Graduated from the Faculty of mechanics and mathematics of the Moscow State University (1971). PhD (1975). DrSc (1991). Professor of the department of higher geometry and topology of the Moscow State University (1996).
Main publications:
Singularities of differentiable maps. Vol. I. The classification of critical points, caustics and wave fronts. Monographs in Mathematics, 82. Birkhäuser Boston, Inc., Boston, MA, 1985 (with V. I. Arnold, A. N. Varchenko).
Singularities of differentiable maps. Vol. II. Monodromy and asymptotics of integrals. Monographs in Mathematics, 83. Birkhäuser Boston, Inc., Boston, MA, 1988 (with V. I. Arnold, A. N. Varchenko).
Sabir Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernández, “Grothendieck ring of pairs of quasi-projective varieties”, Funktsional. Anal. i Prilozhen., 58:1 (2024), 42–49; Funct. Anal. Appl., 58:1 (2024), 33–38
2.
S. M. Gusein-Zade, “Tamanoi Equation for Orbifold Euler Characteristics Revisited”, Trudy Mat. Inst. Steklova, 325 (2024), 119–128; Proc. Steklov Inst. Math., 325 (2024), 111–119
2023
3.
S. M. Gusein-Zade, “Generating series of the classes of exotic unordered configuration spaces”, Sibirsk. Mat. Zh., 64:1 (2023), 72–78; Siberian Math. J., 64:1 (2023), 62–66
2022
4.
S. M. Gusein-Zade, “The Euler Characteristic of a Complete Intersection in Terms of the Newton Polyhedra Revisited”, Trudy Mat. Inst. Steklova, 318 (2022), 66–72; Proc. Steklov Inst. Math., 318 (2022), 59–64
2021
5.
S. M. Gusein-Zade, “Index of a singular point of a vector field or of a $1$-form on an orbifold”, Algebra i Analiz, 33:3 (2021), 73–84; St. Petersburg Math. J., 33:3 (2022), 483–490
S. M. Gusein-Zade, “Connection on the group of diffeomorphisms as a bundle over the space of functions”, Funktsional. Anal. i Prilozhen., 55:3 (2021), 82–84; Funct. Anal. Appl., 55:3 (2021), 242–244
7.
S. M. Gusein-Zade, A.-M. Ya. Rauch, “On Simple ${\mathbb Z}_3$-Invariant Function Germs”, Funktsional. Anal. i Prilozhen., 55:1 (2021), 56–64; Funct. Anal. Appl., 55:1 (2021), 45–51
S. M. Gusein-Zade, A.-M. Ya. Raukh, “On Simple
$\mathbb{Z}_2$-Invariant
and Corner Function Germs”, Mat. Zametki, 107:6 (2020), 855–864; Math. Notes, 107:6 (2020), 939–945
Wolfgang Ebeling, Sabir M. Gusein-Zade, “Dual Invertible Polynomials with Permutation Symmetries and the Orbifold Euler Characteristic”, SIGMA, 16 (2020), 051, 15 pp.
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “The Universal Euler Characteristic of $V$-Manifolds”, Funktsional. Anal. i Prilozhen., 52:4 (2018), 72–85; Funct. Anal. Appl., 52:4 (2018), 297–307
S. M. Gusein-Zade, W. Ebeling, “The Index of a 1-Form on a Real Quotient Singularity”, Funktsional. Anal. i Prilozhen., 52:2 (2018), 78–81; Funct. Anal. Appl., 52:2 (2018), 144–146
S. M. Gusein-Zade, F. Delgado, A. Campillo, “Integration over the space of functions and Poincaré series revisited”, Trudy Mat. Inst. Steklova, 302 (2018), 161–175; Proc. Steklov Inst. Math., 302 (2018), 146–160
2017
13.
