Persons: Natanzon, Sergey Mironovich

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Natanzon, Sergey Mironovich
(1948–2020)

Statistics Math-Net.Ru
in MathSciNet:	61 (59)
in zbMATH:	53 (52)
in Web of Science:	49 (48)
in Scopus:	21 (21)

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:

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.

https://www.mathnet.ru/eng/person8969

List of publications on Google Scholar

https://mathscinet.ams.org/mathscinet/MRAuthorID/129640

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

Articles

1.	M. E. Kazarian, S. K. Lando, S. M. Natanzon, “On framed simple purely real Hurwitz numbers”, Izv. Math., 85:4 (2021), 681–704
2.	S. M. Natanzon, A. Yu. Orlov, “Hurwitz numbers from Feynman diagrams”, Theoret. and Math. Phys., 204:3 (2020), 1172–1200
3.	Anna Felikson, Sergey Natanzon, “Double pants decompositions revisited”, Mosc. Math. J., 17:1 (2017), 51–58
4.	Sergey Natanzon, Anna Pratoussevitch, “Moduli spaces of higher spin Klein surfaces”, Mosc. Math. J., 17:2 (2017), 327–349	1 ^[x]
5.	S. M. Natanzon, A. M. Pratusevich, “Classification of $m$-spin Klein surfaces”, Russian Math. Surveys, 71:2 (2016), 382–384
6.	Sergey Natanzon, Anna Pratoussevitch, “Higher spin Klein surfaces”, Mosc. Math. J., 16:1 (2016), 95–124	3 ^[x]
7.	Anna Felikson, Sergey Natanzon, “Labeled double pants decompositions”, Mosc. Math. J., 11:3 (2011), 505–519
8.	Anna Felikson, Sergey Natanzon, “Double pants decompositions of 2-surfaces”, Mosc. Math. J., 11:2 (2011), 231–258	2 ^[x]
9.	S. M. Natanzon, A. M. Pratusevich, “Moduli spaces of Gorenstein quasi-homogeneous surface singularities”, Russian Math. Surveys, 66:5 (2011), 1009–1011
10.	Sergey A. Loktev, Sergey M. Natanzon, “Klein Topological Field Theories from Group Representations”, SIGMA, 7 (2011), 70–15	5 ^[x]
11.	A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Complete set of cut-and-join operators in the Hurwitz–Kontsevich theory”, Theoret. and Math. Phys., 166:1 (2011), 1–22
12.	S. M. Natanzon, “Simple Hurwitz Numbers of a Disk”, Funct. Anal. Appl., 44:1 (2010), 36–47
13.	A. V. Alekseevskii, S. M. Natanzon, “The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces”, Izv. Math., 72:4 (2008), 627–646
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	2 ^[x]
15.	S. M. Natanzon, “Singularities and Noncommutative Frobenius Manifolds”, Proc. Steklov Inst. Math., 259 (2007), 137–148
16.	A. V. Alekseevskii, S. M. Natanzon, “Algebra of Hurwitz numbers for seamed surfaces”, Russian Math. Surveys, 61:4 (2006), 767–769
17.	S. M. Natanzon, A. M. Pratusevich, “The topology of m–spinor structures on Riemann surfaces”, Russian Math. Surveys, 60:2 (2005), 363–364
18.	S. M. Natanzon, “Witten Solution for the Gelfand–Dikii Hierarchy”, Funct. Anal. Appl., 37:1 (2003), 21–31
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	6 ^[x]
20.	S. M. Natanzon, “Formal series for the $\tau$-function realizing Riemann's theorem about domains in the complex plane”, Russian Math. Surveys, 56:4 (2001), 760–761
21.	S. M. Natanzon, “Recurrence Formulas for $A_n$- and $B_n$-Solutions of the WDVV Equations”, Funct. Anal. Appl., 34:3 (2000), 226–228
22.	S. M. Natanzon, S. V. Shadrin, “Topological classification of unitary functions of arbitrary genus”, Russian Math. Surveys, 55:6 (2000), 1163–1164
23.	S. M. Natanzon, “Moduli of real algebraic surfaces, and their superanalogues. Differentials, spinors, and Jacobians of real curves”, Russian Math. Surveys, 54:6 (1999), 1091–1147
24.	S. M. Natanzon, “Moduli of Riemann surfaces, Hurwitz-type spaces, and their superanalogues”, Russian Math. Surveys, 54:1 (1999), 61–117
25.	S. M. Natanzon, “The topological structure of the space of holomorphic morphisms of Riemann surfaces”, Russian Math. Surveys, 53:2 (1998), 398–400
26.	S. M. Natanzon, “On compatible Poisson structures of hydrodynamic type”, Russian Math. Surveys, 52:6 (1997), 1314–1315
27.	S. M. Natanzon, “Moduli Spaces of Real Algebraic $N=2$ Supercurves”, Funct. Anal. Appl., 30:4 (1996), 237–245
28.	S. M. Natanzon, “Real borderings of complex algebraic curves and Coxeter groups”, Russian Math. Surveys, 51:6 (1996), 1216–1217
29.	S. M. Natanzon, “Trigonometric tensors on algebraic curves of arbitrary genus. An analogue of the Sturm–Hurwitz theorem”, Russian Math. Surveys, 50:6 (1995), 1286–1287
30.	S. M. Natanzon, “On quadratic forms over the field $\mathbb Z_2$”, Russian Math. Surveys, 50:5 (1995), 1090–1091
31.	S. M. Natanzon, “Classification of Pairs of Arf Functions on Orientable and Nonorientable Surfaces”, Funct. Anal. Appl., 28:3 (1994), 178–186
32.	S. M. Natanzon, “Topological types of actions of the group $(Z/2Z)^n$ on surfaces”, Russian Math. Surveys, 48:2 (1993), 199–200
