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Natanzon, Sergey Mironovich
(1948–2020)

Statistics Math-Net.Ru
Total publications: 66
Scientific articles: 62
Presentations: 25

Number of views:
This page:2946
Abstract pages:17827
Full texts:6572
References:1894
Doctor of physico-mathematical sciences (2000)
Website: http://www.hse.ru/en/org/persons/14026884
Keywords: real algebraic geometry, moduli of complex and real algebraic curves and its superanalogs, quantum cohomology, Frobenius manifolds, integrable systems, quantum field theory, string theory.
UDC: 515.171.179.8, 512.7/78, 515.17/.179.8, 519.4, 515.1, 517.912, 517.9, 514.7, 512.7, 513.6
MSC: 57M12, 30F50, 20B30, 57M50, 57R56, 20C05, 14H10, 14G30, 4H99, 20H10, 30F35, 54H15, 57S99

Subject:

Real algebraic geometry. Moduli of complex and real algebraic curves and its superanalogs. Quantum cohomology. Frobenius manifolds. Integrable systems. Quantum field

   
Main publications:
  1. С. М. Натанзон, Moduli of Riemann surfaces, real algebraic curves, and their superanalogs, Translations of Mathematical Monographs, 225, American Mathematical Society, Providence, RI, 2004, 160 pp.  mathscinet

http://www.mathnet.ru/eng/person8969
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/129640