S. M. Gusein-Zade, F. I. Mamedova, “On equivariant indices of 1-forms on varieties”, Funktsional. Anal. i Prilozhen., 51:3 (2017), 22–32; Funct. Anal. Appl., 51:3 (2017), 177–184
S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Uspekhi Mat. Nauk, 72:1(433) (2017), 3–36; Russian Math. Surveys, 72:1 (2017), 1–32
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Equivariant versions of higher order orbifold Euler characteristics”, Mosc. Math. J., 16:4 (2016), 751–765
S. M. Gusein-Zade, “On an Equivariant Analogue of the Monodromy Zeta Function”, Funktsional. Anal. i Prilozhen., 47:1 (2013), 17–25; Funct. Anal. Appl., 47:1 (2013), 14–20
S. M. Gusein-Zade, F. Delgado, A. Campillo, “Alexander polynomials and Poincaré series of sets of ideals”, Funktsional. Anal. i Prilozhen., 45:4 (2011), 40–48; Funct. Anal. Appl., 45:4 (2011), 271–277
S. Gusein-Zade, I. Luengo, A. Melle-Hernández, “On generating series of classes of equivariant Hilbert schemes of fat points”, Mosc. Math. J., 10:3 (2010), 593–602
S. M. Gusein-Zade, “Integration with respect to the Euler characteristic and its applications”, Uspekhi Mat. Nauk, 65:3(393) (2010), 5–42; Russian Math. Surveys, 65:3 (2010), 399–432
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Generating Series of Classes of Hilbert Schemes of Points on Orbifolds”, Trudy Mat. Inst. Steklova, 267 (2009), 132–137; Proc. Steklov Inst. Math., 267 (2009), 125–130
24.
S. M. Gusein-Zade, W. Ebeling, “On Indices of 1-Forms on Determinantal Singularities”, Trudy Mat. Inst. Steklova, 267 (2009), 119–131; Proc. Steklov Inst. Math., 267 (2009), 113–124
S. M. Gusein-Zade, F. Delgado, A. Campillo, “Universal Abelian Covers of Rational Surface Singularities and Multi-Index Filtrations”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 3–10; Funct. Anal. Appl., 42:2 (2008), 83–88
A. Campillo, F. Delgado, S. M. Gusein-Zade, “On Poincaré series of filtrations on equivariant functions of two variables”, Mosc. Math. J., 7:2 (2007), 243–255
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “On the Power Structure over the Grothendieck Ring of Varieties and Its Applications”, Trudy Mat. Inst. Steklova, 258 (2007), 58–69; Proc. Steklov Inst. Math., 258 (2007), 53–64
S. M. Gusein-Zade, W. Ebeling, “A filtration defined by arcs in a space”, Uspekhi Mat. Nauk, 61:2(368) (2006), 163–164; Russian Math. Surveys, 61:2 (2006), 353–355
29.
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Integration over Spaces of Nonparametrized Arcs and Motivic Versions of the Monodromy Zeta Function”, Trudy Mat. Inst. Steklova, 252 (2006), 71–82; Proc. Steklov Inst. Math., 252 (2006), 63–73
S. M. Gusein-Zade, F. Delgado, A. Campillo, “Integrals with Respect to the Euler Characteristic over Spaces of Functions and the Alexander Polynomial”, Trudy Mat. Inst. Steklova, 238 (2002), 144–157; Proc. Steklov Inst. Math., 238 (2002), 134–147
S. M. Gusein-Zade, N. N. Nekhoroshev, “Singularities of Type $A_k$ on Plane Curves of a Chosen Degree”, Funktsional. Anal. i Prilozhen., 34:3 (2000), 69–70; Funct. Anal. Appl., 34:3 (2000), 214–215
S. M. Gusein-Zade, F. Delgado, A. Campillo, “Integration with respect to the Euler characteristic over a function space and the Alexander polynomial of a plane curve singularity”, Uspekhi Mat. Nauk, 55:6(336) (2000), 127–128; Russian Math. Surveys, 55:6 (2000), 1148–1149
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “On the topology of germs of meromorphic functions and its applications”, Algebra i Analiz, 11:5 (1999), 92–99; St. Petersburg Math. J., 11:5 (2000), 775–780
