Algebraic transformation groups; invariant theory; algebraic groups, Lie groups, Lie algebras and their representations; algebraic geometry; automorphism groups of algebraic varieties; discrete reflection groups
Biography
Graduated from Mathematics and Mechanics Faculty of Moscow State University Lomonosov (MSU) (Department of High Algebra) in 1969. PhD (Candidate of Physics and Mathematics) (1972). Habilitation (Doctor of Physics and Mathematics) (1984). Full Professor (1986). Chair of Algebra and Mathematical Logic at Moscow State University MIEM (1995–2012; half-time since 2002).
Since 2012 Professor at Department of Applied Mathematics of MIEM-HSE (part time). Since January 2002 Leading Research Fellow, and since May 2017 Principal Research Fellow at the Steklov Mathematical Institute, Russian Academy of Sciences (main place of work).
Invited speaker at the International Congress of Mathematicians, Berkeley, USA (1986). The results of 1982–1983 are the subject of J. Dixmiers talk at Séminaire N. Bourbaki (J. Dixmier, Quelques résults de finitude en théorie des invariants (daprès V. L. Popov), Séminaire Bourbaki, 38ème année 1985–86, no. 659, pp. 163–175).
Core member of the panel for Section 2, "Algebra" of the Program Committee for the 2010 International Congress of Mathematicians (2008–2010).
Fellow of The American Mathematical Society, the inaugural class (elected in November 2012
``in recognition of distinguished contributions to the profession’’), see http://www.ams.org/profession/fellows-list-institution
Corresponding Member of the Russian Academy of Sciences (elected in October 2016).
Fellow of The Core Academy (Hong Kong) (elected in October 2023), see https://www.coreacad.org/Member.aspx?ProId=43
Invited plenary speaker at the XVth Austrian–German Mathematical Congress
(Ősterreichische Mathematische Gesellschaft–XV Kongress, Jahrestagung der Deutschen Mathematiker-vereinigung), Vienna, 2001.
Honorable International John-von-Neumann Professur awarded by Technische Universität München, Germany (2008).
Invited Noted Scholar, Heidelberg University, Germany (1998–1999).
Invited Noted Scholar, the University of British Columbia, Vancouver, Canada (1996).
Invited speaker at the international colloquia and conferences in Russia, France, UK, Italy, Germany, USA, Canada, Japan, Switzerland, Israel, Netherlands, Belgium, Spain, Norway, Sweden, India, Australia, Singapore, Hungary, Poland, Argentina, Uruguay, in particular, at Colloque en lhonneur de J. Dixmier (Paris, 1989), at the International Conference commemorating 150th birthday of Sophus Lie (Oslo, 1992), at Special Sessions of the Annual American Mathematical Society meetings in Chicago (1995) and Louisville, USA (1998), at the International Colloquium "Algebra, Arithmetic and Geometry" (Tata Institute, Bombay, 2000), at the International Conference commemorating 80th birthday of B. Kostant" (Vancouver, 2008).
Honorable Colligwood Lecture at Durham University, UK (2007).
Delivered courses "Invariant Theory", "Discrete Groups Generated by Complex Reflections", "Algebraic Transformation Groups and Singularities of Algebraic Varieties", "Algebraic Groups", "Algebraic Geometry" at the invitation of several leading mathematical centers in Germany (Heidelberg University, TUM), Switzerland (ETH Zürich), Netherlands (University of Utrecht), USA (University of Michigan), Canada (UBC), Austria (The Erwin Schrödinger Institute, Innsbruck University), Australia (Sydney University), Sweden (Lund University), Russia (Steklov Mathematical Institute, Moscow). For many years conducted seminars at the Mechanics and Mathematics Department of the Moscow State University: from 1970 to 1986 on invariant theory (jointly with E. B. Vinberg), from 1986 to 2000 on Lie groups and invariant theory (jointly with E. B. Vinberg and A. L. Onishchik). They formed the national school of the algebraic transformation group theory.
In 1995, together with E. B. Vinberg, founded the journal "Transformation Groups" published by Birkhäuser Boston.
Editor-in-Chief of this journal from 2020 to present and Executive Managing Editor from 1996 to 2020, see
https://www.springer.com/journal/31?
Member of the Editorial Boards of the journals: "Izvestiya: Mathematics" (2006–present) and "Mathematical Notes" (2003–present) of the Russian Academy of Sciences, "European Mathematical Society Newsletter" (2015–2022) of the EMS, "Transactions of the Moscow Mathematical Society" of the MMS, MCIME, and AMS, "Geometriae Dedicata" of Kluwer (1989–1999), "Journal of Mathematical Sciences" of Springer (2001–2000). Founder and Title Editor of the series "Invariant Theory and Algebraic Transformation Groups" of Encyclopaedia of Mathematical Sciences published by Springer (1998–present).
Member, Board of Moscow Mathematical Society (1998–2000).
