newton polyhedra,
toric geometry,
fewnomials,
real analitik sets,
topological version of Galois theory.
Subject:
The topological version of Galois theory answers the question about the insolvability of differential equations in quadratures by looking at the Riemann surfaces of the solutions. The topological version of Galois theory provides with the strongest results about the insolvability of differential equations in finite terms. The theory of fewnomials describes a wide class of real transcendental arieties, that are very similar to algebraic varieties. The theory of fewnomials is widely used in different areas of mathematics such as real algebraic geometry, logic, the theory of abelian integrals, the theory of elementary functions, and the qualitative theory of differential equations. The theory of Newton polyhedra relates the geometry of convex polyhedra and algebraic geometry. I discovered a connection between the theory of Newton polyhdera and the geometry of toric varieties. This connection is nowadays fundamental in the theory of Newton polyhedra. Using the geometry of polyhedra I was able to calculate many invariants of algebraic varieties. On the other hand, methods of algebraic geometry allowed me to obtain a series of new results in the geometry of polyhedra.
Biography
Graduated from Faculty of Mathematics and Mechanics of M.V. Lomonosov Moscow State University (MSU) in 1970 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1973. D.Sci. thesis was defended in 1988. A list of my works contains about 100 titles.
Main publications:
A. G. Khovanskii, “Newton polyhedra and toroidal varieties”, Funktsional. Anal. i Prilozhen., 11:4 (1977), 56–64; Funct. Anal. Appl., 11:4 (1977), 289–296
Khovanskii A., Fewnomials, Translations of Mathematical Monographs, 88, Providence, RI, Amer. Math. Soc., 1991, viii+139 pp.
A. V. Pukhlikov, A. G. Khovanskii, “The Riemann–Roch theorem for integrals and sums of quasipolynomials on virtual polytopes”, Algebra i Analiz, 4:4 (1992), 188–216; St. Petersburg Math. J., 4:4 (1993), 789–812
Khovanskii A., “Newton polyhedrons, a new formula for mixed volume, product of roots of a system of equations”, The Arnoldfest, Proceedings of a Conference (Toronto, ON, 1997), Fields Inst. Commun., 24, 1999, 325–364
Kaveh K., Khovanskii A. G., “Newton–Okounkov bodies, semigroups of integral points, graded algebras and intersection theory”, Annals of Mathematics, 176:2, 925–978
Khovanskii A. G., Topological Galois theory. Solvability and unsolvability of equations in nite terms, Springer Monographs in Mathematics, XVIII, Springer, Berlin Heidelberg, 2014, 305 pp.
Ivan Yu. Limonchenko, Leonid V. Monin, Askold G. Khovanskii, “Generalized Virtual Polytopes and Quasitoric Manifolds”, Proc. Steklov Inst. Math., 318 (2022), 126–149
3.
V. L. Arlazarov, A. Ya. Belov, V. O. Bugaenko, V. A. Vassiliev, A. L. Gorodentsev, S. A. Dorichenko, Yu. S. Ilyashenko, V. M. Imaykin, S. I. Komarov, A. G. Kushnirenko, Yu. P. Lysov, A. L. Semenov, V. M. Tikhomirov, A. K. Tolpygo, A. G. Khovanskii, P. A. Yakushkin, I. V. Yaschenko, “Nikolai Nikolaevich Konstantinov (obituary)”, Russian Math. Surveys, 77:3 (2022), 531–541
2021
4.
B. Ya. Kazarnovskii, A. G. Khovanskii, A. I. Esterov, “Newton polytopes and tropical geometry”, Russian Math. Surveys, 76:1 (2021), 91–175
2020
5.
Kiumars Kaveh, Askold G. Khovanskii, “Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space”, SIGMA, 16 (2020), 16 , 12 pp., arXiv: 1911.00118;
6.
M. Braverman, V. M. Buchstaber, M. Gromov, V. Ivrii, Yu. A. Kordyukov, P. Kuchment, V. Maz'ya, S. P. Novikov, T. Sunada, L. Friedlander, A. G. Khovanskii, “Mikhail Aleksandrovich Shubin (obituary)”, Russian Math. Surveys, 75:6 (2020), 1143–1152
2019
7.
