01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords:
group theory; knot theory; braid groups; automorphism groups; permutation groups; width of verbal subgroups; equations in groups; partial differential equation; multidimensional inverse problems; evolution equations; integral geometry; systems of kinetic equations.
Subject:
It is proved that any verbal subgroup $V(B_n)$ of braid group $B_n$, $n>2$, defined by a finite set of words $V$ has infinite width. Similar result is proved for some Artin groups. We investigate decompositions of automorphisms of various free modules into products of transvections and dilations. In particular, as a corollary, we obtain that for $n>2$ the width of the spetial linear group $SL_n(Z)$ over ring of integer $Z$, with respect to the set of commutators, does not exceed 10. It is shown that for any integers $k>3$ and $m>0$ any permutation in the alternating group $A_{km}$ of degree $km$ can be expressed as the product of two permutations each of them has $m$ cycles of length $k$ in its cycle decomposition. This proves a conjecture by J. L. Brenner and R. J. Evans. It is proved that if in the HNN-extension $G^*$, the subgroups $A$ and $B$ are distinct from the base group $G$, then every subgroup $V(G^*)$ defined by a finite proper set $V$ of words has infinite width relative to $V$. Similar results are proved for groups with one relation and number generations greater 2 and for some free produts with amalgamations. It is described a new algorithm for calculating the commutator length in free groups and some equations in free groups are investigated. It is proved that there exist continuum many non-isomorphic two-generated groups which each possess a regularly exhausting sequence with polynomial growth and which are but not groups with polynomial growth.
Biography
Graduated from Faculty of Mathematics and Mechanics of Novosibirsk state University in 1963 (department of Algebra and Logic). Ph.D. thesis was defended in 1994. A list of my works containes nearly 50 titles. Since 1995 I have led the algebraic seminar "Evarist Galua" at NSU. Since 2000 I and A. Yu. Vesnin have led the special course "Algebraic methods in knot theory" at NSU.
In 1993 I was awarded the Prize of M. I. Kargapolov for young mathematicians for solving problems from "Kourovka Notebook".
Main publications:
Bardakov V. G. Two inverse problems for a system of quantum kinetic equations // J. Inv.Ill-Posed Problems, 7, 2(1998), 105–119.
V. G. Bardakov, T. A. Kozlovskaya, D. V. Talalaev, “$n$-valued quandles and associated bialgebras”, TMF, 220:1 (2024), 25–43; Theoret. and Math. Phys., 220:1 (2024), 1080–1096
2023
2.
V. G. Bardakov, T. A. Kozlovskaya, “Multivalued groups and Newton polyhedron”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 1590–1596
3.
V. G. Bardakov, D. V. Talalaev, “Extensions of Yang–Baxter sets”, TMF, 215:2 (2023), 176–189; Theoret. and Math. Phys., 215:2 (2023), 609–621
V. G. Bardakov, T. R. Nasybullov, “Multi-switches, representations of virtual braids, and invariants of virtual links”, Algebra Logika, 59:4 (2020), 500–506; Algebra and Logic, 59:4 (2020), 341–345
V. G. Bardakov, M. V. Neshchadim, “Lower central series of Baumslag–Solitar groups”, Algebra Logika, 59:4 (2020), 413–431; Algebra and Logic, 59:4 (2020), 281–294
V. G. Bardakov, M. V. Neshchadim, “A representation of virtual braids by automorphisms”, Algebra Logika, 56:5 (2017), 539–547; Algebra and Logic, 56:5 (2017), 355–361
V. G. Bardakov, Yu. A. Mikhalchishina, M. V. Neshchadim, “Virtual link groups”, Sibirsk. Mat. Zh., 58:5 (2017), 989–1003; Siberian Math. J., 58:5 (2017), 765–777
V. G. Bardakov, M. V. Neshchadim, “Knot groups and nilpotent approximability”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:4 (2017), 43–51; Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S23–S30
V. G. Bardakov, M. V. Neshchadim, “Subgroups, automorphisms, and Lie algebras related to the basis-conjugating automorphism group”, Algebra Logika, 55:6 (2016), 670–703; Algebra and Logic, 55:6 (2017), 436–460
V. G. Bardakov, M. V. Neshchadim, “An Example of a Nonlinearizable Quasicyclic Subgroup in the Automorphism Group of the Polynomial Algebra”, Mat. Zametki, 98:2 (2015), 180–186; Math. Notes, 98:2 (2015), 210–215
12.
