Leksin, Vladimir Pavlovich

Statistics Math-Net.Ru
Total publications: 24
Scientific articles: 20
Presentations: 11

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This page:2799
Abstract pages:9803
Full texts:5003
Associate professor
Doctor of physico-mathematical sciences (2005)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 27.05.1949
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. V. P. Leksin, “Linear Pfaffian Systems and Classical Solutions of Triangular Schlesinger Equations”, Trudy Mat. Inst. Steklova, 308 (2020),  210–221  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 308 (2020), 196–207  isi  scopus
2. V. P. Lexin, “Schlesinger's equations for upper triangular matrices and their solutions”, CMFD, 64:1 (2018),  86–97  mathnet
3. V. P. Leksin, “Kohno systems on Manin–Schechtman configuration spaces”, CMFD, 46 (2012),  120–128  mathnet; Journal of Mathematical Sciences, 201:6 (2014), 796–804  scopus
4. V. P. Leksin, “Multidimensional Jordan–Pochhammer systems and their applications”, Trudy Mat. Inst. Steklova, 278 (2012),  138–147  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 278 (2012), 130–138  isi  elib  scopus
5. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Uspekhi Mat. Nauk, 66:1(397) (2011),  3–36  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 66:1 (2011), 1–33  isi  elib  scopus
6. V. P. Leksin, “Topology of Complements of Hyperplane Arrangements and Isomonodromic Deformations of Fuchsian Systems”, Trudy Mat. Inst. Steklova, 267 (2009),  198–203  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 267 (2009), 190–194  isi  elib  scopus
7. V. P. Leksin, “Monodromy of Fuchsian Systems on Complex Linear Spaces”, Trudy Mat. Inst. Steklova, 256 (2007),  267–277  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 256 (2007), 253–262  elib  scopus
8. V. P. Leksin, “The Lappo–Danilevskii method and trivial intersections of radicals in lower central series terms for certain fundamental groups”, Mat. Zametki, 79:4 (2006),  577–580  mathnet  mathscinet  zmath  elib; Math. Notes, 79:4 (2006), 533–536  isi  scopus
9. S. V. Alenov, V. P. Leksin, “On Diagram Formulas for Knot Invariants”, Trudy Mat. Inst. Steklova, 252 (2006),  10–17  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 252 (2006), 4–11  scopus
10. V. P. Leksin, “A. A. Bolibrukh's works on multidimensional regular and Fuchsian systems”, Uspekhi Mat. Nauk, 59:6(360) (2004),  151–160  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:6 (2004), 1155–1164  isi  scopus
11. V. A. Golubeva, V. P. Leksin, “Algebraic Characterization of the Monodromy of Generalized Knizhnik–Zamolodchikov Equations of $B_n$ Type”, Trudy Mat. Inst. Steklova, 238 (2002),  124–143  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 238 (2002), 115–133
12. V. P. Leksin, “Doubling Operations and Monodromy of Generalized Knizhnik–Zamolodchikov Equations”, Trudy Mat. Inst. Steklova, 236 (2002),  218–225  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 236 (2002), 206–213
13. V. A. Golubeva, V. P. Leksin, “Quadratic Relations in the Cohomology of Generalized Pure Braids and Dunkl Identities”, Funktsional. Anal. i Prilozhen., 30:2 (1996),  73–76  mathnet  mathscinet  zmath; Funct. Anal. Appl., 30:2 (1996), 131–134  isi
14. V. A. Golubeva, V. P. Leksin, “On reconstruction of Veselov–Felder formula in the theory of Calogero–Sutherland operators”, TMF, 106:1 (1996),  62–75  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 106:1 (1996), 50–60  isi
15. M. P. Zamakhovskii, V. P. Leksin, “Vector version of the Matsuo–Cherednik equation for the root system $G_ 2$”, Mat. Zametki, 58:3 (1995),  456–460  mathnet  mathscinet  zmath; Math. Notes, 58:3 (1995), 992–996  isi
16. V. A. Golubeva, V. P. Leksin, “Complete integrability of generalized Knizhnik–Zamolodchikov equations of trigonometric type”, Uspekhi Mat. Nauk, 50:3(303) (1995),  151–152  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:3 (1995), 615–617  isi
17. V. A. Golubeva, V. P. Leksin, “Generalized Knizhnik–Zamolodchikov equations and the factorization of their solutions”, Mat. Zametki, 54:5 (1993),  25–34  mathnet  mathscinet  zmath  elib; Math. Notes, 54:5 (1993), 1100–1105  isi
18. V. A. Golubeva, V. P. Leksin, “Exponential representation of solutions of Pfaffian systems (the one-parameter case)”, Differ. Uravn., 27:9 (1991),  1526–1538  mathnet  mathscinet  zmath; Differ. Equ., 27:9 (1991), 1078–1088
19. V. P. Leksin, “Riemann–Hilbert problem for analytic families of representations”, Mat. Zametki, 50:2 (1991),  89–97  mathnet  mathscinet  zmath; Math. Notes, 50:2 (1991), 823–838
20. V. P. Leksin, “Meromorphic Pfaffian systems on complex projective spaces”, Mat. Sb. (N.S.), 129(171):2 (1986),  201–217  mathnet  mathscinet  zmath; Math. USSR-Sb., 57:1 (1987), 211–227