A. Khovanskii, “Integriruemost v konechnom vide i deistviya grupp Li”, Mosc. Math. J., 19:2 (2019), 329–341
A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, A. N. Shiryaev, “Vladimir Antonovich Zorich (on his 80th birthday)”, Russian Math. Surveys, 73:5 (2018), 935–939
2017
10.
A. G. Khovanskii, Leonid Monin, “The resultant of developed systems of Laurent polynomials”, Mosc. Math. J., 17:4 (2017), 717–740
A. G. Khovanskii, “Newton polytopes and irreducible components of complete intersections”, Izv. Math., 80:1 (2016), 263–284
12.
K. Kaveh, A. Khovanskii, “Complete intersections in spherical varieties”, Special Issue: The Mathematics of Joseph Bernstein, Selecta Mathematica, 22:4 (2016), 2099–2141
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)”, Russian Math. Surveys, 71:6 (2016), 1153–1157
2015
15.
A. G. Khovanskii, “On Algebraic Functions Integrable in Finite Terms”, Funct. Anal. Appl., 49:1 (2015), 50–56
16.
A. Khovanskii, “Irreducible components of generic complete intersections”, Toricheskaya topologiya, teoriya chisel i ikh prilozheniya, Materialy Mezhdunarodnoi konferentsii (06–12 sentyabrya 2015 goda, Khabarovsk), Izdatelstvo TOGU, Khabarovsk, 2015, 27–31
17.
B. Ya. Kazarnovskiǐ, A. G. Hovanskiǐ, “The tropical Noetherity and Gröbner bases”, St. Petersburg Math. J., 26:5 (2015), 797–811
2014
18.
Yuri Burda, Ascold Khovanskii, “Signatures of branched coverings and solvability in quadratures”, Mosc. Math. J., 14:2 (2014), 225–237
V. L. Arlazarov, O. A. Slavin, V. V. Farsobina, A. Khovanskii, “The search for the optimal position during the comparison of digitized images”, Scientific and Technical Information Processing, 41, no. 5, Springer-Verlag New York, Inc., Secaucus, NJ, 2014, 293–301
K. Kaveh, A. Khovanskii, “Note on the Grothendieck group of subspaces of rational functions and Shokurov's $b$-divisors”, Canadian Mathematical Bulletin, 57:3 (2014), 562–572
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
25.
V. L. Arlazarov, E. A. Dinitz, Yu. S. Ilyashenko, A. V. Karzanov, S. M. Karpenko, A. A. Kirillov, N. N. Konstantinov, M. A. Kronrod, O. P. Kuznetsov, L. B. Okun', P. A. Pevzner, A. L. Semenov, I. A. Faradzhev, B. V. Cherkasskii, A. G. Khovanskii, “Georgy Maksimovich Adelson-Velsky (obituary)”, Russian Math. Surveys, 69:4 (2014), 743–751
2013
26.
V. L. Arlazarov, O. A. Slavin, V. V. Farsobina, A. G. Khovanskii, “Poisk optimalnogo polozheniya pri sravnenii otsifrovannykh obrazov”, Iskusstvennyi intellekt i prinyatie reshenii, 2013, no. 3, 48–58
27.
A. G. Khovanskii, “Polinomy Chebyshëva i ikh obrascheniya”, Matem. prosv., ser. 3, 17, Izd-vo MTsNMO, M., 2013, 93–106
K. Kaveh, A. Khovanskii, “On mixed multiplicities of ideals”, 2013, 20 pp., arXiv: 1310.7979v1
2014
30.
V. L. Arlazarov, O. A. Slavin, V. V. Farsobina, A. G. Khovanskii, “Find the best position by comparing digitated images”, Scientific and Technical Information Processing, 41:5 (2014), 293–301
2013
31.
A. G. Khovanskii, Mat. Pros., 17, MCCME, Moscow, 2013, 93–106
32.
A. G. Khovanskii, Mat. Pros., 17, MCCME, Moscow, 2013, 42–60
2012
33.
Kiumars Kaveh, Askold G. Khovanskii, “Convex bodies associated to actions of reductive groups”, Mosc. Math. J., 12:2 (2012), 369–396
A. G. Khovanskii, “Completions of Convex Families of Convex Bodies”, Math. Notes, 91:3 (2012), 415–429
35.