Publications in Math-Net.Ru
2021
1. M. E. Kazarian, S. K. Lando, S. M. Natanzon, “On framed simple purely real Hurwitz numbers”, Izv. RAN. Ser. Mat., 85:4 (2021),  69–95  mathnet; Izv. Math., 85:4 (2021), 681–704  isi  scopus
2020
2. S. M. Natanzon, A. Yu. Orlov, “Hurwitz numbers from Feynman diagrams”, TMF, 204:3 (2020),  396–429  mathnet  elib; Theoret. and Math. Phys., 204:3 (2020), 1166–1194  isi  scopus
2017
3. Sergey Natanzon, Anna Pratoussevitch, “Moduli spaces of higher spin Klein surfaces”, Mosc. Math. J., 17:2 (2017),  327–349  mathnet  mathscinet  isi
4. Anna Felikson, Sergey Natanzon, “Double pants decompositions revisited”, Mosc. Math. J., 17:1 (2017),  51–58  mathnet  mathscinet  isi
2016
5. Sergey Natanzon, Anna Pratoussevitch, “Higher spin Klein surfaces”, Mosc. Math. J., 16:1 (2016),  95–124  mathnet  mathscinet  isi
6. S. M. Natanzon, A. M. Pratusevich, “Classification of $m$-spin Klein surfaces”, Uspekhi Mat. Nauk, 71:2(428) (2016),  211–212  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 71:2 (2016), 382–384  isi  scopus
2011
7. Anna Felikson, Sergey Natanzon, “Labeled double pants decompositions”, Mosc. Math. J., 11:3 (2011),  505–519  mathnet  mathscinet  isi
8. Anna Felikson, Sergey Natanzon, “Double pants decompositions of 2-surfaces”, Mosc. Math. J., 11:2 (2011),  231–258  mathnet  mathscinet  isi
9. S. M. Natanzon, A. M. Pratusevich, “Moduli spaces of Gorenstein quasi-homogeneous surface singularities”, Uspekhi Mat. Nauk, 66:5(401) (2011),  189–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 66:5 (2011), 1009–1011  isi  elib  scopus
10. Sergey A. Loktev, Sergey M. Natanzon, “Klein Topological Field Theories from Group Representations”, SIGMA, 7 (2011), 070, 15 pp.  mathnet  mathscinet  isi  scopus
11. A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Complete set of cut-and-join operators in the Hurwitz–Kontsevich theory”, TMF, 166:1 (2011),  3–27  mathnet  mathscinet; Theoret. and Math. Phys., 166:1 (2011), 1–22  isi  scopus
2010
12. S. M. Natanzon, “Simple Hurwitz Numbers of a Disk”, Funktsional. Anal. i Prilozhen., 44:1 (2010),  44–58  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 44:1 (2010), 36–47  isi  scopus
2008
13. A. V. Alekseevskii, S. M. Natanzon, “The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces”, Izv. RAN. Ser. Mat., 72:4 (2008),  3–24  mathnet  mathscinet  zmath  elib; Izv. Math., 72:4 (2008), 627–646  isi  elib  scopus
2007
14. A. F. Costa, S. M. Natanzon, “Classification of $\mathbb Z_{p_k}^m$ orientation preserving actions on surfaces”, Mosc. Math. J., 7:3 (2007),  419–424  mathnet  mathscinet  zmath  isi
15. S. M. Natanzon, “Singularities and Noncommutative Frobenius Manifolds”, Trudy Mat. Inst. Steklova, 259 (2007),  143–155  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 259 (2007), 137–148  elib  scopus
2006
16. A. V. Alekseevskii, S. M. Natanzon, “Algebra of Hurwitz numbers for seamed surfaces”, Uspekhi Mat. Nauk, 61:4(370) (2006),  185–186  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 61:4 (2006), 767–769  isi  elib  scopus
2005
17. S. M. Natanzon, A. M. Pratusevich, “The topology of m–spinor structures on Riemann surfaces”, Uspekhi Mat. Nauk, 60:2(362) (2005),  169–170  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 60:2 (2005), 363–364  isi  scopus
2003
18. S. M. Natanzon, “Witten Solution for the Gelfand–Dikii Hierarchy”, Funktsional. Anal. i Prilozhen., 37:1 (2003),  25–37  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 37:1 (2003), 21–31  isi  scopus
19. S. M. Natanzon, “Effectivisation of a string solution of the $2D$ Toda hierarchy and the Riemann theorem about complex domains”, Mosc. Math. J., 3:2 (2003),  541–549  mathnet  mathscinet  zmath  isi  elib
20. S. M. Natanzon, “Симметрии поверхностей и вещественные алгебраические кривые”, Mat. Pros., Ser. 3, 7 (2003),  116–125  mathnet
2001
21. S. M. Natanzon, “Formal series for the $\tau$-function realizing Riemann's theorem about domains in the complex plane”, Uspekhi Mat. Nauk, 56:4(340) (2001),  155–156  mathnet  mathscinet  zmath; Russian Math. Surveys, 56:4 (2001), 760–761  isi  scopus
2000
22. S. M. Natanzon, “Recurrence Formulas for $A_n$- and $B_n$-Solutions of the WDVV Equations”, Funktsional. Anal. i Prilozhen., 34:3 (2000),  81–84  mathnet  mathscinet  zmath; Funct. Anal. Appl., 34:3 (2000), 226–228  isi
23. S. M. Natanzon, S. V. Shadrin, “Topological classification of unitary functions of arbitrary genus”, Uspekhi Mat. Nauk, 55:6(336) (2000),  151–152  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:6 (2000), 1163–1164  isi  scopus
1999
24. S. M. Natanzon, “Moduli of real algebraic surfaces, and their superanalogues. Differentials, spinors, and Jacobians of real curves”, Uspekhi Mat. Nauk, 54:6(330) (1999),  3–60  mathnet  mathscinet  zmath; Russian Math. Surveys, 54:6 (1999), 1091–1147  isi  scopus
25. S. M. Natanzon, “Moduli of Riemann surfaces, Hurwitz-type spaces, and their superanalogues”, Uspekhi Mat. Nauk, 54:1(325) (1999),  61–116  mathnet  mathscinet  zmath; Russian Math. Surveys, 54:1 (1999), 61–117  isi  scopus
1998
26. S. M. Natanzon, “The topological structure of the space of holomorphic morphisms of Riemann surfaces”, Uspekhi Mat. Nauk, 53:2(320) (1998),  155–156  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:2 (1998), 398–400  isi  scopus
1997
27. S. M. Natanzon, “On compatible Poisson structures of hydrodynamic type”, Uspekhi Mat. Nauk, 52:6(318) (1997),  173–174  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:6 (1997), 1314–1315  isi  scopus
1996
28. S. M. Natanzon, “Moduli Spaces of Real Algebraic $N=2$ Supercurves”, Funktsional. Anal. i Prilozhen., 30:4 (1996),  19–30  mathnet  mathscinet  zmath; Funct. Anal. Appl., 30:4 (1996), 237–245  isi
29. S. M. Natanzon, “Real borderings of complex algebraic curves and Coxeter groups”, Uspekhi Mat. Nauk, 51:6(312) (1996),  215–216  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:6 (1996), 1216–1217  isi  scopus
1995
30. S. M. Natanzon, “Trigonometric tensors on algebraic curves of arbitrary genus. An analogue of the Sturm–Hurwitz theorem”, Uspekhi Mat. Nauk, 50:6(306) (1995),  199–200  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:6 (1995), 1286–1287  isi
31. S. M. Natanzon, “On quadratic forms over the field $\mathbb Z_2$”, Uspekhi Mat. Nauk, 50:5(305) (1995),  243–244  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:5 (1995), 1090–1091  isi
