real algebraic geometry, moduli of complex and real algebraic curves and its superanalogs, quantum cohomology, Frobenius manifolds, integrable systems, quantum field theory, string theory.
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.
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
2.
B. A. Dubrovin, S. M. Natanzon, “Real two-zone solutions of the sine-Gordon equation”, Funct. Anal. Appl., 16:1 (1982), 21–33
3.
S. M. Natanzon, “Klein surfaces”, Russian Math. Surveys, 45:5 (1990), 53–108
4.
B. A. Dubrovin, S. M. Natanzon, “Real theta-function solutions of the Kadomtsev–Petviashvili equation”, Math. USSR-Izv., 32:2 (1989), 269–288
5.
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
6.
S. M. Natanzon, “Moduli of Riemann surfaces, Hurwitz-type spaces, and their superanalogues”, Russian Math. Surveys, 54:1 (1999), 61–117
7.
A. V. Alekseevskii, S. M. Natanzon, “The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces”, Izv. Math., 72:4 (2008), 627–646
8.
S. M. Natanzon, “Moduli space of super–Riemann surfaces”, Math. Notes, 45:4 (1989), 341–345
9.
A. V. Alekseevskii, S. M. Natanzon, “Algebra of Hurwitz numbers for seamed surfaces”, Russian Math. Surveys, 61:4 (2006), 767–769
10.
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
11.
S. M. Natanzon, “Spaces of moduli of real curves”, Tr. Mosk. Mat. Obs., 37, MSU, M., 1978, 219–253
12.
S. M. Natanzon, “Simple Hurwitz Numbers of a Disk”, Funct. Anal. Appl., 44:1 (2010), 36–47
13.
S. M. Natanzon, “Topological classification of pairs of commuting antiholomorphic involutions of Riemann surfaces”, Russian Math. Surveys, 41:5 (1986), 159–160
14.
S. M. Natanzon, “Automorphisms of the Riemann surface of an $M$-curve”, Funct. Anal. Appl., 12:3 (1978), 228–229
15.
S. M. Natanzon, “Klein supersurfaces”, Math. Notes, 48:2 (1990), 766–772
16.
S. M. Natanzon, “Prymians of real curves and their applications to the effectivization of Schrödinger operators”, Funct. Anal. Appl., 23:1 (1989), 33–45
17.
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
18.
S. M. Natanzon, “Invariant lines of Fuchsian groups”, Russian Math. Surveys, 27:4 (1972), 161–177
19.
S. M. Natanzon, “Nonsingular finite-zone two-dimensional Schrödinger operators and prymians of real curves”, Funct. Anal. Appl., 22:1 (1988), 68–70
20.
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
21.
S. M. Natanzon, “Moduli of real algebraic curves”, Uspekhi Mat. Nauk, 30:1(181) (1975), 251–252
22.
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
S. M. Natanzon, “Witten Solution for the Gelfand–Dikii Hierarchy”, Funct. Anal. Appl., 37:1 (2003), 21–31
28.
S. M. Natanzon, “Spinor bundles over real algebraic curves”, Russian Math. Surveys, 44:3 (1989), 208–209
29.
S. M. Natanzon, A. Yu. Orlov, “Hurwitz numbers from Feynman diagrams”, Theoret. and Math. Phys., 204:3 (2020), 1172–1200
30.
S. M. Natanzon, A. M. Pratusevich, “The topology of m–spinor structures on Riemann surfaces”, Russian Math. Surveys, 60:2 (2005), 363–364
31.
S. M. Natanzon, “Moduli Spaces of Real Algebraic $N=2$ Supercurves”, Funct. Anal. Appl., 30:4 (1996), 237–245
32.
S. M. Natanzon, “Real borderings of complex algebraic curves and Coxeter groups”, Russian Math. Surveys, 51:6 (1996), 1216–1217
33.
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
34.
S. M. Natanzon, “Real meromorphic functions on real algebraic curves”, Dokl. Math., 36:3 (1988), 425–427
35.
S. M. Natanzon, “Automorphisms and real forms of a class of complex algebraic curves”, Funct. Anal. Appl., 13:2 (1979), 148–150
36.
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
37.
Sergey Natanzon, Anna Pratoussevitch, “Higher spin Klein surfaces”, Mosc. Math. J., 16:1 (2016), 95–124
S. M. Natanzon, A. M. Pratusevich, “Moduli spaces of Gorenstein quasi-homogeneous surface singularities”, Russian Math. Surveys, 66:5 (2011), 1009–1011
43.
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
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
45.
S. M. Natanzon, “The topological structure of the space of holomorphic morphisms of Riemann surfaces”, Russian Math. Surveys, 53:2 (1998), 398–400
46.
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
47.
S. M. Natanzon, “A topological classification of a pair of spinor forms on surfaces”, Russian Math. Surveys, 47:1 (1992), 265–266
48.
S. M. Natanzon, “Supercoverings, $SNEC$-groups, and interior groups of Riemann and Klein supersurfaces”, Russian Math. Surveys, 45:2 (1990), 225–226
49.
S. M. Natanzon, “The total number of ovals of four complex-isomorphic real algebraic curves”, Russian Math. Surveys, 35:4 (1980), 177
50.
M. E. Kazarian, S. K. Lando, S. M. Natanzon, “On framed simple purely real Hurwitz numbers”, Izv. Math., 85:4 (2021), 681–704
51.
Sergey Natanzon, Anna Pratoussevitch, “Moduli spaces of higher spin Klein surfaces”, Mosc. Math. J., 17:2 (2017), 327–349
S. M. Natanzon, “Singularities and Noncommutative Frobenius Manifolds”, Proc. Steklov Inst. Math., 259 (2007), 137–148
59.
S. M. Natanzon, “Recurrence Formulas for $A_n$- and $B_n$-Solutions of the WDVV Equations”, Funct. Anal. Appl., 34:3 (2000), 226–228
60.
S. M. Natanzon, “Topological types of actions of the group $(Z/2Z)^n$ on surfaces”, Russian Math. Surveys, 48:2 (1993), 199–200
61.
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
62.
S. E. Kuznetsov, S. M. Natanzon, “A certain functional equation that has applications in game theory”, Siberian Math. J., 11:1 (1970), 105–111
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
66.
S. M. Natanzon, Mat. Pros., 7, MCCME, Moscow, 2003, 116–125
67.
S. M. Natanzon, “Erratum”, Russian Math. Surveys, 42:2 (1987), 311
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
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
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
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
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
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
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
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
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