K. Kaveh, A. Khovanskii, “Newton–Okounkov bodies, semigroups of integral points, graded algebras and intersection theory”, Annals of Mathematics, 176:2 (2012), 925–978
A. Khovanskii, A. Varchenko, “Arnold's Seminar, First Years”, Notices of the AMS, 59:3 (2012), 393–396
37.
K. Kaveh, A. Khovanskii, “Algebraic equations and convex bodies”, Perspectives in Analysis, Geometry and Topology, Progress in Mathematics, 296, Springer Science+Business Media, 2012, 263–282
V. I. Arnold, A. N. Varchenko, A. B. Givental, A. G. Khovanskii, Singularities of functions, wave fronts, caustics and multidimensional integrals, Reviews in Mathematics and Mathematical Physics, 14, no. 2, Cambridge Scientific Publishers, Cambridge, 2012, 122 pp.
2011
39.
A. G. Khovanskii, “Intersection theory and Hilbert function”, Funct. Anal. Appl., 45:4 (2011), 305–315
40.
Kiumars Kaveh, A. G. Khovanskii, “Newton polytopes for horospherical spaces”, Mosc. Math. J., 11:2 (2011), 265–283
Yu. Burda, A. Khovanskii, “Branching data for algebraic functions and representability in radicals”, Algebraic method in dinamical systems, 94, Banach Center Publ., Warsaw, 2011, 131–142
42.
B. Kazarnovskii, A. Khovanskii, “Universal Groebner basis”, Proceedings of the International Conference on Polynomial Computer Algebra, Saint Peterburg, 2011, 65–69
43.
V. Arlazarov, O. Slavin, A. Khovanskii, “Estimation of the distance between images for translation”, Doklady Mathematics, 83:2 (2011), 272–274
K. Kaveh, A. Khovanskii, “Moment polytopes, semigroup of representations and Kazarnovskii's theorem”, Journal of Fixed Point Theory and Applications, 7:2 (2010), 401–417
S. B. Artemov, A. A. Belavin, V. M. Buchstaber, A. I. Esterov, B. L. Feigin, V. A. Ginzburg, E. A. Gorsky, Yu. S. Ilyashenko, A. A. Kirillov, A. G. Khovanskii, S. K. Lando, G. A. Margulis, Yu. A. Neretin, S. P. Novikov, S. B. Shlosman, A. B. Sossinsky, M. A. Tsfasman, A. N. Varchenko, V. A. Vassiliev, S. G. Vlăduţ, “Sabir Medgidovich Gusein-Zade”, Mosc. Math. J., 10:4 (2010), 831–832
50.
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
51.
A. M. Abramov, V. I. Arnol'd, A. V. Bolsinov, A. N. Varchenko, L. Galgani, B. I. Zhilinskii, Yu. S. Il'yashenko, V. V. Kozlov, A. I. Neishtadt, V. I. Piterbarg, A. G. Khovanskii, V. V. Yashchenko, “Nikolai Nikolaevich Nekhoroshev (obituary)”, Russian Math. Surveys, 64:3 (2009), 561–566
2008
52.
A. Khovanskii, “Mnogogranniki i algebra”, Trudy Instituta sistemnogo analiza RAN, 38 (2008), 23–35
53.
Yu. Burda, A. Khovanskii, “Degree of rational mapping, and the theorems of Sturm and Tarski”, Journal of Fixed Point Theory and Applications, 3:1 (2008), 79–93
A. Esterov, A. Khovanskii, “Elimination theory and Newton polyhedra”, Functional Analysis and Other Mathematics, 2, no. 1, Springer Berlin/Heidelberg, 2008, 45–71
A. Khovanskii, Topological Galois theory. Solvability and unsolvability of equations in finite terms, Translated by Valentina Kiritchenko and Vladlen Timorin, Springer Monographs in Mathematics, Springer Berlin Heidelberg, 2014, xviii+305 pp.
2008
57.
K. Kaveh, A. Khovanskii, “Convex bodies and algebraic equations on affine varieties”, 2008, 44 pp., arXiv: 0804.4095
2007
58.
A. Khovanskii, “Logarithmic Functional and the Weil Reciprocity Law”, Proceedings of the Waterloo Workshop on Computer Algebra 2006, eds. Kotsireas I., Zima E., World Scientific Press, 2007, 85–108
59.