1994
32. S. M. Natanzon, “Classification of Pairs of Arf Functions on Orientable and Nonorientable Surfaces”, Funktsional. Anal. i Prilozhen., 28:3 (1994),  35–46  mathnet  mathscinet  zmath; Funct. Anal. Appl., 28:3 (1994), 178–186  isi
1993
33. S. M. Natanzon, “Topological types of actions of the group $(Z/2Z)^n$ on surfaces”, Uspekhi Mat. Nauk, 48:2(290) (1993),  195–196  mathnet  mathscinet  zmath; Russian Math. Surveys, 48:2 (1993), 199–200  isi
34. S. M. Natanzon, “Topological invariants and moduli of hyperbolic $n=2$ Riemann supersurfaces”, Mat. Sb., 184:5 (1993),  19–38  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 79:1 (1994), 15–31  isi
1992
35. S. M. Natanzon, “Differential equations on the Prym theta function. a realness criterion for two-dimensional, finite-zone, potential Schrödinger operators”, Funktsional. Anal. i Prilozhen., 26:1 (1992),  17–26  mathnet  mathscinet  zmath; Funct. Anal. Appl., 26:1 (1992), 13–20  isi
36. S. M. Natanzon, “A topological classification of a pair of spinor forms on surfaces”, Uspekhi Mat. Nauk, 47:1(283) (1992),  215–216  mathnet  mathscinet  zmath; Russian Math. Surveys, 47:1 (1992), 265–266  isi
1991
37. S. M. Natanzon, “Discrete subgroups of $GL(2,C)$ and spinor bundles on Riemann and Klein surfaces”, Funktsional. Anal. i Prilozhen., 25:4 (1991),  76–78  mathnet  mathscinet  zmath; Funct. Anal. Appl., 25:4 (1991), 293–294  isi
1990
38. S. M. Natanzon, “Klein supersurfaces”, Mat. Zametki, 48:2 (1990),  72–82  mathnet  mathscinet  zmath; Math. Notes, 48:2 (1990), 766–772  isi
39. S. M. Natanzon, “Klein surfaces”, Uspekhi Mat. Nauk, 45:6(276) (1990),  47–90  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:5 (1990), 53–108  isi
40. S. M. Natanzon, “Supercoverings, $SNEC$-groups, and interior groups of Riemann and Klein supersurfaces”, Uspekhi Mat. Nauk, 45:2(272) (1990),  217–218  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:2 (1990), 225–226  isi
1989
41. S. M. Natanzon, “Prymians of real curves and their applications to the effectivization of Schrödinger operators”, Funktsional. Anal. i Prilozhen., 23:1 (1989),  41–56  mathnet  mathscinet  zmath; Funct. Anal. Appl., 23:1 (1989), 33–45  isi
42. S. M. Natanzon, “Moduli space of super–Riemann surfaces”, Mat. Zametki, 45:4 (1989),  111–116  mathnet  mathscinet  zmath; Math. Notes, 45:4 (1989), 341–345  isi
43. S. M. Natanzon, “Spinor bundles over real algebraic curves”, Uspekhi Mat. Nauk, 44:3(267) (1989),  165–166  mathnet  mathscinet  zmath; Russian Math. Surveys, 44:3 (1989), 208–209  isi
1988
44. S. M. Natanzon, “Nonsingular finite-zone two-dimensional Schrödinger operators and prymians of real curves”, Funktsional. Anal. i Prilozhen., 22:1 (1988),  79–80  mathnet  mathscinet  zmath; Funct. Anal. Appl., 22:1 (1988), 68–70  isi
45. B. A. Dubrovin, S. M. Natanzon, “Real theta-function solutions of the Kadomtsev–Petviashvili equation”, Izv. Akad. Nauk SSSR Ser. Mat., 52:2 (1988),  267–286  mathnet  mathscinet  zmath; Math. USSR-Izv., 32:2 (1989), 269–288
46. S. M. Natanzon, “Finite groups of homeomorphisms of surfaces, and real forms of complex algebraic curves”, Tr. Mosk. Mat. Obs., 51 (1988),  3–53  mathnet  mathscinet  zmath
47. S. M. Natanzon, “Topological type and moduli of Riemannian and Klein supersurfaces”, Zap. Nauchn. Sem. LOMI, 167 (1988),  179–185  mathnet  mathscinet  zmath
1987
48. S. M. Natanzon, “Real meromorphic functions on real algebraic curves”, Dokl. Akad. Nauk SSSR, 297:1 (1987),  40–43  mathnet  mathscinet  zmath; Dokl. Math., 36:3 (1988), 425–427
49. S. M. Natanzon, “The Fricke space of super-Fuchsian groups”, Funktsional. Anal. i Prilozhen., 21:2 (1987),  80–81  mathnet  mathscinet  zmath; Funct. Anal. Appl., 21:2 (1987), 158–159  isi
1986
50. S. M. Natanzon, “Uniformization of spaces of meromorphic functions”, Dokl. Akad. Nauk SSSR, 287:5 (1986),  1058–1061  mathnet  mathscinet  zmath
51. S. M. Natanzon, “Topological classification of pairs of commuting antiholomorphic involutions of Riemann surfaces”, Uspekhi Mat. Nauk, 41:5(251) (1986),  191–192  mathnet  mathscinet; Russian Math. Surveys, 41:5 (1986), 159–160  isi
1984
52. S. M. Natanzon, “Spaces of real meromorphic functions on real algebraic curves”, Dokl. Akad. Nauk SSSR, 279:4 (1984),  803–805  mathnet  mathscinet  zmath
1982
53. B. A. Dubrovin, S. M. Natanzon, “Real two-zone solutions of the sine-Gordon equation”, Funktsional. Anal. i Prilozhen., 16:1 (1982),  27–43  mathnet  mathscinet  zmath; Funct. Anal. Appl., 16:1 (1982), 21–33  isi
1980
54. S. M. Natanzon, “The total number of ovals of four complex-isomorphic real algebraic curves”, Uspekhi Mat. Nauk, 35:4(214) (1980),  184  mathnet  mathscinet  zmath; Russian Math. Surveys, 35:4 (1980), 177  isi
55. S. M. Natanzon, “On the total number of ovals of real forms of a complex algebraic curve”, Uspekhi Mat. Nauk, 35:1(211) (1980),  207–208  mathnet  mathscinet  zmath; Russian Math. Surveys, 35:1 (1980), 223–224  isi
1979
56. S. M. Natanzon, “Automorphisms and real forms of a class of complex algebraic curves”, Funktsional. Anal. i Prilozhen., 13:2 (1979),  89–90  mathnet  mathscinet  zmath; Funct. Anal. Appl., 13:2 (1979), 148–150
1978
57. S. M. Natanzon, “On the order of a finite group of homeomorphisms of a surface onto itself and the number of real forms of a complex algebraic curve”, Dokl. Akad. Nauk SSSR, 242:4 (1978),  765–768  mathnet  mathscinet  zmath
58. S. M. Natanzon, “Automorphisms of the Riemann surface of an $M$-curve”, Funktsional. Anal. i Prilozhen., 12:3 (1978),  82–83  mathnet  mathscinet  zmath; Funct. Anal. Appl., 12:3 (1978), 228–229
59. S. M. Natanzon, “Spaces of moduli of real curves”, Tr. Mosk. Mat. Obs., 37 (1978),  219–253  mathnet  mathscinet  zmath
1975
60. S. M. Natanzon, “Moduli of real algebraic curves”, Uspekhi Mat. Nauk, 30:1(181) (1975),  251–252  mathnet  mathscinet  zmath
1972
61. S. M. Natanzon, “Invariant lines of Fuchsian groups”, Uspekhi Mat. Nauk, 27:4(166) (1972),  145–160  mathnet  mathscinet  zmath; Russian Math. Surveys, 27:4 (1972), 161–177
1970
62. S. E. Kuznetsov, S. M. Natanzon, “A certain functional equation that has applications in game theory”, Sibirsk. Mat. Zh., 11:1 (1970),  128–136  mathnet  mathscinet  zmath; Siberian Math. J., 11:1 (1970), 105–111

2010
63. V. M. Buchstaber, L. O. Chekhov, S. Yu. Dobrokhotov, S. M. Gusein-Zade, Yu. S. Ilyashenko, S. M. Natanzon, S. P. Novikov, G. I. Olshanski, A. K. Pogrebkov, O. K. Sheinman, S. B. Shlosman, M. A. Tsfasman, “Igor Krichever”, Mosc. Math. J., 10:4 (2010),  833–834  mathnet
2009
64. V. Buchstaber, S. Gusein-Zade, Yu. Ilyashenko, A. Kirillov, I. Krichever, S. Natanzon, S. Novikov, A. Sergeev, A. Sossinsky, M. Tsfasman, “Oleg Sheinman”, Mosc. Math. J., 9:3 (2009),  723–724  mathnet
65. V. Buchstaber, S. Gusein-Zade, Yu. Ilyashenko, V. Kozlov, S. Natanzon, O. Sheinman, A. Sossinsky, D. Treschev, M. Tsfasman, “Armen Sergeev”, Mosc. Math. J., 9:2 (2009),  439–440  mathnet  mathscinet
1987
66. S. M. Natanzon, “Erratum”, Uspekhi Mat. Nauk, 42:2(254) (1987),  283  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:2 (1987), 311  isi

Presentations in Math-Net.Ru
1. Dubrovin-Frobenius manifolds
S. M. Natanzon
Automorphic forms and their applications
November 19, 2019 18:00
2. Формальные решения иерархии h-КП
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
September 19, 2018 18:30
3. Бездисперсионная 2D Тода иерархия, числа Гурвица и теорема Римана
S. M. Natanzon
Knots and Representation Theory
April 24, 2018 18:30
4. Dispersionless 2d Toda hierarchy, Hurwitz numbers and Riemann theorem
S. M. Natanzon
Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
March 14, 2018 14:00
5. Higher spin Riemann and Klein surfaces
S. Natanzon
Transformation groups 2017. Conference dedicated to Prof. Ernest B. Vinberg on the occasion of his 80th birthday
December 14, 2017 14:30
6. Клейновы пены
S. M. Natanzon