More than 190 publications, among them 4 monographs, 1 textbook and the papers published in
Annals of Mathematics, Journal of the American Mathematical Society, Compositio Mathematica, Transformation Groups, Izvestiya: Mathematics, Sbornik: Mathematics, Journal fur die reine und angewandte Mathematik, Commentarii Mathematici Helvetici, Contemporary Mathematics, Journal of Algebra, Functional Analysis and Its Applications, Comptes Rendus de lAcademie des Sciences Paris, Transactions of the Moscow Mathematical Society, Indagationes Mathematicae, Mathematical Notes, Russian Mathematical Surveys, Journal of the Ramanujan Mathematical Society, Documenta Mathematica, Pacific Journal of Mathematics, European Journal of Mathematics. The results are included in many monographs and textbooks (D. Mumford, J. Fogarty, Geometric Invariant Theory; H. Kraft, Geometrische Methoden in der Invariantentheorie; H. Derksen, G. Kemper, Computational Invariant Theory; F. Grosshans, Algebraic Homogeneous Spaces and Invariant Theory; H. Kraft, P. Slodowy, T. A. Springer, Algebraic Transformation Groups and Invariant Theory; W. F. Santos, A. Rittatore, Actions and Invariants of Algebraic Groups; B. Sturmfels, Algorithms in Invariant Theory; G. Freudenburg, Algebraic Theory of Locally Nilpotent Derivations; M. Lorenz, Multiplicative Invariant Theory; E. A. Tevelev, Projective Duality and Homogeneous Spaces and the others).
Organizer of several international conferences, in particular, "Semester on Algebraic Transformation Groups" at The Erwin Schrödinger Institute, Vienna (joint with B. Kostant, 2000), and the conference "Interesting Algebraic Varieties Arising in Algebraic Transformation Groups Theory" at The Erwin Schrödinger Institute, Vienna (2001).
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The results obtained include the following:
● A criterion for closedness of orbits in general position, one of the basic facts of modern Invariant theory (1970–72).
● Pioneering results of modern theory of embeddings (compactifications) of homogeneous algebraic varieties (in particular, toric and spherical varieties), which determined its rapid modern development (1972–73).
● Computing the Picard group of any homogeneous algebraic variety of any linear algebraic group (1972–74).
● Creation of a new direction in Invariant theory—classifying linear actions with certain exceptional properties, e.g., with a free algebra of invariants (jointly with V. G. Kac and E. B. Vinberg), with a free module of covariants, with an equidimensional quotient, and the others. Developing the appropriate methods and obtaining the classifications themselves. Finiteness theorems for the actions with a fixed length of the chain of syzygies (1976–83). The ideology of exceptional properties has then became wide spreaded.
● Solution to the generalized Hilbert’s 14th problem (1979).
● The estimates of the degrees of basic invariants of connected semisimple linear groups first obtained 100 years after the attempt by Hilbert to obtain them (1981–82). They gave rise to modern constructive Invariant theory .
● A theory of contractions of any actions to horospherical ones, which has become an indispensable tool for the modern theory of algebraic transformation groups (1986).
● Pioneering results on the description of algebraic subgroups of the affine Cremona groups that led to a surge of activity in this area in recent decades are obtained (1986–2011).
● The characterization of affine algebraic groups as automorphism groups of simple finite-dimensional (not necessarily associative) algebras (2003, jointly with N. L. Gordeev). In particular, the extension to any finite group of the famous characterization of the largest simple sporadic finite group (the Fischer–Griess Monster). The result is published in Annals of Mathematics and recognized as one of the best in the Steklov Mathematical Institute in 2002.
● A theory of the phenomenon discovered in 1846 by Cayley (2005, jointly with N. Lemire, Z. Reichstein): classification of algebraic groups admitting a birational equivariant map on its Lie algebra. Solution to the old (1975) problem of classifying Caley unimodular groups. The result is published in Journal of the American Mathematical Society and recognized as one of the best in the Russian Academy of Sciences in 2005.
● Proving the algorithmic solvability of the belonging problem of a point of an algebraic variety to the orbit closure of another its point with respect to the action of an algebraic group on this variety and, in particular, proving the algorithmic solvability of the coincidence problem of the orbits of these points (2009).
● Classification of simple Lie algebras whose fields of rational functions are purely transcendental over the subfields of adjoint invariants (2010, jointly with J.-L. Colliot-Thélène, B. Kunyavskiĭ, Z. Reichstein). This result is at the heart of counter-examples to the famous Gelfand–Kirillov conjecture of 1966 on the fields of fractions of the universal enveloping algebras of simple Lie algebras. It is published in Compositio Mathematica and recognized as one of the best in the Steklov Mathematical Institute in 2010.
● Answers to the old (1969) questions of Grothendieck to Serre on the cross-sections and quotients for the actions of semisimple algebraic groups on themselves by conjugation. Constructing the minimal system of generators of the algebras of class functions and that of the representations of rings of such groups (2011).
● Defining the general notion of Jordan group and initiating exploration (carried out since then by many specialists) of the Jordan property of automorphism groups of varieties and manifolds, in particular, groups of birational self-maps and biregular automorphisms of algebraic varieties. Obtaining classification of algebraic surfaces and curves whose groups of birational self-maps are Jordan (2011).
● Solving the problem, posed in 1965 by A. Borel: obtaining the classification of infinite discrete groups generated by complex affine unitary reflections; exploring their remarkable connections with number theory, combinatorics, coding theory, algebraic geometry and singularity theory (1967, 1980–82, 2005, 2023).
===================================
On the results obtained (citations):
● From Introduction to the book J. Olver, Classical Invariant Theory, London Math. Soc. Student Texts 44 Cambridge Univ. Press, 1999:
``[…] a vigorous, new Russian school of invariant theorists, led by Popov [181] and Vinberg [226] who have pushed the theory into fertile new areas. […]"
● On the book Popov, V. L. Groups, Generators, Syzygies, and Orbits in Invariant Theory. Transl. of Math. Monographs, 100. Amer. Math. Soc., Providence, RI, 1992. vi+245 pp.:
– From the review by G. Schwarz (Bull of Amer. Math. Soc., 29 (1993), no. 2, 299–304):
``[…] Popov is a leader in Invariant theory, and the articles in this book were important to that field’s development. […]’’
``[…] There has been an explosion of activity in this area over the last ten years.