A. G. Khovanskii, “Variations on the Theme of Solvability by Radicals”, Proc. Steklov Inst. Math., 259 (2007), 82–100
2013
60.
A. Khovanskii, Galois theory, coverings, and Riemann surfaces, Translated by V. Kiritchenko and V. Timorin, Springer Berlin Heidelberg, 2013, 81 pp.
2007
61.
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
62.
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”, Proc. Steklov Inst. Math., 259 (2007), 1–5
2006
63.
A. G. Khovanskii, “An Analog of Determinant Related to Parshin–Kato Theory and Integer Polytopes”, Funct. Anal. Appl., 40:2 (2006), 126–133
64.
A. G. Khovanskii, S. P. Chulkov, “The Hilbert polynomial for systems of linear partial differential equations with analytic coefficients”, Izv. Math., 70:1 (2006), 153–169
65.
A. G. Khovanskii, D. Novikov, “On affine hypersurfaces with everywhere nondegenerate second quadratic form”, Mosc. Math. J., 6:1 (2006), 135–152
A. Khovanskii, “Combinatorics of sections of polytopes and Coxeter groups in Lobachevsky spaces”, Proceedings of the International Conference, Coxeter Legacy: Reflections and Projections, v. 46, Fields Institute Communications, American Mathematical Society, Providence, RI, 2006, 129–157
70.
A. G. Khovanskii, S. P. Chulkov, Geometriya polugruppy $\mathbf Z^n_{\geq 0}$. Prilozheniya k kombinatorike, algebre i differentsialnym uravneniyam, Izd-vo MTsNMO, Moskva, 2006, 128 pp.
71.
V. I. Arnol'd, V. M. Buchstaber, Yu. S. Ilyashenko, M. E. Kazarian, A. G. Khovanskii, S. K. Lando, S. P. Novikov, A. B. Sossinski, M. A. Tsfasman, “Victor A. Vassiliev”, Mosc. Math. J., 6:1 (2006), 1–3
2005
72.
A. G. Khovanskii, S. P. Chulkov, “Hilbert and Hilbert–Samuel polynomials and partial differential equations”, Math. Notes, 77:1 (2005), 130–139
73.
D. V. Anosov, V. I. Arnol'd, A. A. Glutsyuk, A. S. Gorodetski, V. Y. Kaloshin, A. B. Katok, A. G. Khovanskii, S. K. Lando, A. B. Sossinski, M. A. Tsfasman, S. Yu. Yakovenko, “Yulij S. Ilyashenko”, Mosc. Math. J., 5:1 (2005), 3–4
74.
A. Khovanskii, Journal of Complexity, 21:1, Special Issue: Foundations of Computational Mathematics 2002 Workshops (2005)
2004
75.
A. G. Khovanskii, “On solvability and unsolvability of equations in explicit form”, Russian Math. Surveys, 59:4 (2004), 661–736
76.
A. Khovanskii, D. Novikov, “Comments to the Arnold problem 1987-4”, Arnold's Problems, Springer-Verlag, Berlin; PHASIS, Moscow, 2004, 457–458
77.
A. Khovanskii, “Solvability of equations by explicit formulae”: V. B. Alekseev, Abel's Theorem in Problems and Solutions Based on the lectures of Professor V. I. Arnold, Kluwer Academic Publishers, 2004, 221–263
78.
A. Khovanskii, “Résolubilité des équations par formules explicites (théorie de Liouville, théorie de Galois différentielle et obstructions topologiques)”: V. B. Alekseev, Le theoreme d'Abel: un cours d'Arnold, Vuibert, Cassini, 2004
79.
A. G. Khovanskii, Kompleksnyi analiz, Izd-vo MTsNMO, Moskva, 2004, 48 pp.
2003
80.
A. G. Khovanskii, “On the Nonrepresentability of Functions of Several Variables by Quadratures”, Funct. Anal. Appl., 37:4 (2003), 302–310
81.
A. G. Khovanskii, “On the Monodromy of a Multivalued Function Along Its Ramification Locus”, Funct. Anal. Appl., 37:2 (2003), 134–141
82.
A. G. Khovanskii, D. Novikov, “$L$-convex-concave sets in real projective space and $L$-duality”, Mosc. Math. J., 3:3 (2003), 1013–1037
A. Khovanskii, D. Novikov, “$L$-convex-concave body in ${\mathbf R}P^3$ contains a line”, Geometric and Functional Analysis (GAFA), 13 (2003), 1082–1118
84.