S. M. Gusein-Zade, F. Delgado, A. Campillo, “On the Monodromy of a Plane Curve Singularity and the Poincaré Series of the Ring of Functions on the Curve”, Funktsional. Anal. i Prilozhen., 33:1 (1999), 66–68; Funct. Anal. Appl., 33:1 (1999), 56–57
S. M. Gusein-Zade, F. Delgado, A. Campillo, “On the monodromy at infinity of a plane curve and the Poincaré series of its coordinate ring”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 68 (1999), 49–54; J. Math. Sci. (New York), 105:2 (2001), 1839–1842
S. M. Gusein-Zade, F. Delgado, A. Campillo, “The Alexander polynomial of plane curve singularities and rings of functions on curves”, Uspekhi Mat. Nauk, 54:3(327) (1999), 157–158; Russian Math. Surveys, 54:3 (1999), 634–635
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “On Atypical Values and Local Monodromies of Meromorphic Functions”, Trudy Mat. Inst. Steklova, 225 (1999), 168–176; Proc. Steklov Inst. Math., 225 (1999), 156–164
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “Zeta Functions for Germs of Meromorphic Functions, and Newton Diagrams”, Funktsional. Anal. i Prilozhen., 32:2 (1998), 26–35; Funct. Anal. Appl., 32:2 (1998), 93–99
S. M. Gusein-Zade, F. S. Duzhin, “On the number of topological types of plane curves”, Uspekhi Mat. Nauk, 53:3(321) (1998), 197–198; Russian Math. Surveys, 53:3 (1998), 626–627
S. M. Gusein-Zade, F. Delgado, A. Campillo, “The Extended Semigroup of a Plane Curve Singularity”, Trudy Mat. Inst. Steklova, 221 (1998), 149–167; Proc. Steklov Inst. Math., 221 (1998), 139–156
S. M. Gusein-Zade, “On the Existence of Deformations without Critical Points (the Teissier problem for functions of two variables)”, Funktsional. Anal. i Prilozhen., 31:1 (1997), 74–77; Funct. Anal. Appl., 31:1 (1997), 58–60
S. M. Gusein-Zade, “Dynkin diagrams of some complete intersections and real morsifications”, Trudy Mat. Inst. Steklov., 209 (1995), 124–132; Proc. Steklov Inst. Math., 209 (1995), 107–113
S. M. Gusein-Zade, “On Singularities from which an $A_1$ Can be Split off”, Funktsional. Anal. i Prilozhen., 27:1 (1993), 68–71; Funct. Anal. Appl., 27:1 (1993), 57–60
S. M. Gusein-Zade, “Number of critical points for a quasiperiodic potential”, Funktsional. Anal. i Prilozhen., 23:2 (1989), 55–56; Funct. Anal. Appl., 23:2 (1989), 129–130
S. M. Gusein-Zade, “Frequency Distribution of Letters in the Russian Language”, Probl. Peredachi Inf., 24:4 (1988), 102–107; Problems Inform. Transmission, 24:4 (1988), 338–342
S. M. Gusein-Zade, “Singularities admitting perturbations with a small number of critical values”, Funktsional. Anal. i Prilozhen., 21:1 (1987), 76–77; Funct. Anal. Appl., 21:1 (1987), 66–68
1984
48.
S. M. Gusein-Zade, “Index of a singular point of a gradient vector field”, Funktsional. Anal. i Prilozhen., 18:1 (1984), 7–12; Funct. Anal. Appl., 18:1 (1984), 6–10
A. N. Varchenko, S. M. Gusein-Zade, “The topology of caustics, wave fronts, and degeneracies of critical points”, Uspekhi Mat. Nauk, 39:2(236) (1984), 141–142; Russian Math. Surveys, 39:2 (1984), 209–210
S. M. Gusein-Zade, N. N. Nekhoroshev, “Contiguity of $A_k$-singularities at points of the stratum $\mu=\operatorname{const}$ of a singularity”, Funktsional. Anal. i Prilozhen., 17:4 (1983), 82–83; Funct. Anal. Appl., 17:4 (1983), 312–313
S. M. Gusein-Zade, “The monodromy groups of isolated singularities of hypersurfaces”, Uspekhi Mat. Nauk, 32:2(194) (1977), 23–65; Russian Math. Surveys, 32:2 (1977), 23–69
S. M. Gusein-Zade, “Characteristic polynomial of classical monodromy for singular series”, Funktsional. Anal. i Prilozhen., 10:3 (1976), 78–79; Funct. Anal. Appl., 10:3 (1976), 229–231
1974
54.