Popovs work was seminal. […]’’
– From the review by M. Brion (Math. Reviews 92g:14054:
``[… ] The author’s results have been the starting point for research trends in invariant theory: for example, classification of representations of semisimple groups with ``good " properties, and also embedding theory of homogeneous spaces. […]’’
● On the work V. L. Popov, E. B. Vinberg, Invariant Theory, Encycl. Math. Sci., Vol. 55, Springer-Verlag, Berlin, 1994, pp. 123–284:
– From the review by N. Andruskiewitsch (Zentralblatt Math. 735.14010):
``[…] The paper under review, written by two of the main contributors in this last
period, […] should be considered as a book, which is probably the format it would have if translated. […]"
– From the review by P. E. Newstead (Math. Reviews 92d:14010) :
``This article is […] by two of today’s leading experts in the field and will undoubtedly serve as a major source of information on the subject. […]"
— From the paper S. Fomin, P. Pylyavskyy, Tensor diagrams and cluster algebras,
Adv. Math. 300 (2016), 717--787:
``Our main sources of inspiration outside cluster theory included the timeless texts by H. Weyl [57] and V. Popov--E. Vinberg [48]"
(here [48] is the reference to the paper V. L. Popov, E. B. Vinberg,
Invariant theory, in: Algebraic geometry. IV, Encyclopaedia of Mathematical Sciences, Vol. 55, Springer-Verlag, Berlin, 1994,
pp. 123–284).
● From the paper Y. André, Solution algebras of differential equations and quasi-homogeneous varieties: a new differential Galois correspondence,
Ann. Sci. Ec. Norm. Sup. (4) 47 (2014), no. 2, 449--467:
``After pioneering work by Grosshans, Luna, Popov, Vinberg and others in the seventies, the study of quasi-homogeneous G-varieties, i.e., algebraic G-varieties with a dense G-orbit, has now become a rich and deep theory.’’
● From the paper D. Luna et Th. Vust, Plongements d’espaces homogènes, Comment. Math. Helvetici 58 (1983), 186–245:
``Nous devons notre point de départ bien évidemment à la théorie des plongements toriques ([5], [6]), mais aussi à article [10] de V. L. Popov, dans lequel est donnée la classification des espaces Presque-homogènes affines normaux sous SL(2)’’ (here [10] stands for V. L. Popov, “Quasihomogeneous affine algebraic varieties of the group SL(2)”, Math. USSR-Izv., 7:4 (1973), 793–831).
● From the Introduction to Chap. III of the book H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspekte der Mathematik, Bd. D1, Vieweg, Braunschweig, 1985:
``[…] Zum Abschluss geben wir – sozusagen als Krönung der hier entwickelten Methoden – die vollständige Klassifikation der sogenannten SL(2)-Einbettungen, d.h. derjenigen affinen SL(2)-Varietäten, welche einen dichten Orbit enthalten. Dieses schöne Resultat geht auf V. L. Popov zurück [P1] (here [Po1] stands for V. L. Popov, “Quasihomogeneous affine algebraic varieties of the group SL(2)”, Math. USSR-Izv., 7:4 (1973), 793–831).
● From the book Algebraic Transformation Groups and Invariant Theory, DMV Seminar, Band 13, Birkhäuser, 1989, p. 72:
``In this paragraph we explain some classical results about the Picard group Pic G
([…]; [Po 74]; […])" (here [Po 74] stands for V. L. Popov, Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles, Math. USSR Izv. 8 (1974), 301–327).
● From the paper H. Derksen, H. Kraft, Constructive Invariant theory, in: Algèbre Non Commutative, Groupes Quantiques et Invariants (Reims, 1995), Sémin. Congr., Vol. 36, Soc. Math. France, Paris, 1997, pp. 221–244:
``It took almost a century until Vladimir Popov determined a general bound for
β(V ) for any semi-simple group G ([Pop 81/82])" (here [Pop 81/82] stands for V.
Popov, Constructive Invariant theory, Ast_erisque 87{88 (1981), 303–334, and V. L. Popov, The constructive theory of invariants, Math. USSR Izv. 19 (1982), 359–376.
● From the paper K. D. Mulmuley, Geometric Complexity Theory V: Equivalence between blackbox derandomization of polynomial identity testing and derandomization of
Noethers Normalization Lemma, in: 2012 IEEE 53rd Annual Symposium on
Foundations of Computer Science,
New Brunswick, New Jersey, 2012, pp. 629--638:
``$\ldots$ But Hilbert could only show that his algorithm for constructing finitely many generators for $K[V]^G$
worked in finite time. He could not prove any explicit upper bound
on its running time. Such a bound was proved in $[\rm P]$ a century later $\ldots$"
(here $[\rm P]$ is the reference to the paper V. Popov, The constructive theory of
invariants, Math. USSR Izv. 10 (1982), 359--376).
● From the paper J. Elmer, M. Kohls, Zero-separating invariants for finite groups,
J. Algebra 411 (2014), 92–113:
``One of the most celebrated results of 20th century
invariant theory is the theorem of Nagata [12] and Popov [13] which states that
$k[X]^G$ is finitely generated for all affine G-varieties X if and only if G is reductive.
(here [13] stands for V. L. Popov, Hilberts theorem on invariants,
Soviet Math. Dokl., 20:6 (1979), 1318–1322).
● From the book (p. 161) D. Mumford, J. Fogarty, Geometric Invariant Theory, 2nd ed., Ergebnisse der Math. Und ihrer Grenzgebiete, Bd. 34, Springer-Verlag, Berlin, 1982:
``[…] The striking result due to Kac, Popov, Vinberg ([…], [166], […]) is the following Theorem […]‘’ (here [166] stands for V. G. Kac, V. L. Popov, E. B. Vinberg, “Sur les groupes linéaires algébriques dont lalgèbre des invariants est libre”, C. R. Acad. Sci. Paris Sér. A-B, 283:12 (1976), A875–A878).
● From the paper H. Flenner, M. Zaidenberg, Locally nilpotent derivations on affine surfaces with a C-action, Osaka J. Math. 42 (2005), no. 4, 931–974:
``By classical results […] of Popov [Po], […]" (here [Po] stands for
V. L. Popov, Classification of affine algebraic surfaces that are quasihomogeneous with respect to an algebraic group, Math. USSR Izv. 7 (1974), 1039–1055 (1975)).
● From the paper L. E. Renner, Orbits and invariants of visible group actions, Transform. Groups 17 (2012), no. 4, 1191–1208:
``We now introduce the following definition (Definition 1.10 below). It is one of the key notions in the study of invariants.[...] The notion of a stable action was first introduced in [7] by V. L. Popov. There he establishes a criterion of stability for semisimple groups (Theorem 1 of [7])‘’ (here Definition 1.10 is the definition of stable action and [7] is the reference to paper V. Popov, On the stability of the action of an algebraic group on an algebraic
variety, Math. USSR Izv. 6 (1973), 367–379).
● From the paper N. Perrin, On the geometry of spherical varieties, Transform. Groups 19 (2014), no. 1, 171–223:
``It is a classical problem to ask which product of projective rational homogeneous
spaces
$\prod_i G/P_i$ has a dense G-orbit. This is solved in
[141] if all the parabolic subgroups
agree‘’ (here [141] is the reference to the paper
V. L. Popov, Generically multiple transitive algebraic group actions, in:
Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces (Mumbai, 2004), Tata Institute of Fundamental Research, Vol. 19, Narosa, internat. distrib. by AMS, New Delhi, 2007, pp. 481–523).
● From the paper A. Guld, Boundedness properties of automorphism groups of forms of flag varieties, arXiv:1806.05400v1 [math.AG] 14 Jun 2018:
`` Recently there have been great interest in investigating the finite subgroups of
biregular and birational automorphism groups of algebraic varieties. The Jordan
property lies in the center of attention. <…> Research about investigating Jordan properties for birational and biregular automorphism groups of varieties was initiated by V. L. Popov in [Po11]” (here [Po11] is the reference to the paper V. L. Popov. On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties, Proceedings of the conference on Affine Algebraic Geometry held in Professor Russell’s honour, 1–5 June 2009, McGill Univ., Montreal., Centre de Recherches Mathématiques CRM Proc. and Lect. Notes, Vol. 54, 289–311, 2011).
● From the paper Bharat Adsul, Milind Sohoni, K. V. Subrahmanyam, Geometric Complexity Theory --- Lie Algebraic Methods for Projective Limits of Stable Points, arXiv:2201.00135v1 [math.RT] 1 Jan 2022:
``A fundamental problem of invariant theory is that of obtaining a good description of the G orbit closures of points y ∈ V and deciding whether a point x belongs to the orbit closure of y. These problems go back to Hilbert and are of fundamental importance in the construction of moduli spaces […] The ubiquitous appearance of this problem in many areas of mathematics is also surveyed in the introduction of [Pop09]. […] In Popov [Pop09] the author gives a constructive algorithm to determine if x is in the orbit closure of y. He does this in both, the affine as well as the projective setting. This establishes the decidability of the orbit closure membership problem in the sense of computability theory.’’ (Here [Pop09] is the reference to the paper Vladimir L Popov. Two orbits: When is one in the closure of the other? , Proc. Steklov Inst. of Math., 264(1):146–158, 2009).
Main publications:
V. L. Popov, “Group varieties and group structures”, Izv. Math., 86:5 (2022), 903–924
Vladimir L. Popov, “On the equations defining affine algebraic groups”, Pacific J. Math., 279:1-2, Special issue. In memoriam: Robert Steinberg (2015), 423–446http://msp.org/pjm/2015/279-1/p19.xhtml, arXiv: 1508.02860
J.-L. Colliot-Thélène, B. Kunyavskiĭ, V. L. Popov, Z. Reichstein, “Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?”, Compos. Math., 147:2 (2011), 428–466
V. L. Popov, “Cross-sections, quotients, and representation rings of semisimple algebraic groups”, Transform. Groups, 16:3, special issue dedicated to Tonny Springer on the occasion of his 85th birthday (2011), 827–856
N. Lemire, V. L. Popov, Z. Reichstein, “Cayley groups”, J. Amer. Math. Soc., 19:4 (2006), 921–967
N. L. Gordeev, V. L. Popov, “Automorphism groups of finite dimensional simple algebras”, Annals of Math. (2), 158:3 (2003), 1041–1065
V. L. Popov, Groups, Generators, Syzygies, and Orbits in Invariant Theory, Translations of Mathematical Monographs, 100, Amer. Math. Soc., Providence, RI, 1992 , vi+245 pp.