33.	S. M. Natanzon, “Topological invariants and moduli of hyperbolic $n=2$ Riemann supersurfaces”, Russian Acad. Sci. Sb. Math., 79:1 (1994), 15–31
34.	S. M. Natanzon, “Differential equations on the Prym theta function. a realness criterion for two-dimensional, finite-zone, potential Schrödinger operators”, Funct. Anal. Appl., 26:1 (1992), 13–20
35.	S. M. Natanzon, “A topological classification of a pair of spinor forms on surfaces”, Russian Math. Surveys, 47:1 (1992), 265–266
36.	S. M. Natanzon, “Discrete subgroups of $GL(2,C)$ and spinor bundles on Riemann and Klein surfaces”, Funct. Anal. Appl., 25:4 (1991), 293–294
37.	S. M. Natanzon, “Klein supersurfaces”, Math. Notes, 48:2 (1990), 766–772
38.	S. M. Natanzon, “Klein surfaces”, Russian Math. Surveys, 45:5 (1990), 53–108
39.	S. M. Natanzon, “Supercoverings, $SNEC$-groups, and interior groups of Riemann and Klein supersurfaces”, Russian Math. Surveys, 45:2 (1990), 225–226
40.	S. M. Natanzon, “Prymians of real curves and their applications to the effectivization of Schrödinger operators”, Funct. Anal. Appl., 23:1 (1989), 33–45
41.	S. M. Natanzon, “Moduli space of super–Riemann surfaces”, Math. Notes, 45:4 (1989), 341–345
42.	S. M. Natanzon, “Spinor bundles over real algebraic curves”, Russian Math. Surveys, 44:3 (1989), 208–209
43.	S. M. Natanzon, “Nonsingular finite-zone two-dimensional Schrödinger operators and prymians of real curves”, Funct. Anal. Appl., 22:1 (1988), 68–70
44.	B. A. Dubrovin, S. M. Natanzon, “Real theta-function solutions of the Kadomtsev–Petviashvili equation”, Math. USSR-Izv., 32:2 (1989), 269–288
45.	S. M. Natanzon, “Finite groups of homeomorphisms of surfaces, and real forms of complex algebraic curves”, Tr. Mosk. Mat. Obs., 51, MSU, M., 1988, 3–53
46.	S. M. Natanzon, “Topological type and moduli of Riemannian and Klein supersurfaces”, Investigations in topology. Part 6, Zap. Nauchn. Sem. LOMI, 167, “Nauka”, Leningrad. Otdel., Leningrad, 1988, 179–185
47.	S. M. Natanzon, “The Fricke space of super-Fuchsian groups”, Funct. Anal. Appl., 21:2 (1987), 158–159
48.	S. M. Natanzon, “Real meromorphic functions on real algebraic curves”, Dokl. Math., 36:3 (1988), 425–427
49.	S. M. Natanzon, “Topological classification of pairs of commuting antiholomorphic involutions of Riemann surfaces”, Russian Math. Surveys, 41:5 (1986), 159–160
50.	S. M. Natanzon, “Uniformization of spaces of meromorphic functions”, Dokl. Akad. Nauk SSSR, 287:5 (1986), 1058–1061
51.	S. M. Natanzon, “Spaces of real meromorphic functions on real algebraic curves”, Dokl. Akad. Nauk SSSR, 279:4 (1984), 803–805
52.	B. A. Dubrovin, S. M. Natanzon, “Real two-zone solutions of the sine-Gordon equation”, Funct. Anal. Appl., 16:1 (1982), 21–33
53.	S. M. Natanzon, “The total number of ovals of four complex-isomorphic real algebraic curves”, Russian Math. Surveys, 35:4 (1980), 177
54.	S. M. Natanzon, “On the total number of ovals of real forms of a complex algebraic curve”, Russian Math. Surveys, 35:1 (1980), 223–224
55.	S. M. Natanzon, “Automorphisms and real forms of a class of complex algebraic curves”, Funct. Anal. Appl., 13:2 (1979), 148–150
56.	S. M. Natanzon, “Automorphisms of the Riemann surface of an $M$-curve”, Funct. Anal. Appl., 12:3 (1978), 228–229
57.	S. M. Natanzon, “Spaces of moduli of real curves”, Tr. Mosk. Mat. Obs., 37, MSU, M., 1978, 219–253
58.	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
59.	S. M. Natanzon, “Moduli of real algebraic curves”, Uspekhi Mat. Nauk, 30:1(181) (1975), 251–252
60.	S. M. Natanzon, “Invariant lines of Fuchsian groups”, Russian Math. Surveys, 27:4 (1972), 161–177
61.	S. E. Kuznetsov, S. M. Natanzon, “A certain functional equation that has applications in game theory”, Siberian Math. J., 11:1 (1970), 105–111
Popular science or education materials

62.	S. M. Natanzon, Mat. Pros., 7, MCCME, Moscow, 2003, 116–125
Personalia

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
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
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
Letters, errata

66.	S. M. Natanzon, “Erratum”, Russian Math. Surveys, 42:2 (1987), 311
67.	Theoret. and Math. Phys., 205:2 (2020), 1546

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 (Novikov Seminar) 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 (Novikov Seminar) 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 (Novikov Seminar) 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 (Novikov Seminar) 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 (Novikov Seminar) 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 (Novikov Seminar) 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 (Novikov Seminar) 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 (Novikov Seminar) 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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