Leksin Vladimir Pavlovich

Statistics Math-Net.Ru
Total publications: 22
Scientific articles: 18
Cited articles: 11
Citations in Math-Net.Ru: 19
Presentations: 10

Number of views:
This page:1138
Abstract pages:6145
Full texts:2942
Associate professor
Doctor of physico-mathematical sciences (2005)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 27.05.1949
Phone: +7 (4966) 13 32 87
Fax: +7 (4966) 13 25 62
E-mail: ,
Keywords: differential equation on complex manifolds; monodromy and isomonodromy deformation equations; KZ equation associated with different Coxeter groups and their monodromy; knots and links with additional symmetries and their finite order invarints; quantum integrable models of the Calogero–Moser–Sutherland type; bispectral problem for KZ operators and their connections Isomonodromic deformations.
UDC: 512.54, 513.83, 513.838, 514, 517.538, 517.774, 517.93, 519.1, 519.4, 517.9, 517.925
MSC: 34M45, 32G34, 34M55, 34M50, 57M27, 33C70, 33D80, 20F36, 20F55


For linear pfaffian systems of the Fuchs type on complex manifolds, the Frobenius conditions of the integrability were expressed across iterated Chen integrals and commutator relations in fundamental group of complement to the singularity divisor of the system. The multi-dimensional generalization of the Lappo–Danilevskii theory for fuchsian systems on complex projective spaces was formulated. For any hyperplane configuration in a complex projective space and an analytic deformation of the unit representation of the fundamental group of the complement to the hyperplane configuration the multi-dimensional Riemann–Hilbert problem is solved. The universal KZ operators (uKZ) and universal Calogero–Mozer–Sutherland(uCMS) hamiltonians associated to a root system are defined. On Bete and Dunkl manifolds are defined. The connections between uKZ and uCMS on Bete–Dunkl manifolds were studied. The $B_n$-Coxeter analog of the Drinfeld theory of the braided quasi-bialgebras and the $B_n$-analog of the main theorem in this theory (Drinfeld-Kohno theorem) was formulated and proved. On base of the $B_n$ quasi-bialgebra theory the universal Kontsevich–Vassiliev invarint of knots and links with additional order two symmetry was constructed. With point of view of the KZ equations the characterization of a simplest solutions of Schlesinger equations was given.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1972 (department higher geometry and topology). Ph.D. thesis was defended in 1991. A list of my works contains more than 30 titles. Since 1990 I and V. A. Golubeva and E. E. Petrov have lrd the research seminar in Kolomna State Pedagogical Institute.

Main publications:
  • Golubeva V. A., Leksin V. P. On two types of representations of the braid groups associated with the Knizhnik–Zamolodchikov equations // Journal Dynamical and Control Systems, 1999, 5, no. 4, 565–596.
  • Lexin V. P. Monodromy for the KZ equations of the $B_n$ type and accompanying algebraic structures // Functional Differential Equations, 2001, 8, no. 3–4, 330–344.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. Kohno systems on Manin–Schechtman configuration spaces
V. P. Leksin
CMFD, 46 (2012),  120–128
2. Multidimensional Jordan–Pochhammer systems and their applications
V. P. Leksin
Tr. Mat. Inst. Steklova, 278 (2012),  138–147
3. Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations
D. V. Anosov, V. P. Leksin
Uspekhi Mat. Nauk, 66:1(397) (2011),  3–36
4. Topology of Complements of Hyperplane Arrangements and Isomonodromic Deformations of Fuchsian Systems
V. P. Leksin
Tr. Mat. Inst. Steklova, 267 (2009),  198–203
5. Monodromy of Fuchsian Systems on Complex Linear Spaces
V. P. Leksin
Tr. Mat. Inst. Steklova, 256 (2007),  267–277
6. The Lappo–Danilevskii method and trivial intersections of radicals in lower central series terms for certain fundamental groups
V. P. Leksin
Mat. Zametki, 79:4 (2006),  577–580
7. On Diagram Formulas for Knot Invariants
S. V. Alenov, V. P. Leksin
Tr. Mat. Inst. Steklova, 252 (2006),  10–17
8. A. A. Bolibrukh's works on multidimensional regular and Fuchsian systems
V. P. Leksin
Uspekhi Mat. Nauk, 59:6(360) (2004),  151–160
9. Algebraic Characterization of the Monodromy of Generalized Knizhnik–Zamolodchikov Equations of $B_n$ Type
V. A. Golubeva, V. P. Leksin
Tr. Mat. Inst. Steklova, 238 (2002),  124–143
10. Doubling Operations and Monodromy of Generalized Knizhnik–Zamolodchikov Equations
V. P. Leksin
Tr. Mat. Inst. Steklova, 236 (2002),  218–225
11. Quadratic Relations in the Cohomology of Generalized Pure Braids and Dunkl Identities
V. A. Golubeva, V. P. Leksin
Funktsional. Anal. i Prilozhen., 30:2 (1996),  73–76
12. On reconstruction of Veselov–Felder formula in the theory of Calogero–Sutherland operators
V. A. Golubeva, V. P. Leksin
TMF, 106:1 (1996),  62–75
13. Vector version of the Matsuo–Cherednik equation for the root system $G_ 2$
M. P. Zamakhovskii, V. P. Leksin
Mat. Zametki, 58:3 (1995),  456–460
14. Complete integrability of generalized Knizhnik–Zamolodchikov equations of trigonometric type
V. A. Golubeva, V. P. Leksin
Uspekhi Mat. Nauk, 50:3(303) (1995),  151–152
15. Generalized Knizhnik–Zamolodchikov equations and the factorization of their solutions
V. A. Golubeva, V. P. Leksin
Mat. Zametki, 54:5 (1993),  25–34
16. Exponential representation of solutions of Pfaffian systems (the one-parameter case)
V. A. Golubeva, V. P. Leksin
Differ. Uravn., 27:9 (1991),  1526–1538
17. Riemann–Hilbert problem for analytic families of representations
V. P. Leksin
Mat. Zametki, 50:2 (1991),  89–97
18. Meromorphic Pfaffian systems on complex projective spaces
V. P. Leksin
Mat. Sb. (N.S.), 129(171):2 (1986),  201–217

19. Dmitrii Viktorovich Anosov (obituary)
S. M. Aseev, V. M. Buchstaber, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, A. A. Davydov, A. Yu. Zhirov, E. V. Zhuzhoma, M. I. Zelikin, A. B. Katok, A. V. Klimenko, V. V. Kozlov, V. P. Leksin, M. I. Monastyrskii, A. I. Neishtadt, S. P. Novikov, E. A. Sataev, Ya. G. Sinai, A. M. Stepin
Uspekhi Mat. Nauk, 70:2(422) (2015),  181–191
20. Reminiscences about Andrei Andreevich Bolibrukh
A. V. Chernavskii, V. P. Leksin, M. Butuzov, I. V. Vyugin, R. R. Gontsov, V. A. Poberezhnyi, Yu. S. Ilyashenko, A. G. Sergeev, S. P. Konovalov
Uspekhi Mat. Nauk, 59:6(360) (2004),  207–215
21. Andrei Andreevich Bolibrukh in life and science (30 January 1950 – 11 November 2003)
D. V. Anosov, V. P. Leksin
Uspekhi Mat. Nauk, 59:6(360) (2004),  3–22
22. Andrei Andreevich Bolibrukh (obituary)
D. V. Anosov, V. I. Arnol'd, V. M. Buchstaber, V. A. Golubeva, A. A. Gonchar, A. B. Zhizhchenko, Yu. S. Ilyashenko, V. V. Kozlov, S. P. Konovalov, L. D. Kudryavtsev, V. P. Leksin, O. B. Lupanov, A. A. Mal'tsev, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, M. M. Postnikov, V. A. Sadovnichii, A. G. Sergeev, L. D. Faddeev, A. V. Chernavskii
Uspekhi Mat. Nauk, 58:6(354) (2003),  139–142

Presentations in Math-Net.Ru
1. Anosov's theorem on the Lefshetz and Nilson numbers
Seminar on analytic theory of differential equations
November 30, 2016 15:20   
2. Трехточечный интеграл Концевича для кос
Knots and Representation Theory
October 18, 2016 18:30
3. Интеграл Концевича для кос Артина и Брискорна
Knots and Representation Theory
May 12, 2015 18:30
4. Заседание посвящено памяти Дмитрия Викторовича Аносова
Meetings of the Moscow Mathematical Society
April 7, 2015
5. Теорема Аносова о числах Нильсена для нильмногообразий
Algebraic topology and its applications. Postnikov memorial seminar
October 14, 2014 16:45
6. Linear reduction of Schlesinger equations and their solutions
The Seventh International Conference on Differential and Functional Differential Equations
August 25, 2014 16:40   
7. Regularization of improper integrals and solutions of linear meromorphic differential equations
International Conference on Differential Equations and Dynamical Systems
July 7, 2014 14:30
8. Линейные фуксовы системы на конфигурационных пространствах
P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics
March 5, 2012 18:30
9. Seminar dedicated to the 60th anniversary of the birthday of academician A. A. Bolibrukh
Steklov Mathematical Institute Seminar
April 22, 2010 16:00   
10. О работах А. А. Болибруха по многомерным фуксовым системам и изомонодромным деформациям
Meetings of the Moscow Mathematical Society
December 28, 2004

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