A. Khovanskii, “A topological version of Galois theory”, Proceeding of International Conference, Kolmogorov and Cotemporary Mathematics, 2003, 777–780
85.
A. Khovanskii, “Three lectures on Fewnomials and Noetherian intersections”, Proceeding of workshops (November 5–8, 2002), Research Institute for Mathematical Sciences, no. 6, Kyoto University, Kyoto, Kokyuroku, 2003, 42–72
86.
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
2002
87.
O. A. Gelfond, A. G. Khovanskii, “Toric geometry and Grothendieck residues”, Mosc. Math. J., 2:1 (2002), 99–112
A. G. Khovanskii, “On the Continuability of Multivalued Analytic Functions to an Analytic Subset”, Funct. Anal. Appl., 35:1 (2001), 52–60
89.
A. Khovanskii, “Three lectures on Newton polyhedra. Newton polyhedrons and Singularities”, Proceeding of workshops (28–31 May, 2001), Research Institute for Mathematical Sciences, no. 10, Kyoto University, Kyoto, Kokyuroku, 2001, 1–17
2000
90.
A. G. Khovanskii, “Families of Sections of Quadrics and Classical Geometries”, Funct. Anal. Appl., 34:3 (2000), 235–238
91.
A. Khovanskii, “Geometricheskoe obobschenie zadachi o preobrazovanii nomogramm iz vyrovnennykh tochek v tsirkulnye nomogrammy”, Nomograficheskii sbornik, no. 17, VTs RAN, 2000, 73–88
1999
92.
A. Khovanskii, “Newton polyhedrons, a new formula for mixed volume, product of roots of a system of equations”, The Arnoldfest (Proceedings of a Conference in Honor of V. I. Arnold for his Sixtieth Birthday), Fields Institute Communications, 24, Amer. Math. Soc., Providence, RI, 1999, 325–364
93.
A. Khovanskii, The Arnoldfest, Proceedings of a Conference in Honor of V. I. Arnold for his Sixtieth Birthday, Fields Institute Communications, 24, Amer. Math. Soc., Providence, RI, 1999
94.
A. G. Khovanskii, “Boundary indices of polynomial 1-forms with homogeneous components”, St. Petersburg Math. J., 10:3 (1999), 553–575
1998
95.
A. Gabrielov, A. Khovanskii, “Multiplicity of a Noetherian Intersection”, Geometry of Differential Equations, Amer. Math. Soc. Transl., Ser. 2, 186, Amer. Math. Soc., Providence, RI, 1998, 119–130
A. G. Khovanskii, Malochleny, Fazis, Moskva, 1997, xii+217 pp.
101.
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)”, Russian Math. Surveys, 52:5 (1997), 1117–1139
102.
A. Khovanskii, Topics in Singularity Theory: V. I. Arnold's 60th Anniversary Collection, Amer. Math. Soc. Transl., Ser. 2, 180, Amer. Math. Soc., Providence, RI, 1997
A. G. Khovanskii, “Sums of Finite Sets, Orbits of Commutative Semigroups, and Hilbert Functions”, Funct. Anal. Appl., 29:2 (1995), 102–112
108.
A. Khovanskii, “Topological obstructions for representability of functions by quadratures”, Journal of dynamical and control systems, 1:1 (1995), 99–132
A. Khovanskii, A. Pukhlikov, “Integral transforms based on Euler characteristic and their application”, Integral transforms and special function, 1:1 (1993), 19–26
J.-M. Kantor, A. Khovanskii, “Une application du Theoreme de Riemann–Roch combinatoire au polynome d'Ehrhart des polytopes entier de R”, C. R. Acad. Sci. Paris. Ser. I, 317 (1993), 501–507
111.
A. V. Pukhlikov, A. G. Khovanskii, “The Riemann–Roch theorem for integrals and sums of quasipolynomials on virtual polytopes”, St. Petersburg Math. J., 4:4 (1993), 789–812
112.
A. V. Pukhlikov, A. G. Khovanskii, “Finitely additive measures of virtual polyhedra”, St. Petersburg Math. J., 4:2 (1993), 337–356
1992
113.
A. G. Khovanskii, “Newton polyhedron, Hilbert polynomial, and sums of finite sets”, Funct. Anal. Appl., 26:4 (1992), 276–281
114.
J.-M. Kantor, A. Khovanskii, Integral points in convex polyhedra, combinatorial Riemann–Roch theorem and generalized Euler–MacLaurin formula, Preprint IHES, France, 1992
1991
115.
A. Khovanskii, Fewnomials, AMS translated monographs, 88, USA, 1991, viii+139 pp.
Yu. S. Ilyashenko, A. G. Khovanskii, “Galois groups, Stokes operators and a theorem of Ramis”, Funct. Anal. Appl., 24:4 (1990), 286–296
117.
A. Khovanskii, G. S. Khovanskii, “Issledovanie sposobov predstavleniya uravnenii $(f_{34}-f_{12})/(g_{34}-g_{12})=(f_{56}-f_{12})/(g_{56}-g_{12})$ nomogrammami s orientirovannym transparantom, nesuschim krivolineinyi indeks”, Nomograficheskii sbornik, no. 16, VTs AN SSSR, M., 1990, 63–81
1992
118.
A. Khovanskii, “Newton Polyhedra (algebra and geometry)”, Amer. Math. Soc. Transl. (2), 153 (1992), 183–199
1988
119.
A. Khovanskii, “Algebra and mixed volumes”: Y. D. Burago, V. A. Zalgaller, Geometric inequalities, 285, Springer-Verlag, Berlin and New York, 1988, 182–207
120.
A. G. Khovanskii, Mnogogranniki Nyutona i malochleny, diss. … dokt. fiz.-matem. nauk, Moskva, 1988, 332 pp.
1987
121.
A. Khovanskii, “Sopostavlenie ob'ektivno-obuslovlennykh otsenok i normativov effektivnosti v razlichnykh malosektornykh modelyakh ekonomiki”, Sbornik trudov VNIISI, no. 9, 1987, 10–23
1986
122.
A. G. Khovanskii, “Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskii space”, Funct. Anal. Appl., 20:1 (1986), 41–50
1987
123.
V. I. Danilov, A. G. Khovanskii, “Newton polyhedra and an algorithm for computing Hodge–Deligne numbers”, Math. USSR-Izv., 29:2 (1987), 279–298
1985
124.
A. Khovanskii, “Lineinoe programmirovanie i obobschennaya teorema Nikulina”, Sbornik trudov VNIISI, no. 7, 1985, 81–86
125.
A. Khovanskii, “Lineinoe programmirovanie i geometriya vypuklykh mnogogrannikov”, Sbornik trudov VNIISI, no. 7, 1985, 73–80
126.
L. V. Kantorovich, L. I. Korkina, A. Khovanskii, “Sopostavlenie modelei i otsenka vliyaniya sokraschennogo laga stroitelstva i laga NTP na dinamiku ekonomicheskikh pokazatelei”, Sbornik trudov VNIISI, no. 7, 1985, 3–12
127.
E. I. Korkina, A. G. Khovanskii, “Dvukhsektornaya ekonomika s razlichnymi koeffitsientami amortizatsii v razlichnykh sektorakh”, Teoriya, metodologiya i praktika sistemnykh issledovanii, Vsesoyuz. konf., Sektsiya 7. Sistem. issled. nauch.-tekhn. razvitiya: Tez. dokl. (29–31 yanvarya 1985 g.), Nauka, M., 1985, 135–137
128.
A. Varchenko, A. Khovanskii, “Asymptotics of integrals over vanishing cycles and the Newton polyhedron”, Soviet Math. Dokl., 32:1 (1985), 122–127
129.
A. N. Varchenko, A. G. Khovanskii, “Asymptotic behavior of integrals over vanishing cycles and the Newton polyhedron”, Dokl. Akad. Nauk SSSR, 283:3 (1985), 521–525
1984
130.
A. G. Khovanskii, “Real analytic varieties with the finiteness property and complex abelian integrals”, Funct. Anal. Appl., 18:2 (1984), 119–127
131.
A. Khovanskii, “On analogues of Alexandrov–Fenchel inequalities for hyperbolic forms”, Soviet Math. Dokl., 29:3 (1984), 710–713
132.
A. Khovanskii, “Smeshannye ob'emy”, UMN, 39:5 (1984), 227–228
1985
133.
A. Khovanskii, “Cycles of dynamic systems on a plane and Roll theorem”, Siberian Math. J., 25:3 (1985), 502–506
1984
134.
V. I. Arnol'd, A. N. Varchenko, A. B. Givental', A. G. Khovanski\u{i}, “Singularities of functions, wave fronts, caustics and multidimensional integrals”, Mathematical physics reviews, v. 4, Soviet Sci. Rev. Sect. C Math. Phys. Rev., 4, Harwood Academic Publ., Chur, 1984, 1–92
135.
A. G. Khovanskii, “Analogues of Aleksandrov–Fenchel inequalities for hyperbolic forms”, Dokl. Akad. Nauk SSSR, 276:6 (1984), 1332–1334
136.
A. G. Khovanskii, “Newton polyhedra (resolution of singularities)”, J. Soviet Math., 27:3 (1984), 2811–2830
1983
137.
L. Kantorovich, E. Korkina, A. Khovanskii, “Optimizatsiya potrebleniya v nepreryvnoi i diskretnoi modelyakh dvukhsektornoi ekonomiki”, Sbornik trudov VNIISI, no. 9, 1983, 14–20
1984
138.
L. Kantorovich, L. Korkina, A. Khovanskii, “Asymptotic optimization of consumption in a model of two-sector economy”, Siberian Math. J., 24:5 (1984), 704–708
1982
139.
E. Korkina, A. Khovanskii, “Printsip differentsialnoi optimizatsii i malosektornye modeli ekonomiki”, Sbornik trudov VNIISI, no. 8, 1982, 3–10
140.
A. Khovanskii, G. S. Khovanskii, “Metody nomografirovaniya nekotorykh zavisimostei, osnovannye na ispolzovanii dvukhparametricheskikh semeistv pryamykh, okruzhnostei i ellipsov”, Nomograficheskii sbornik, no. 14, M., VTs AN SSSR, 1982, 70–105
141.
A. Khovanskii, G. S. Khovanskii, “Preobrazovanie nomogrammy iz vyrovnennykh tochek i s parallelnym indeksom v nomogrammy iz ravnoudalennykh tochek i issledovanie ikh prisposoblyaemosti”, Nomograficheskii sbornik, no. 14, M., VTs AN SSSR, 1982, 56–77
A. Khovanskii, “Local multiplicity of a holomorphic map”: V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, Monographs in Mathematics, 82, Birkhauser Einheitssacht, 1985, 84–114
1982
144.
A. Khovanskii, “Crafoord Prize for Soviet mathematician”, Priroda, 1982, no. 10, 107–108
1981
145.
E. Korkina, A. Khovanskii, ““Zolotoe pravilo” dlya modeli dvusektornoi ekonomiki”, Trudy seminara “Metody issledovaniya slozhnykh sistem”, VNIISI AN SSSR, M., 1981, 11–18
146.
A. Khovanskii, “Mnogogrannik Nyutona i indeks vektornogo polya”, UMN, 36:4 (1981), 234
147.
A. Khovanskii, “Sur les racines complexes de systemes d'equations algebraiques avant un petit nombre de monomes”, C. R. Acad. Sc. Paris, 292 (1981), 937–940
148.
A. Khovanskii, Theorem de Bezout pour les fonctions de Liouville, Preprint IHES, 81/85, 1981, 31 pp.
149.
A. Khovanskii, G. S. Khovanskii, “O predstavlenii klassicheskikh kanonicheskikh form nomogrammami s orientirovannym transparantom i iz ravnoudalennykh tochek”, Sovremennye problemy nomografii (Tezisy dokladov Mezhvuzovskogo seminara), 1981, 50–52
1980
150.
O. A. Gelfond, A. G. Khovanskii, “Real Liouville functions”, Funct. Anal. Appl., 14:2 (1980), 122–123
1981
151.
A. Khovanskii, “Rectification of circles”, Siberian Math. J., 21:4 (1981), 649–652
1980
152.
A. Khovanskii, “Rectification of parallel curves”, Soviet Math. Dokl., 21:1 (1980), 284–286
153.
A. G. Khovanskii, “O chisle nulei veschestvennykh uravnenii”, UMN, 35:5 (1980), 213
A. Khovanskii, “On one class of transcendental equation systems”, Soviet Math. Dokl., 22:3 (1980), 762–765
1979
155.
A. G. Khovanskii, “Index of a polynomial field”, Funct. Anal. Appl., 13:1 (1979), 38–45
156.
A. Khovanskii, G. S. Khovanskii, “Transformation of the nomograms consisting of aligned points and with parallel index into nomograms of C of equidistant points”, Soviet Math. Dokl., 20:5 (1979), 1041–1048
157.
A. G. Khovanskii, “Geometriya vypuklykh mnogogrannikov i algebraicheskaya geometriya”, UMN, 34:4 (1979), 160–161
F. John, J. Leray, S. P. Novikov, A. G. Khovanskii, S. A. Molchanov, N. V. Krylov, B. L. Rozovskii, N. R. Sibgatullin, A. V. Uglanov, S. Yu. Dobrokhotov, V. P. Maslov, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 34:3(207) (1979), 221–226
1978
159.
A. G. Khovanskii, “Newton polyhedra and the genus of complete intersections”, Funct. Anal. Appl., 12:1 (1978), 38–46
160.
A. G. Khovanskii, “Newton polyhedra and the Euler–Jacobi formula”, Russian Math. Surveys, 33:6 (1978), 237–238
161.
L. V. Kantorovich, V. I. Zhiyanov, A. G. Khovanskii, “Analiz dinamiki ekonomicheskikh pokazatelei na osnove odnoproduktovykh dinamicheskikh modelei”, Sbornik trudov VNIISI, no. 9, 1978, 5–25
162.
V. I. Zhiyanov, A. G. Khovanskii, “Eksponentsialnoe razvitie ekonomiki v dinamicheskoi modeli s uchetom nauchno-tekhnicheskogo progressa”, Sbornik trudov VNIISI, no. 9, 1978, 25–36
163.
L. Kantorovich, V. Zhiyanov, A. Khovanskii, “Principle of differential optimization applied to a single-product dynamical model of an economic structure”, Siberian Math. J., 19:5 (1978), 744–752
164.
V. I. Zhiyanov, A. G. Khovanskii, “Yavnye resheniya v odnosektornoi modeli ekonomiki s nepreryvno raspredelennymi fondami”, Sistemnyi analiz i upravlenie nauchno-tekhnicheskim progressom, Tez. k teoret. konf. (Obninsk), 1978, 235–239
1977
165.
A. G. Khovanskii, “Newton polyhedra and toroidal varieties”, Funct. Anal. Appl., 11:4 (1977), 289–296
1976
166.
D. N. Bernshtein, A. G. Kushnirenko, A. G. Khovanskii, “Newton polyhedra”, Uspekhi Mat. Nauk, 31:3(189) (1976), 201–202
1974
167.
Yu. S. Ilyashenko, A. G. Khovanskii, Teoriya Galua sistem differentsialnykh uravnenii tipa Fuksa s malymi koeffitsientam, preprint № 117, IPM AN SSSR, M., 1974
1973
168.
A. G. Khovanskii, O predstavimosti funktsii v kvadraturakh, diss. … kand. fiz.-matem. nauk, Moskva, 1973, 76 pp.
1972
169.
A. G. Khovanskii, “Rimanovy poverkhnosti funktsii, predstavimykh v kvadraturakh”, VI Vsesoyuznaya topologicheskaya konferentsiya Tbilisi 2–7 oktyabrya: tezisy, Metsniereba, Tbilisi, 1972
1971
170.
A. G. Khovanskii, “The representability of functions by quadratures”, Uspekhi Mat. Nauk, 26:4(160) (1971), 251–252
171.
A. G. Khovanskii, “Superpositions of holomorphic functions with radicals”, Uspekhi Mat. Nauk, 26:3(159) (1971), 213–214
1970
172.
A. G. Khovanskii, “The representability of algebroidal functions by superpositions of analytic functions and algebroidal functions of one variable”, Funct. Anal. Appl., 4:2 (1970), 152–156
Co-convex bodies and multiplicities Askold Khovanskii International conference "Algebraic Topology and Abelian Functions" in honour of Victor Buchstaber on occasion of his 70th birthday June 22, 2013 10:00
Algebraic geometry and convex geometry A. G. Khovanskii International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold December 17, 2012 10:30
2023
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