21. 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, “Dmitrii Viktorovich Anosov (obituary)”, Uspekhi Mat. Nauk, 70:2(422) (2015),  181–191  mathnet  mathscinet  elib; Russian Math. Surveys, 70:2 (2015), 369–381  isi
22. 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, “Reminiscences about Andrei Andreevich Bolibrukh”, Uspekhi Mat. Nauk, 59:6(360) (2004),  207–215  mathnet  mathscinet; Russian Math. Surveys, 59:6 (2004), 1213–1224  isi
23. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh in life and science (30 January 1950 – 11 November 2003)”, Uspekhi Mat. Nauk, 59:6(360) (2004),  3–22  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:6 (2004), 1009–1028  isi
24. 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, “Andrei Andreevich Bolibrukh (obituary)”, Uspekhi Mat. Nauk, 58:6(354) (2003),  139–142  mathnet  mathscinet  zmath; Russian Math. Surveys, 58:6 (2003), 1185–1189  isi

Presentations in Math-Net.Ru
1. О линейных системах Веселова и их решениях
V. P. Leksin
Seminar on analytic theory of differential equations
June 5, 2019 14:30
2. Anosov's theorem on the Lefshetz and Nilson numbers
V. P. Leksin
Seminar on analytic theory of differential equations
November 30, 2016 15:20   
3. Трехточечный интеграл Концевича для кос
V. P. Leksin
Knots and Representation Theory
October 18, 2016 18:30
4. Интеграл Концевича для кос Артина и Брискорна
V. P. Leksin
Knots and Representation Theory
May 12, 2015 18:30
5. Заседание посвящено памяти Дмитрия Викторовича Аносова
A. M. Stepin, L. M. Lerman, V. Z. Grines, S. Yu. Pilyugin, M. I. Zelikin, V. P. Leksin, A. V. Klimenko, Yu. S. Ilyashenko
Meetings of the Moscow Mathematical Society
April 7, 2015
6. Теорема Аносова о числах Нильсена для нильмногообразий
V. M. Buchstaber, V. P. Leksin
Algebraic topology and its applications. Postnikov memorial seminar
October 14, 2014 16:45
7. Linear reduction of Schlesinger equations and their solutions
V. P. Leksin
The Seventh International Conference on Differential and Functional Differential Equations
August 25, 2014 16:40   
8. Regularization of improper integrals and solutions of linear meromorphic differential equations
V. P. Leksin
International Conference on Differential Equations and Dynamical Systems
July 7, 2014 14:30
9. Линейные фуксовы системы на конфигурационных пространствах
V. P. Leksin
P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics
March 5, 2012 18:30
10. Seminar dedicated to the 60th anniversary of the birthday of academician A. A. Bolibrukh
D. V. Anosov, Yu. S. Ilyashenko, V. P. Leksin, R. R. Gontsov
Steklov Mathematical Institute Seminar
April 22, 2010 16:00   
11. О работах А. А. Болибруха по многомерным фуксовым системам и изомонодромным деформациям
V. P. Leksin
Meetings of the Moscow Mathematical Society
December 28, 2004

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