V. Bardakov, K. Gongopadhyay, M. Singh, A. Vesnin, J. Wu, “Some problems on knots, braids, and automorphism groups”, Sib. Èlektron. Mat. Izv., 12 (2015), 394–405
V. G. Bardakov, M. S. Petukhova, “On potential counterexamples to the problem of zero divisors”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015), 30–50; J. Math. Sci., 221:6 (2017), 778–797
V. G. Bardakov, A. A. Simonov, “Rings and groups of matrices with a nonstandard product”, Sibirsk. Mat. Zh., 54:3 (2013), 504–519; Siberian Math. J., 54:3 (2013), 393–405
V. G. Bardakov, T. R. Nasybullov, M. V. Neshchadim, “Twisted conjugacy classes of the unit element”, Sibirsk. Mat. Zh., 54:1 (2013), 20–34; Siberian Math. J., 54:1 (2013), 10–21
Yu. E. Anikonov, N. B. Aiupova, V. G. Bardakov, V. P. Golubyatnikov, M. V. Neshchadim, “Inversion of mapping and inverse problems”, Sib. Èlektron. Mat. Izv., 9 (2012), 382–432
V. G. Bardakov, M. V. Neshchadim, “On the number of relations in free products of abelian groups”, Sibirsk. Mat. Zh., 53:4 (2012), 741–751; Siberian Math. J., 53:4 (2012), 591–599
2007
20.
V. G. Bardakov, R. V. Mikhailov, “On the residual properties of link groups”, Sibirsk. Mat. Zh., 48:3 (2007), 485–495; Siberian Math. J., 48:3 (2007), 387–394
V. G. Bardakov, O. V. Bryukhanov, “On linear representations of some extensions”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 7:3 (2007), 45–58
V. G. Bardakov, “Linear representations of the group of conjugating automorphisms and the braid groups of some manifolds”, Sibirsk. Mat. Zh., 46:1 (2005), 17–31; Siberian Math. J., 46:1 (2005), 13–23
V. G. Bardakov, “On D. I. Moldavanskii's question about $p$-separable subgroups of a free group”, Sibirsk. Mat. Zh., 45:3 (2004), 505–509; Siberian Math. J., 45:3 (2004), 416–419
V. G. Bardakov, “Solution of the inverse problem for a matrix transport equation”, Sib. Zh. Ind. Mat., 5:3 (2002), 35–52
2001
30.
V. G. Bardakov, “Construction of a Regularly Exhausting Sequence for Groups with Subexponential Growth”, Algebra Logika, 40:1 (2001), 22–29; Algebra and Logic, 40:1 (2001), 12–16
V. G. Bardakov, “The classification of differential equations with two independent variables on the basis of the principal part”, Differ. Uravn., 36:2 (2000), 187–197; Differ. Equ., 36:2 (2000), 213–223
1998
33.
V. G. Bardakov, “On orthogonal bases of rational lattices”, Sibirsk. Mat. Zh., 39:6 (1998), 1236–1250; Siberian Math. J., 39:6 (1998), 1067–1079
1997
34.
V. G. Bardakov, “On the width of verbal subgroups of some free constructions”, Algebra Logika, 36:5 (1997), 494–517
V. G. Bardakov, “Even permutations not representable in the form of a product of two permutations of given order”, Mat. Zametki, 62:2 (1997), 169–177; Math. Notes, 62:2 (1997), 141–147
V. G. Bardakov, “On the decomposition of automorphisms of free modules into simple factors”, Izv. RAN. Ser. Mat., 59:2 (1995), 109–128; Izv. Math., 59:2 (1995), 333–351
V. G. Bardakov, “Factorization of even permutations into two factors of given cyclic structure”, Diskr. Mat., 5:1 (1993), 70–90; Discrete Math. Appl., 3:4 (1993), 385–406
Yu. L. Ershov, S. S. Goncharov, V. D. Mazurov, V. G. Bardakov, N. V. Bayanova, V. V. Bludov, L. A. Bokut', S. V. Varaksin, A. V. Vasil'ev, E. P. Vdovin, M. A. Grechkoseeva, A. V. Zenkov, P. S. Kolesnikov, L. L. Maksimova, I. A. Mal'tsev, A. S. Morozov, N. A. Peryazev, A. G. Pinus, K. N. Ponomarev, A. M. Popova, V. N. Remeslennikov, V. A. Roman'kov, N. S. Romanovskii, E. I. Timoshenko, V. A. Churkin, I. P. Shestakov, “In memory of Valeriy Matveevich Kopytov”, Algebra Logika, 61:6 (2022), I–IV
1993
40.
V. G. Bardakov, “To the theory of braid groups”, Sibirsk. Mat. Zh., 34:2 (1993), 220–221
Contact us: