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.
B. Ya. Kazarnovskii, A. G. Khovanskii, A. I. Esterov, “Newton polytopes and tropical geometry”, Russian Math. Surveys, 76:1 (2021), 91–175
4.
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
5.
A. Khovanskii, “Integriruemost v konechnom vide i deistviya grupp Li”, Mosc. Math. J., 19:2 (2019), 329–341
A. G. Khovanskii, “Newton polytopes and irreducible components of complete intersections”, Izv. Math., 80:1 (2016), 263–284
9.
K. Kaveh, A. Khovanskii, “Complete intersections in spherical varieties”, Special Issue: The Mathematics of Joseph Bernstein, Selecta Mathematica, 22:4 (2016), 2099–2141
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
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
20.
A. G. Khovanskii, “Polinomy Chebyshëva i ikh obrascheniya”, Matem. prosv., ser. 3, 17, Izd-vo MTsNMO, M., 2013, 93–106
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
23.
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
25.
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
27.
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
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
31.
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
A. Khovanskii, “Mnogogranniki i algebra”, Trudy Instituta sistemnogo analiza RAN, 38 (2008), 23–35
38.
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, “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
42.
A. G. Khovanskii, “Variations on the Theme of Solvability by Radicals”, Proc. Steklov Inst. Math., 259 (2007), 82–100
43.
A. G. Khovanskii, “An Analog of Determinant Related to Parshin–Kato Theory and Integer Polytopes”, Funct. Anal. Appl., 40:2 (2006), 126–133
44.
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
45.
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
50.
A. G. Khovanskii, S. P. Chulkov, “Hilbert and Hilbert–Samuel polynomials and partial differential equations”, Math. Notes, 77:1 (2005), 130–139
51.
A. G. Khovanskii, “On solvability and unsolvability of equations in explicit form”, Russian Math. Surveys, 59:4 (2004), 661–736
52.
A. Khovanskii, D. Novikov, “Comments to the Arnold problem 1987-4”, Arnold's Problems, Springer-Verlag, Berlin; PHASIS, Moscow, 2004, 457–458
53.
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
54.
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
55.
A. G. Khovanskii, “On the Nonrepresentability of Functions of Several Variables by Quadratures”, Funct. Anal. Appl., 37:4 (2003), 302–310
56.
A. G. Khovanskii, “On the Monodromy of a Multivalued Function Along Its Ramification Locus”, Funct. Anal. Appl., 37:2 (2003), 134–141
57.
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
59.
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
61.
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
62.
A. G. Khovanskii, “Families of Sections of Quadrics and Classical Geometries”, Funct. Anal. Appl., 34:3 (2000), 235–238
63.
A. Khovanskii, “Geometricheskoe obobschenie zadachi o preobrazovanii nomogramm iz vyrovnennykh tochek v tsirkulnye nomogrammy”, Nomograficheskii sbornik, no. 17, VTs RAN, 2000, 73–88
64.
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
65.
A. G. Khovanskii, “Boundary indices of polynomial 1-forms with homogeneous components”, St. Petersburg Math. J., 10:3 (1999), 553–575
66.
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, “Sums of Finite Sets, Orbits of Commutative Semigroups, and Hilbert Functions”, Funct. Anal. Appl., 29:2 (1995), 102–112
74.
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
77.
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
78.
A. V. Pukhlikov, A. G. Khovanskii, “Finitely additive measures of virtual polyhedra”, St. Petersburg Math. J., 4:2 (1993), 337–356
79.
A. G. Khovanskii, “Newton polyhedron, Hilbert polynomial, and sums of finite sets”, Funct. Anal. Appl., 26:4 (1992), 276–281
80.
Yu. S. Ilyashenko, A. G. Khovanskii, “Galois groups, Stokes operators and a theorem of Ramis”, Funct. Anal. Appl., 24:4 (1990), 286–296
81.
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
82.
A. Khovanskii, “Newton Polyhedra (algebra and geometry)”, Amer. Math. Soc. Transl. (2), 153 (1992), 183–199
83.
A. Khovanskii, “Algebra and mixed volumes”: Y. D. Burago, V. A. Zalgaller, Geometric inequalities, 285, Springer-Verlag, Berlin and New York, 1988, 182–207
84.
A. Khovanskii, “Sopostavlenie ob'ektivno-obuslovlennykh otsenok i normativov effektivnosti v razlichnykh malosektornykh modelyakh ekonomiki”, Sbornik trudov VNIISI, no. 9, 1987, 10–23
85.
A. G. Khovanskii, “Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskii space”, Funct. Anal. Appl., 20:1 (1986), 41–50
86.
V. I. Danilov, A. G. Khovanskii, “Newton polyhedra and an algorithm for computing Hodge–Deligne numbers”, Math. USSR-Izv., 29:2 (1987), 279–298
87.
A. Khovanskii, “Lineinoe programmirovanie i obobschennaya teorema Nikulina”, Sbornik trudov VNIISI, no. 7, 1985, 81–86
88.
A. Khovanskii, “Lineinoe programmirovanie i geometriya vypuklykh mnogogrannikov”, Sbornik trudov VNIISI, no. 7, 1985, 73–80
89.
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
90.
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
91.
A. Varchenko, A. Khovanskii, “Asymptotics of integrals over vanishing cycles and the Newton polyhedron”, Soviet Math. Dokl., 32:1 (1985), 122–127
92.
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
93.
A. G. Khovanskii, “Real analytic varieties with the finiteness property and complex abelian integrals”, Funct. Anal. Appl., 18:2 (1984), 119–127
94.
A. Khovanskii, “On analogues of Alexandrov–Fenchel inequalities for hyperbolic forms”, Soviet Math. Dokl., 29:3 (1984), 710–713
95.
A. Khovanskii, “Smeshannye ob'emy”, UMN, 39:5 (1984), 227–228
96.
A. Khovanskii, “Cycles of dynamic systems on a plane and Roll theorem”, Siberian Math. J., 25:3 (1985), 502–506
97.
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
98.
A. G. Khovanskii, “Analogues of Aleksandrov–Fenchel inequalities for hyperbolic forms”, Dokl. Akad. Nauk SSSR, 276:6 (1984), 1332–1334
99.
A. G. Khovanskii, “Newton polyhedra (resolution of singularities)”, J. Soviet Math., 27:3 (1984), 2811–2830
100.
L. Kantorovich, E. Korkina, A. Khovanskii, “Optimizatsiya potrebleniya v nepreryvnoi i diskretnoi modelyakh dvukhsektornoi ekonomiki”, Sbornik trudov VNIISI, no. 9, 1983, 14–20
101.
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
102.
E. Korkina, A. Khovanskii, “Printsip differentsialnoi optimizatsii i malosektornye modeli ekonomiki”, Sbornik trudov VNIISI, no. 8, 1982, 3–10
103.
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
104.
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
107.
E. Korkina, A. Khovanskii, ““Zolotoe pravilo” dlya modeli dvusektornoi ekonomiki”, Trudy seminara “Metody issledovaniya slozhnykh sistem”, VNIISI AN SSSR, M., 1981, 11–18
108.
A. Khovanskii, “Mnogogrannik Nyutona i indeks vektornogo polya”, UMN, 36:4 (1981), 234
109.
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
110.
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
111.
O. A. Gelfond, A. G. Khovanskii, “Real Liouville functions”, Funct. Anal. Appl., 14:2 (1980), 122–123
112.
A. Khovanskii, “Rectification of parallel curves”, Soviet Math. Dokl., 21:1 (1980), 284–286
113.
A. G. Khovanskii, “O chisle nulei veschestvennykh uravnenii”, UMN, 35:5 (1980), 213
A. G. Khovanskii, “Index of a polynomial field”, Funct. Anal. Appl., 13:1 (1979), 38–45
115.
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
116.
A. G. Khovanskii, “Geometriya vypuklykh mnogogrannikov i algebraicheskaya geometriya”, UMN, 34:4 (1979), 160–161
A. G. Khovanskii, “Newton polyhedra and the genus of complete intersections”, Funct. Anal. Appl., 12:1 (1978), 38–46
118.
A. G. Khovanskii, “Newton polyhedra and the Euler–Jacobi formula”, Russian Math. Surveys, 33:6 (1978), 237–238
119.
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
120.
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
121.
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
122.
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
123.
A. G. Khovanskii, “Newton polyhedra and toroidal varieties”, Funct. Anal. Appl., 11:4 (1977), 289–296
124.
D. N. Bernshtein, A. G. Kushnirenko, A. G. Khovanskii, “Newton polyhedra”, Uspekhi Mat. Nauk, 31:3(189) (1976), 201–202
125.
A. G. Khovanskii, “Rimanovy poverkhnosti funktsii, predstavimykh v kvadraturakh”, VI Vsesoyuznaya topologicheskaya konferentsiya Tbilisi 2–7 oktyabrya: tezisy, Metsniereba, Tbilisi, 1972
126.
A. G. Khovanskii, “The representability of functions by quadratures”, Uspekhi Mat. Nauk, 26:4(160) (1971), 251–252
127.
A. G. Khovanskii, “Superpositions of holomorphic functions with radicals”, Uspekhi Mat. Nauk, 26:3(159) (1971), 213–214
128.
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
Books
129.
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.
130.
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.
131.
A. Khovanskii, Galois theory, coverings, and Riemann surfaces, Translated by V. Kiritchenko and V. Timorin, Springer Berlin Heidelberg, 2013, 81 pp.
132.
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.
133.
A. G. Khovanskii, Kompleksnyi analiz, Izd-vo MTsNMO, Moskva, 2004, 48 pp.
134.
A. G. Khovanskii, Malochleny, Fazis, Moskva, 1997, xii+217 pp.
135.
G. S. Khovanskii, A. G. Khovanskii, E. G. Kozlova, O nekotorykh voprosakh teoreticheskoi i prikladnoi nomografii, VTs RAN, 1996, 99 pp.
136.
A. Khovanskii, Fewnomials, AMS translated monographs, 88, USA, 1991, viii+139 pp.
A. G. Khovanskii, Mnogogranniki Nyutona i malochleny, diss. … dokt. fiz.-matem. nauk, Moskva, 1988, 332 pp.
138.
A. G. Khovanskii, O predstavimosti funktsii v kvadraturakh, diss. … kand. fiz.-matem. nauk, Moskva, 1973, 76 pp.
Proceedings
139.
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
140.
B. Kazarnovskii, A. Khovanskii, “Universal Groebner basis”, Proceedings of the International Conference on Polynomial Computer Algebra, Saint Peterburg, 2011, 65–69
141.
A. Khovanskii, “A topological version of Galois theory”, Proceeding of International Conference, Kolmogorov and Cotemporary Mathematics, 2003, 777–780
142.
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
Preprints
143.
J.-M. Kantor, A. Khovanskii, Integral points in convex polyhedra, combinatorial Riemann–Roch theorem and generalized Euler–MacLaurin formula, Preprint IHES, France, 1992
144.
A. Khovanskii, Theorem de Bezout pour les fonctions de Liouville, Preprint IHES, 81/85, 1981, 31 pp.
145.
Yu. S. Ilyashenko, A. G. Khovanskii, Teoriya Galua sistem differentsialnykh uravnenii tipa Fuksa s malymi koeffitsientam, preprint № 117, IPM AN SSSR, M., 1974
ArXiv
146.
K. Kaveh, A. Khovanskii, “On mixed multiplicities of ideals”, 2013, 20 pp., arXiv: 1310.7979v1
147.
K. Kaveh, A. Khovanskii, “Convex bodies and algebraic equations on affine varieties”, 2008, 44 pp., arXiv: 0804.4095
Popular science or education materials
148.
A. G. Khovanskii, Mat. Pros., 17, MCCME, Moscow, 2013, 93–106
149.
A. G. Khovanskii, Mat. Pros., 17, MCCME, Moscow, 2013, 42–60
Information matherials
150.
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
151.
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
Personalia
152.
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
153.
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
154.
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
155.
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
156.
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
157.
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
158.
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
159.
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
160.
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
161.
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
162.
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
163.
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
164.
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
165.
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
Miscellaneous
166.
A. Khovanskii, Journal of Complexity, 21:1, Special Issue: Foundations of Computational Mathematics 2002 Workshops (2005)
167.
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
168.
A. Khovanskii, Geometry of Differential Equations, Amer. Math. Soc. Transl., Ser. 2, 186, Amer. Math. Soc., Providence, RI, 1998
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