V. L. Popov, Discrete Somplex Reflection Groups, Lectures delivered at the Math. Institute Rijksuniversiteit Utrecht in October 1980, Commun. Math. Inst. Rijksuniv. Utrecht, 15, Rijksuniversiteit Utrecht Mathematical Institute, Utrecht, 1982 , 89 pp. www.researchgate.net/publication/261552178_Discrete_complex_reflection_groups . Second enlarged edition published in Communications in Mathematics, vol. 30 (2022), no. 3 (published August 22, 2023), 303–375, cm.episciences.org/11725
V. L. Popov, “Hilbert's theorem on invariants”, Soviet Math. Dokl., 20:6 (1979), 1318–1322
Vladimir L. Popov, “Rationality of adjoint orbits”, Pure Appl. Math. Q., 20:1, Special Issue dedicated to Corrado De Concini (2024), 525–535 , arXiv: 2206.14040;
2.
Vladimir L. Popov, The variety of flexes of plane cubics, 2024 (to appear) , 22 pp., arXiv: 2408.16488
2023
3.
V. L. Popov, “Embeddings of automorphism groups of free groups into automorphism groups of affine algebraic varieties”, Algebra and Arithmetic, Algebraic, and Complex Geometry. In Memory of Academician Alexey Nikolaevich Parshin, Proceedings of the Steklov Institute of Mathematics, 320, Pleiades Publ., 2023, 267–277rdcu.be/ddUYG
4.
Vladimir L. Popov, Picard group of connected affine algebraic group, 2023 , 3 pp., arXiv: 2302.13374
5.
Vladimir L. Popov, Rational differential forms on the variety of flexes of plane cubics, 2023 , 3 pp., arXiv: 2302.13364
6.
V. L. Popov, “Picard group of a connected affine algebraic group”, Russian Math. Surveys, 78:4 (2023), 794–796
7.
Vladimir L. Popov, Discrete complex reflection groups, 2023 , 67 pp., arXiv: 2304.08941
8.
Vladimir L. Popov, “Faithful actions of automorphism groups of free groups on algebraic varieties”, Transform. Groups, 28:3 (2023), 1277–1297 , arXiv: 2207.08912;
9.
Vladimir L. Popov, “Discrete complex reflection groups”, Commun. Math., 30:3 (2023), 303–375 , arXiv: 2304.08941v5;
10.
Algebra, arifmeticheskaya, algebraicheskaya i kompleksnaya geometriya, Sbornik statei. Posvyaschaetsya pamyati akademika Alekseya Nikolaevicha Parshina, Trudy MIAN, 320, ed. V. L. Popov, S. O. Gorchinskii, A. B. Zheglov, D. V. Osipov, MIAN, M., 2023 , 324 pp.
11.
F. A. Bogomolov, A. M. Vershik, S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarhin, S. V. Konyagin, Vik. S. Kulikov, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, I. A. Panin, V. P. Platonov, V. L. Popov, Yu. G. Prokhorov, A. L. Smirnov, “Alexey Nikolaevich Parshin (obituary)”, Russian Math. Surveys, 78:3 (2023), 549–554
12.
S. O. Gorchinskiy, Vik. S. Kulikov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, V. L. Popov, N. A. Tyurin, G. B. Shabat, A. I. Shafarevich, V. V. Shokurov, “Igor Rostislavovich Shafarevich (on the centenary of his birthday)”, Russian Math. Surveys, 78:6 (2023), 1167–1178
2022
13.
V. L. Popov, “Group varieties and group structures”, Izv. Math., 86:5 (2022), 903–924
14.
Vladimir L. Popov, Faithful actions of automorphism groups of free groups on algebraic varieties, 2022 , 22 pp., arXiv: 2207.08912
15.
Vladimir L. Popov, Embeddings of automorphism groups of free groups into automorphism groups of affine algebraic varieties, 2022 , 14 pp., arXiv: 2207.13072
16.
V. L. Popov, “Vspominaya A. N. Parshina”, Vospominaniya ob A. N. Parshine, ISBN 978-5-4439-1767-2, MTsNMO, Moskva, 2022, 12–15
17.
F. A. Bogomolov, S. O. Gorchinskiy, A. B. Zheglov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, A. N. Parshin, V. L. Popov, V. V. Przyjalkowski, Yu. G. Prokhorov, M. Reid, A. G. Sergeev, D. V. Treschev, A. K. Tsikh, I. A. Cheltsov, E. M. Chirka, “Viktor Stepanovich Kulikov (on his 70th birthday)”, Russian Math. Surveys, 77:3 (2022), 555–557
18.
A. A. Agrachev, R. V. Gamkrelidze, V. V. Kozlov, Yu. I. Zhuravlev, A. V. Mikhalev, A. V. Ovchinnikov, D. O. Orlov, V. L. Popov, V. G. Romanov, A. L. Semenov, V. G. Chirskii, V. A. Shamolin, “To the 55th anniversary of Professor M. V. Shamolin”, Geometry, Mechanics, and Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 210, VINITI, Moscow, 2022, 3–5
2021
19.
Vladimir L. Popov, “Algebraic groups whose orbit closures contain only finitely many orbits”, Transform. Groups, 26:2 (2021), 671–689 , arXiv: 1707.06914v2
Vladimir L. Popov, “Variations on the theme of Zariski${}^{,}$s Cancellation Problem”, Polynomial Rings and Affine Algebraic Geometru, PRAAG 2018, Tokyo, Japan, February 12–16, 2018, Springer Proc. Math. Statist., 319, eds. S. Kuroda et al., Springer, Cham, 2020, 233–250 , arXiv: 1901.07030;
V. L. Popov, Yu. G. Zarhin, “Rings of integers in number fields, and root lattices”, Dokl. Math., 101:3 (2020), 221–223
29.
S. I. Adian, V. M. Buchstaber, E. I. Zelmanov, S. V. Kislyakov, V. V. Kozlov, Yu. V. Matiyasevich, S. P. Novikov, D. O. Orlov, A. N. Parshin, V. L. Popov, D. V. Treschev, “Vladimir Petrovich Platonov (on his 80th birthday)”, Russian Math. Surveys, 75:2 (2020), 387–391
30.
V. L. Popov, G. V. Sukhotskii, Analiticheskaya geometriya : uchebnik i praktikum dlya vuzov, 2-e izd., pererab. i dop., Yurait, Moskva, 2020 , 232 pp. http://urait.ru/bcode/451230
2019
31.
V. L. Popov, “Three plots about the Cremona groups”, Izv. Math., 83:4 (2019), 830–859
32.
Vladimir L. Popov, “On conjugacy of stabilizers of reductive group actions”, Mathematical Notes, 105:4 (2019), 580–581 , arXiv: 1901.10858
33.
V. L. Popov, “Orbit closures of the Witt group actions”, Proc. Steklov Inst. Math., 307, Algebra, Number Theory, and Algebraic Geometry. Collected papers. In Memory of Academician Igor Rostislavovich Sharafevich (2019), 193–197
34.
V. L. Popov, “Rational differential forms on the variety of flexes of plane cubics”, Russian Math. Surveys, 74:3 (2019), 543–545
35.
V. L. Popov, “Sistemy kornei i reshetki kornei v chislovykh polyakh”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii. Materialy XVII Mezhdunarodnoi konferentsii, posvyaschennoi stoletiyu so dnya rozhdeniya professora N. I. Feldmana i devyanostoletiyu so dnya rozhdeniya professorov A. I. Vinogradova, A. V. Malysheva i B. F. Skubenko (Tula, 23–28 sentyabrya 2019 g.), ISBN 5–87954–388–9, Biblioteka Chebyshevskogo sbornika, Tulskii gosudarstvennyi pedagogichekii universitet im. L. N. Tolstogo, Tula, 2019, 223–226
36.
S. O. Gorchinskiy, Vik. S. Kulikov, A. N. Parshin, V. L. Popov, “Igor Rostislavovich Shafarevich and his mathematical heritage”, Proceedings of the Steklov Institute of Mathematics, 307, Algebra, Number Theory, and Algebraic Geometry, Collected papers. In Memory of Academician Igor Rostislavovich Shafarevich (2019), 1–21
37.
Algebra, teoriya chisel i algebraicheskaya geometriya, Sbornik statei. Posvyaschaetsya pamyati akademika Igorya Rostislavovicha Shafarevicha, Trudy MIAN, 307, ed. A. N. Parshin, V. L. Popov, S. O. Gorchinskii, Vik. S. Kulikov, MIAN, M., 2019 , 328 pp.
2018
38.
Vladimir L. Popov, “The Jordan property for Lie groups and automorphism groups of complex spaces”, Math. Notes, 103:5 (2018), 811–819
39.
Vladimir L. Popov, Three plots about the Cremona groups, 2018 , 27 pp., arXiv: 1810.00824
40.
Victor G. Kac, Vladimir L. Popov, Editors, Lie Groups, Geometry, and Representation Theory. A Tribute to the Life and Work of Bertram Kostant, Series ISSN 0743-1643, ISBN 978-3-030-02191-7, Progress in Mathematics, 326, First Edition, Birkhäuser Basel (Copyright Holder: Springer Nature Switzerland AG), Basel, 2018 , X, 538 pp. www.springer.com/us/book/9783030021900
41.
Vladimir L. Popov, Yuri G. Zarhin, Root symstems in number fields, Preprint MPIM 18-38, Max-Planck-Institut für Mathematik, Bonn, 2018 , 19 pp. www.mpim-bonn.mpg.de/preblob/5898
42.
Vladimir L. Popov, “Modality of representations, and packets for $\theta$-groups”, Lie Groups, Geometry, and Representation Theory. A Tribute to the Life and Work of Bertram Kostant, Prog. Math., 326, Birkhäuser Basel (Copyright Holder: Springer Nature Switzerland AG), Basel, 2018, 459–479 , arXiv: 1707.07720
V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415
44.
V. L. Popov, Yu. G. Zarhin, “Types of root systems in number fields”, Dokl. Math., 98:3 (2018), 600–602
2017
45.
Vladimir L. Popov, “Do we create mathematics or do we gradually discover theories which exist somewhere independently of us?”, Eur. Math. Soc. Newsl., 103 (2017), 37
46.
V. L. Popov, “Borel subgroups of Cremona groups”, Mathematical Notes, 102:1 (2017), 60-67
47.
Vladimir L. Popov, Algebraic groups whose orbit closures contain only finitely many orbits, 2017 , 12 pp., arXiv: 1707.06914v1
48.
Vladimir L. Popov, “Bass' triangulability problem”, Algebraic varieties and automorphism groups, Adv. Stud. Pure Math., 75, Math. Soc. Japan, Kinokuniya, Tokyo, 2017, 425–441bookstore.ams.org/aspm-75/, arXiv: 1504.03867
49.
Vladimir L. Popov, “Discrete groups generated by complex reflections”, VI-th conference on algebraic geometry and complex analysis for young mathematicians of Russia (Northern (Arctic) Federal University named after M. V. Lomonosov, Koryazhma, Arkhangelsk region, Russia, August 25–30, 2017), Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 2017, 13–14www.mathnet.ru/php/conference.phtml?confid=1006&option_lang=eng
50.
V. L. Popov, “On modality of representations”, Dokl. Math., 96:1 (2017), 312–314
51.
Gene Freudenburg, Algebraic Theory of Locally Nilpotent Derivations, Subseries: Invariant Theory and Algebraic Transformation Groups, Encyclopaedia of Mathematical Sciences, 136, no. VII, 2nd ed., eds. Revaz V. Gamkrelidze, Vladimir L. Popov, Springer, Berlin, 2017 , 316+i-xxii pp. https://link.springer.com/content/pdf/bfm
V. L. Popov, G. V. Sukhotskii, Analiticheskaya geometriya. Uchebnik i praktikum, Bakalavr. Akademicheskii kurs, 2-e izd., per. i dop., Yurait, Moskva, 2016 , 232 pp. http://urait.ru/catalog/388730
54.
V. L. Popov, “Algebras of General Type: Rational Parametrization and Normal Forms”, Proc. Steklov Inst. Math., 292:1 (2016), 202–215
55.
V. L. Popov, “Subgroups of the Cremona groups: Bass' problem”, Dokl. Math., 93:3 (2016), 307–309
56.
V. L. Popov, “Rationality of (co)adjoint orbits”, International conference on algebraic geometry, complex analysis and computer algebra (Northern (Arctic) Federal University named after M. V. Lomonosov, Koryazhma, Arkhangelsk region, Russia, August 03–09, 2016), Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 2016, 84–85http://www.mathnet.ru/ConfLogos/805/thesis.pdf
2015
57.
Vladimir L. Popov, “Around the Abhyankar–Sathaye conjecture”, Documenta Mathematica, 2015, Extra Volume:Alexander S. Merkurjev's Sixtieth Birthday (The Book Series, Vol. 7), 513–528https://www.math.uni-bielefeld.de/documenta/vol-merkurjev/popov.html, arXiv: 1409.6330 (ISSN 1431-0643 (INTERNET), 1431-0635 (PRINT))
58.
V. L. Popov, “Finite subgroups of diffeomorphism groups”, Proc. Steklov Inst. Math., 289 (2015), 221–226 , arXiv: 1310.6548v2
59.
V. L. Popov, “Problema Bassa o trianguliruemosti podgrupp grupp Kremony”, V shkola-konferentsiya po algebraicheskoi geometrii i kompleksnomu analizu dlya molodykh matematikov Rossii (g. Koryazhma Arkhangelskoi oblasti, Filial Severnogo (Arkticheskogo) federalnogo universiteta im. M. V. Lomonosova, 17–22 avgusta 2015 g.), Matematicheskii institut im. V.A. Steklova Rossiiskoi akademii nauk, Moskva, 2015, 83–87http://www.mathnet.ru/ConfLogos/604/thesis-Koryazhma.pdf
60.
V. L. Popov, “Number of components of the nullcone”, Proc. Steklov Inst. of Math., 290 (2015), 84–90 , arXiv: 1503.08303
61.
Vladimir L. Popov, “On the equations defining affine algebraic groups”, Pacific J. Math., 279:1-2, Special issue. In memoriam: Robert Steinberg (2015), 423–446http://msp.org/pjm/2015/279-1/p19.xhtml, arXiv: 1508.02860
62.
Vladimir L. Popov, “Is one of the two orbits in the closure of the other?”, Appendix B in: H. Derksen, G. Kemper, Computational Invariant Theory, Subseries “Invariant Theory and Algebraic Transformation Groups”, no. VIII, Encyclopaedia of Mathematical Sciences, 130, 2nd Enlarged Ed., Springer, Berlin, 2015, 309–322www.springer.com/gp/book/9783662484203
Vladimir L. Popov, “Stratification of the nullcone”, Appendix C in: H. Derksen, G. Kemper, Computational Invariant Theory, Subseries “Invariant Theory and Algebraic Transformation Groups”, no. VIII, Encyclopaedia of Mathematical Sciences, 130, 2nd Enlarged Ed. with two Appendices by V. L. Popov, and an Addendum by N. A. Campo and V. L. Popov, Springer, Berlin, 2015, 323–344www.springer.com/gp/book/9783662484203
64.
Norbert A'Campo, Vladimir L. Popov, “The source code of HNC”, Addendum to Appendix C in: H. Derksen, G. Kemper, Computational Invariant Theory, Subseries “Invariant Theory and Algebraic Transformation Groups”, no. VIII, Encyclopaedia of Mathematical Sciences, 130, 2nd Enlarged Ed. with two Appendices by V. L. Popov, and an Addendum by N. A. Campo and V. L. Popov, Springer, Berlin, 2015, 345–358www.springer.com/gp/book/9783662484203
65.
H. Derksen, G. Kemper, Computational Invariant Theory, with two Appendices by Vladimir L. Popov, and an Addendum by Norbert A'Campo and Vladimir L. Popov, Encyclopaedia of Mathematical Sciences, subseries “Invariant Theory and Algebraic Transformation Groups”, 130, no. VIII, Second Enlarged Edition, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, Heidelberg, 2015 , 387 pp.
V. L. Popov, “Quotients by conjugation action, cross-sections, singularities,and representation rings”, Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras (Mathematisches Forschungsinstitut Oberwolfach, 19 January – 25 January 2014), Oberwolfach Reports, 11, no. 1, European Mathematical Society, 2014, 156–159
67.