S. M. Gusein-Zade, “Dynkin diagrams for singularities of functions of two variables”, Funktsional. Anal. i Prilozhen., 8:4 (1974), 23–30; Funct. Anal. Appl., 8:4 (1974), 295–300
S. M. Gusein-Zade, “Intersection matrices for certain singularities of functions of two variables”, Funktsional. Anal. i Prilozhen., 8:1 (1974), 11–15; Funct. Anal. Appl., 8:1 (1974), 10–13
S. M. Gusein-Zade, “$U$-actions of a circle and fixed points”, Izv. Akad. Nauk SSSR Ser. Mat., 35:5 (1971), 1120–1136; Math. USSR-Izv., 5:5 (1971), 1127–1143
S. M. Gusein-Zade, “Oh a game connected with a Wiener process”, Teor. Veroyatnost. i Primenen., 14:4 (1969), 732–735; Theory Probab. Appl., 14:4 (1969), 701–704
S. M. Gusein-Zade, “The problem of choice and the optimal stopping rule for a sequence of random trials”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 534–537; Theory Probab. Appl., 11:3 (1966), 472–476
A. Bufetov, A. Glutsyuk, N. Goncharuk, S. Gusein-Zade, Yu. Kudryashov, S. Lando, A. Sosinskii, V. Timorin, M. Tsfasman, “Yulij Ilyashenko is 75”, Mosc. Math. J., 19:2 (2019), 185–188
2017
63.
A. Chernavski, D. Fuchs, S. Gusein-Zade, Yu. Ilyashenko, O. Karpenkov, A. Kirillov, S. Lando, S. Matveev, M. Skopenkov, V. Tikhomirov, M. Tsfasman, V. Vassiliev, “Alexei Bronislavovich Sossinsky turns 80”, Mosc. Math. J., 17:3 (2017), 555–558
64.
S. M. Gusein-Zade, “О работах В. И. Арнольда по теории особенностей”, Mat. Pros., Ser. 3, 21 (2017), 27–36
2016
65.
V. M. Buchstaber, S. M. Gusein-Zade, M. È. Kazarian, V. V. Kozlov, S. K. Lando, S. P. Novikov, D. O. Orlov, A. G. Khovanskii, “Viktor Anatol'evich Vassiliev (on his 60th birthday)”, Uspekhi Mat. Nauk, 71:6(432) (2016), 167–171; Russian Math. Surveys, 71:6 (2016), 1153–1157
2015
66.
S. M. Gusein-Zade, Yu. S. Ilyashenko, S. K. Lando, Yu. I. Manin, N. S. Nadirashvili, D. Yu. Nogin, S. Yu. Rybakov, A. B. Sossinsky, A. I. Zykin, “M. Tsfasman, S. Vlăduţ”, Mosc. Math. J., 15:4 (2015), 607–608
67.
P. Etingof, S. Loktev, L. Rybnikov, S. Gusein-Zade, Yu. Ilyashenko, S. Lando, M. Tsfasman, V. Vassiliev, “Boris Feigin”, Mosc. Math. J., 15:2 (2015), 185–186
2014
68.
A. I. Bufetov, A. A. Glutsyuk, S. M. Gusein-Zade, A. S. Gorodetski, V. Yu. Kaloshin, A. G. Khovanskii, V. A. Kleptsyn, S. Yu. Nemirovskii, A. B. Sossinsky, M. A. Tsfasman, V. A. Vassiliev, S. Yu. Yakovenko, “Yulij Sergeevich Ilyashenko”, Mosc. Math. J., 14:2 (2014), 173–179
A. A. Agrachev, D. V. Anosov, I. A. Bogaevskii, A. S. Bortakovskii, A. B. Budak, V. A. Vassiliev, V. V. Goryunov, S. M. Gusein-Zade, A. A. Davydov, V. R. Zarodov, V. D. Sedykh, D. V. Treshchev, V. N. Chubarikov, “Vladimir Mikhailovich Zakalyukin (obituary)”, Uspekhi Mat. Nauk, 67:2(404) (2012), 187–190; Russian Math. Surveys, 67:2 (2012), 375–379
2011
70.
S. Gusein-Zade, Yu. Ilyashenko, V. Malyshev, S. Shlosman, Ya. Sinai, M. Tsfasman, “Robert Adolphovich Minlos”, Mosc. Math. J., 11:2 (2011), 403–404
71.
A. N. Varchenko, S. M. Gusein-Zade, “V. I. Arnold: 12.06.1937 – 03.06.2010”, Tr. Mosk. Mat. Obs., 72:1 (2011), 1–4; Trans. Moscow Math. Soc., 72 (2011), viii–xi
2010
72.
