valued variables. Simple Diophantine representations of recurrent sequences of order 3 and 4 wee found. It was found for which $k$'s the triangle group $T(2,3,k)$ coincides with the projective image of the special unitary group $SU(2,R)$ over some ring $R$ of algebraic integers.
Biography
Graduated from St.Petersburg State University (department of higher algebra and number theory) in 1994. Completed post-graduate studies in Steklov Institute of Mathematics at St. Petersburg in 1997. I am a member of St. Petersburg Mathematical Society (since 1998). Elected as a member of its Council in 2001.
A member of the Council of St. Petersburg Mathematical Socoety (elected in 2001).
Main publications:
Vsemirnov M., “The Woods–Erdős conjecture for polynomial rings”, Annals of Pure and Applied Logic, 113:1-3 (2002), 331–344
Vsemirnov M., Mysovskikh V., Tamburini M. C., “Triangle groups as subgroups of unitary groups”, J. Algebra, 245:2 (2001), 562–583
Vsemirnov M. A., “Beskonechnye mnozhestva prostykh chisel, dopuskayuschie diofantovy predstavleniya s vosemyu peremennymi”, Zapiski nauchnykh seminarov POMI, 220, 1995, 36–48
Vsemirnov M. A., “Diofantovy predstavleniya lineinykh rekurrentnykh posledovatelnostei, I”, Zapiski nauchnykh seminarov POMI, 227, 1995, 52–60
Vsemirnov M. A., “Diofantovy predstavleniya lineinykh rekurrentnykh posledovatelnostei, II”, Zapiski nauchnykh seminarov POMI, 241, 1997, 5–29
M. A. Vsemirnov, R. I. Gvozdev, Ya. N. Nuzhin, T. B. Shaipova, “On the Generation of the Groups $\mathrm{SL}_n(\mathbb{Z}+i\mathbb{Z})$ and $\mathrm{PSL}_n(\mathbb{Z}+i\mathbb{Z})$
by Three Involutions Two of Which Commute. II”, Mat. Zametki, 115:3 (2024), 317–329; Math. Notes, 115:3 (2024), 289–300
2020
2.
M. A. Vsemirnov, “On $(2,3)$-generation of matrix groups over the ring of integers, II”, Algebra i Analiz, 32:5 (2020), 62–85; St. Petersburg Math. J., 32:5 (2021), 865–884
2007
3.
M. A. Vsemirnov, “On (2,3)-generation of matrix groups over the ring of integers”, Algebra i Analiz, 19:6 (2007), 22–58; St. Petersburg Math. J., 19:6 (2008), 883–910
M. A. Vsemirnov, “Is the group $\mathrm{SL}(6,\mathbb{Z})$$(2,3)$-generated?”, Zap. Nauchn. Sem. POMI, 330 (2006), 101–130; J. Math. Sci. (N. Y.), 140:5 (2007), 660–675
M. A. Vsemirnov, M. G. Rzhevskii, “An upper bound for the contact number in dimension 9”, Uspekhi Mat. Nauk, 57:5(347) (2002), 149–150; Russian Math. Surveys, 57:5 (2002), 1015–1016
M. A. Vsemirnov, “Two elementary proofs of the Fueter–Pólya theorem on pairing polynomials”, Algebra i Analiz, 13:5 (2001), 1–15; St. Petersburg Math. J., 13:5 (2002), 705–715
M. A. Vsemirnov, E. A. Hirsch, E. Ya. Dantsin, S. V. Ivanov, “Algorithms for SAT and upper bounds on their complexity”, Zap. Nauchn. Sem. POMI, 277 (2001), 14–46; J. Math. Sci. (N. Y.), 118:2 (2003), 4948–4962
M. A. Vsemirnov, “Diophantine representations of linear recurrent sequences. II”, Zap. Nauchn. Sem. POMI, 241 (1997), 5–29; J. Math. Sci. (New York), 98:4 (2000), 427–441
M. A. Vsemirnov, “Macdonald identities and multidimensional theta-functions”, Zap. Nauchn. Sem. POMI, 240 (1997), 67–77; J. Math. Sci. (New York), 96:5 (1999), 3486–3492
1995
10.
M. A. Vsemirnov, “Diophantine representations of linear recurrences. I”, Zap. Nauchn. Sem. POMI, 227 (1995), 52–60; J. Math. Sci. (New York), 89:2 (1998), 1113–1118
M. A. Vsemirnov, “Infinite sets of primes, admitting Diophantine representations in eight variables”, Zap. Nauchn. Sem. POMI, 220 (1995), 36–48; J. Math. Sci. (New York), 87:1 (1997), 3200–3208
M. A. Vsemirnov, “On a class of primality criteria”, Mat. Zametki, 56:1 (1994), 146–148; Math. Notes, 56:1 (1994), 754–755
2024
13.
N. N. Andreev, M. A. Vsemirnov, S. O. Gorchinskiy, D. N. Zaporozhets, S. V. Kislyakov, V. V. Kozlov, M. A. Korolev, D. O. Orlov, Yu. S. Osipov, D. V. Treschev, P. A. Yaskov, “Steklov Institute – 90!”, Uspekhi Mat. Nauk, 79:3(477) (2024), 189–193; Russian Math. Surveys, 79:3 (2024), 557–562
2015
14.
D. G. Benua, M. V. Bondarko, N. A. Vavilov, M. A. Vsemirnov, A. I. Generalov, N. L. Gordeev, I. B. Zhukov, G. A. Leonov, B. B. Lur'e, I. A. Panin, A. L. Smirnov, I. B. Fesenko, A. V. Yakovlev, “To the anniversary of Sergei Vladimirovich Vostokov”, Algebra i Analiz, 27:6 (2015), 3–5; St. Petersburg Math. J., 27:6 (2016), 861–862
2013
15.
M. A. Vsemirnov, È. A. Hirsch, D. Yu. Grigor'ev, G. V. Davydov, E. Ya. Dantsin, I. D. Zaslavskii, È. F. Karavaev, B. Yu. Konev, N. K. Kossovskii, V. A. Lifschitz, M. Margenstern, Yu. V. Matiyasevich, G. E. Mints, V. P. Orevkov, R. Pliuškevičius, A. O. Slisenko, S. V. Solov'ev, V. P. Chernov, “Nikolai Aleksandrovich Shanin (obituary)”, Uspekhi Mat. Nauk, 68:4(412) (2013), 173–176; Russian Math. Surveys, 68:4 (2013), 763–767
2001
16.
M. A. Vsemirnov, E. A. Hirsch, D. Yu. Grigor'ev, G. V. Davydov, E. Ya. Dantsin, A. A. Ivanov, B. Yu. Konev, V. A. Lifshits, Yu. V. Matiyasevich, G. E. Mints, V. P. Orevkov, A. O. Slisenko, “Nikolai Aleksandrovich Shanin (on his 80th birthday)”, Uspekhi Mat. Nauk, 56:3(339) (2001), 181–184; Russian Math. Surveys, 56:3 (2001), 601–605
Гурвицевы группы и гурвицевы образующие M. A. Vsemirnov Conference of Professors of the RAS in the Department of Mathematical Sciences of the Russian Academy of Sciences June 15, 2016 11:20
Hurwitz and (2,3)-generated matrix groups M. A. Vsemirnov General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences February 12, 2007
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