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.
S. M. Natanzon, A. M. Pratusevich, “Moduli spaces of Gorenstein quasi-homogeneous surface singularities”, Russian Math. Surveys, 66:5 (2011), 1009–1011
11.
Sergey A. Loktev, Sergey M. Natanzon, “Klein Topological Field Theories from Group Representations”, SIGMA, 7 (2011), 70–15
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
13.
S. M. Natanzon, “Simple Hurwitz Numbers of a Disk”, Funct. Anal. Appl., 44:1 (2010), 36–47
14.
A. V. Alekseevskii, S. M. Natanzon, “The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces”, Izv. Math., 72:4 (2008), 627–646
15.
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, “Singularities and Noncommutative Frobenius Manifolds”, Proc. Steklov Inst. Math., 259 (2007), 137–148
17.
A. V. Alekseevskii, S. M. Natanzon, “Algebra of Hurwitz numbers for seamed surfaces”, Russian Math. Surveys, 61:4 (2006), 767–769
18.
S. M. Natanzon, A. M. Pratusevich, “The topology of m–spinor structures on Riemann surfaces”, Russian Math. Surveys, 60:2 (2005), 363–364
19.
S. M. Natanzon, “Witten Solution for the Gelfand–Dikii Hierarchy”, Funct. Anal. Appl., 37:1 (2003), 21–31
20.
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, “Formal series for the $\tau$-function realizing Riemann's theorem about domains in the complex plane”, Russian Math. Surveys, 56:4 (2001), 760–761
22.
S. M. Natanzon, “Recurrence Formulas for $A_n$- and $B_n$-Solutions of the WDVV Equations”, Funct. Anal. Appl., 34:3 (2000), 226–228
23.
S. M. Natanzon, S. V. Shadrin, “Topological classification of unitary functions of arbitrary genus”, Russian Math. Surveys, 55:6 (2000), 1163–1164
24.
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
25.
S. M. Natanzon, “Moduli of Riemann surfaces, Hurwitz-type spaces, and their superanalogues”, Russian Math. Surveys, 54:1 (1999), 61–117
26.
S. M. Natanzon, “The topological structure of the space of holomorphic morphisms of Riemann surfaces”, Russian Math. Surveys, 53:2 (1998), 398–400
27.
S. M. Natanzon, “On compatible Poisson structures of hydrodynamic type”, Russian Math. Surveys, 52:6 (1997), 1314–1315
28.
S. M. Natanzon, “Moduli Spaces of Real Algebraic $N=2$ Supercurves”, Funct. Anal. Appl., 30:4 (1996), 237–245
29.
S. M. Natanzon, “Real borderings of complex algebraic curves and Coxeter groups”, Russian Math. Surveys, 51:6 (1996), 1216–1217
30.
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
31.
S. M. Natanzon, “On quadratic forms over the field $\mathbb Z_2$”, Russian Math. Surveys, 50:5 (1995), 1090–1091
32.
S. M. Natanzon, “Classification of Pairs of Arf Functions on Orientable and Nonorientable Surfaces”, Funct. Anal. Appl., 28:3 (1994), 178–186
33.
S. M. Natanzon, “Topological types of actions of the group $(Z/2Z)^n$ on surfaces”, Russian Math. Surveys, 48:2 (1993), 199–200
34.
S. M. Natanzon, “Topological invariants and moduli of hyperbolic $n=2$ Riemann supersurfaces”, Russian Acad. Sci. Sb. Math., 79:1 (1994), 15–31
35.
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
36.
S. M. Natanzon, “A topological classification of a pair of spinor forms on surfaces”, Russian Math. Surveys, 47:1 (1992), 265–266
37.
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
38.
S. M. Natanzon, “Klein supersurfaces”, Math. Notes, 48:2 (1990), 766–772
39.
S. M. Natanzon, “Klein surfaces”, Russian Math. Surveys, 45:5 (1990), 53–108
40.
S. M. Natanzon, “Supercoverings, $SNEC$-groups, and interior groups of Riemann and Klein supersurfaces”, Russian Math. Surveys, 45:2 (1990), 225–226
41.
S. M. Natanzon, “Prymians of real curves and their applications to the effectivization of Schrödinger operators”, Funct. Anal. Appl., 23:1 (1989), 33–45
42.
S. M. Natanzon, “Moduli space of super–Riemann surfaces”, Math. Notes, 45:4 (1989), 341–345
43.
S. M. Natanzon, “Spinor bundles over real algebraic curves”, Russian Math. Surveys, 44:3 (1989), 208–209
44.
S. M. Natanzon, “Nonsingular finite-zone two-dimensional Schrödinger operators and prymians of real curves”, Funct. Anal. Appl., 22:1 (1988), 68–70
45.
B. A. Dubrovin, S. M. Natanzon, “Real theta-function solutions of the Kadomtsev–Petviashvili equation”, 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, MSU, M., 1988, 3–53
47.
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
48.
S. M. Natanzon, “The Fricke space of super-Fuchsian groups”, Funct. Anal. Appl., 21:2 (1987), 158–159
49.
S. M. Natanzon, “Real meromorphic functions on real algebraic curves”, Dokl. Math., 36:3 (1988), 425–427
50.
S. M. Natanzon, “Topological classification of pairs of commuting antiholomorphic involutions of Riemann surfaces”, Russian Math. Surveys, 41:5 (1986), 159–160
51.
S. M. Natanzon, “Uniformization of spaces of meromorphic functions”, Dokl. Akad. Nauk SSSR, 287:5 (1986), 1058–1061
52.
S. M. Natanzon, “Spaces of real meromorphic functions on real algebraic curves”, Dokl. Akad. Nauk SSSR, 279:4 (1984), 803–805
53.
B. A. Dubrovin, S. M. Natanzon, “Real two-zone solutions of the sine-Gordon equation”, Funct. Anal. Appl., 16:1 (1982), 21–33
54.
S. M. Natanzon, “The total number of ovals of four complex-isomorphic real algebraic curves”, Russian Math. Surveys, 35:4 (1980), 177
55.
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
56.
S. M. Natanzon, “Automorphisms and real forms of a class of complex algebraic curves”, Funct. Anal. Appl., 13:2 (1979), 148–150
57.
S. M. Natanzon, “Automorphisms of the Riemann surface of an $M$-curve”, Funct. Anal. Appl., 12:3 (1978), 228–229
58.
S. M. Natanzon, “Spaces of moduli of real curves”, Tr. Mosk. Mat. Obs., 37, MSU, M., 1978, 219–253
59.
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
60.
S. M. Natanzon, “Moduli of real algebraic curves”, Uspekhi Mat. Nauk, 30:1(181) (1975), 251–252
61.
S. M. Natanzon, “Invariant lines of Fuchsian groups”, Russian Math. Surveys, 27:4 (1972), 161–177
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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