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
D. Anosov, V. Buchstaber, S. Gusein-Zade, Yu. Ilyashenko, A. Khovanskii, S. Lando, S. Novikov, A. Sossinsky, M. Tsfasman, V. Vassiliev, “Vladimir Igorevich Arnold”, Mosc. Math. J., 10:3 (2010), 481–483
2009
74.
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
75.
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
76.
S. Gusein-Zade, Yu. Ilyashenko, D. Kaledin, A. Kuznetsov, S. Lando, A. Sossinski, M. Tsfasman, V. Vassiliev, A. Vershik, “A tribute to Pierre Deligne”, Mosc. Math. J., 9:1 (2009), 1–2
2008
77.
S. M. Gusein-Zade, Yu. S. Ilyashenko, G. A. Kabatiansky, S. K. Lando, A. G. Sergeev, O. K. Sheinman, O. V. Schwarzman, M. A. Tsfasman, È. B. Vinberg, “Sergey Natanzon”, Mosc. Math. J., 8:4 (2008), 843–844
78.
I. V. Arzhantsev, S. M. Gusein-Zade, Yu. S. Ilyashenko, A. L. Onishchik, A. B. Sossinsky, D. A. Timashev, M. A. Tsfasman, “Ernest Borisovich Vinberg”, Mosc. Math. J., 8:4 (2008), 617–620
2007
79.
S. M. Gusein-Zade, Yu. S. Ilyashenko, M. E. Kazarian, A. G. Khovanskii, S. K. Lando, A. B. Sossinski, M. A. Tsfasman, V. A. Vassiliev, V. M. Zakalyukin, “Vladimir Igorevich Arnold”, Mosc. Math. J., 7:3 (2007), 571
80.
S. M. Gusein-Zade, “International conference “Analysis and Singularities” dedicated to the 70th birthday of V. I. Arnol'd”, Uspekhi Mat. Nauk, 62:5(377) (2007), 185–186; Russian Math. Surveys, 62:5 (2007), 1031–1033
81.
A. N. Varchenko, V. A. Vassiliev, S. M. Gusein-Zade, A. A. Davydov, V. M. Zakalyukin, Yu. S. Ilyashenko, M. E. Kazarian, A. G. Kushnirenko, S. K. Lando, A. G. Khovanskii, “Vladimir Igorevich Arnold in the Eyes of His Students: On the occasion of his 70th birthday”, Trudy Mat. Inst. Steklova, 259 (2007), 5–9; Proc. Steklov Inst. Math., 259 (2007), 1–5
2004
82.
S. M. Gusein-Zade, “About the impact factor”, Uspekhi Mat. Nauk, 59:5(359) (2004), 186–188; Russian Math. Surveys, 59:5 (2004), 1005–1007
S. M. Gusein-Zade, Yu. S. Ilyashenko, A. G. Khovanskii, M. A. Tsfasman, V. A. Vassiliev, “Vladimir Igorevich Arnold”, Mosc. Math. J., 3:2 (2003), 261
1997
84.
D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Uspekhi Mat. Nauk, 52:5(317) (1997), 235–255; Russian Math. Surveys, 52:5 (1997), 1117–1139
Сбоку от зеркальной симметрии - 4 S. M. Gusein-Zade The 9th International Summer School-Conference on Geometrical Methods in Mathematical Physics July 10, 2022 09:30
6.
Сбоку от зеркальной симметрии - 3 S. M. Gusein-Zade The 9th International Summer School-Conference on Geometrical Methods in Mathematical Physics July 9, 2022 09:30
7.
Сбоку от зеркальной симметрии - 2 S. M. Gusein-Zade The 9th International Summer School-Conference on Geometrical Methods in Mathematical Physics July 8, 2022 11:00
8.
Сбоку от зеркальной симметрии - 1 S. M. Gusein-Zade The 9th International Summer School-Conference on Geometrical Methods in Mathematical Physics July 7, 2022 15:00
Многочлен Александера алгебраического зацепления с симметриями S. M. Gusein-Zade Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) November 16, 2016 18:30
О рядах Пуанкаре и полиномах Александера алгебраических узлов S. M. Gusein-Zade Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) October 15, 2008