May 25, 2017 10:20   
7. KP and n-KdV hierarchies and its solutions
S. M. Natanzon
Complex analysis and mathematical physics
April 11, 2017 16:00
8. Formal solution to the h-KP hierarchy
S. M. Natanzon
5th Workshop on Combinatorics of Moduli Spaces, Hurwitz Spaces and Cohomological Field Theories
June 10, 2016 16:00   
9. Symmetric solutions of the dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics
S. M. Natanzon
International Conference on Mathematical Control Theory and Mechanics
July 5, 2015 09:40
10. Двумерные топологические теории поля
S. M. Natanzon
Knots and Representation Theory
November 11, 2014 18:30
11. Construction of conformal maps via integrable systems
S. M. Natanzon
The International Conference "Geometric Control Theory and Analysis on Metric Structures"
August 5, 2014 11:00
12. Symmetric solutions to dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics
S. M. Natanzon
Fourth international workshop "Combinatorics of Moduli Spaces, Cluster Algebras and Topological Recursion"
May 31, 2014 11:00
13. Симметричные решения бездисперсионной 2D-Тода иерархии и числа Гурвица
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
August 7, 2013 14:00
14. Foam Hurwitz operators realizing open-closed strings
S. M. Natanzon
International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold
December 21, 2012 14:30   
15. Full algebra of cut-and-join operators
S. M. Natanzon
International conference "Geometrical Methods in Mathematical Physics"
December 12, 2011 16:00   
16. Полная алгебра Cut-and-Join операторов
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
September 28, 2011 18:30
17. Топологические инварианты и пространства модулей квази-однородных горенштеновых особенностей
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
November 10, 2010 18:30
18. Алгебра Cut-and-Join операторов
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
July 28, 2010 14:00
19. Клейнова пена
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
March 24, 2010 18:30
20. Топологическая теория струн
S. M. Natanzon
Meetings of the Moscow Mathematical Society
March 17, 2009
21. Числа Гурвица накрытий Смита–Дольда
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
October 1, 2008
22. Topological field theories
S. M. Natanzon
Meetings of the St. Petersburg Mathematical Society
June 14, 2005
23. Топологические теории поля
S. M. Natanzon
Meetings of the Moscow Mathematical Society
March 29, 2005
24. Пространство модулей $m$-spin структур
S. M. Natanzon
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
November 24, 2004
25. Topological field theory and Hurwitz numbers (based on a joint work with A. V. Alekseevsky)
S. M. Natanzon
Lie groups and invariant theory
April 7, 2004 16:20

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