V. L. Popov, “On infinite dimensional algebraic transformation groups”, Transform. Groups, 19:2, special issue dedicated to E. B. Dynkin's 90th anniversary (2014), 549–568https://www.math.uni-bielefeld.de/LAG/man/523.pdf, arXiv: 1401.0278
V. L. Popov, “Jordan groups and automorphism groups of algebraic varieties”, Automorphisms in birational and affine geometry, Springer Proceedings in Mathematics & Statistics, 79, Springer, 2014, 185–213https://www.math.uni-bielefeld.de/LAG/man/508.pdf, arXiv: 1307.5522
V. L. Popov, “Jordaness of the automorphism groups of varieties and manifolds”, Modern Problems of Mathematics and Natural Sciences (Koryazhma, September 15–18, 2014), Northern (Arctic) Federal M. V. Lomonosov University, Koryazhma, 2014, 66–70
70.
N. A. Vavilov, È. B. Vinberg, I. A. Panin, A. N. Panov, A. N. Parshin, V. P. Platonov, V. L. Popov, “Valentin Evgen'evich Voskresenskii (obituary)”, Russian Math. Surveys, 69:4 (2014), 753–754
V. L. Popov, “Some subgroups of the Cremona groups”, Affine algebraic geometry, Proceedings of the conference on the occasion of M. Miyanishi's 70th birthday (Osaka, Japan, 3–6 March 2011), World Scientific Publishing Co., Singapore, 2013, 213–242https://www.math.uni-bielefeld.de/LAG/man/448.pdf
V. L. Popov, “Algebraic groups and the Cremona group”, Algebraic groups (Mathematisches Forschungsinstitut Oberwolfach, 7 April – 13 April 2013), Oberwolfach Reports, 10, no. 2, European Mathematical Society, 2013, 1053–1055
74.
V. L. Popov, “Rationality and the FML invariant”, Journal of the Ramanujan Mathematical Society, 28A (2013), 409–415http://www.mathjournals.org/jrms/2013-028-000/2013-28A-SPL-017.html, https://www.math.uni-bielefeld.de/LAG/man/485.pdf (special Issue-2013 dedicated to C. S. Seshadri's 80th birthday)
75.
S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197
2012
76.
V. L. Popov, Editor's preface to the Russian translation of the book: D. A. Cox, S. Katz, Mirror symmetry and algebraic geometry, ed. V. L. Popov, MCCME, Moscow, 2012, 5
77.
V. L. Popov, “Problems for the problem session”, International conference “Groups of Automorphisms in Birational and Affine Geometry” (Levico Terme (Trento), October 29th – November 3rd, 2012), 2012 , 2 pp. http://www.science.unitn.it/cirm/Trento_postersession.html
2011
78.
J.-L. Colliot-Thélène, B. Kunyavskiĭ, V. L. Popov, Z. Reichstein, “Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?”, Compos. Math., 147:2 (2011), 428–466
V. L. Popov, “Cross-sections, quotients, and representation rings of semisimple algebraic groups”, Transform. Groups, 16:3, special issue dedicated to Tonny Springer on the occasion of his 85th birthday (2011), 827–856
V. L. Popov, “On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties”, Affine algebraic geometry: the Russell Festschrift, CRM Proceedings and Lecture Notes, 54, Amer. Math. Soc., 2011, 289–311https://www.math.uni-bielefeld.de/LAG/man/375.pdf
V. L. Popov, “Invariant rational functions on semisimple Lie algebras and the Gelfand–Kirillov conjecture”, Algebra and Mathematical Logic, International conference commemorating $100$th birthday of professor V. V. Morozov (Kazan, September 25–30, 2011), Kazan Federal Univ., Kazan, 2011, 19
82.
D. A. Timashev, Homogeneous spaces and equivariant embeddings, Encyclopaedia of Mathematical Sciences, Subseries Invariant Theory and Algebraic Transformation Groups, VIII, 138, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2011 , 253 pp.
H. E. A. E. Campbell, D. L. Wehlau, Modular invariant theory, Encyclopaedia of Mathematical Sciences, Subseries Invariant Theory and Algebraic Transformation Groups, IX, 139, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2011 , 233 pp.
V. Popov, “Discrete complex reflection groups”, Geometry, topology, algebra and number theory, applications, The international conference dedicated to the 120th anniversary of Boris Nikolaevich Delone (1890–1980) (August 16–20, 2010), Steklov Mathematical Institute, Moscow State University, Moscow, 2010, 140
2009
85.
V. L. Popov, “Two orbits: When is one in the closure of the other?”, Proc. Steklov Inst. Math., 264 (2009), 146–158
86.
V. L. Popov, “Algebraic Cones”, Math. Notes, 86:6 (2009), 892–894
2008
87.
V. L. Popov, “Irregular and singular loci of commuting varieties”, Transformation Groups, 13:3-4, special issue dedicated to Bertram Kostant on the occasion of his 80th birthday (2008), 819–837
V. Lakshmibai, K. N. Raghavan, Standard Monomial Theory. Invariant Theoretic Approach, Encyclopaedia of Mathematical Sciences, Subseries Invariant Theory and Algebraic Transformation Groups, VIII, 137, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2008 , 265 pp.
V. L. Popov, “Generically multiple transitive algebraic group actions”, Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces (Mumbai, 2004), Tata Institute of Fundamental Research, 19, Narosa Publishing House, Internat. distrib. by American Mathematical Society, New Delhi, 2007, 481–523
90.
V. L. Popov, “Tensor product decompositions and open orbits in multiple flag varieties”, J. Algebra, 313:1 (2007), 392–416
N. Lemire, V. L. Popov, Z. Reichstein, “On the Cayley degree of an algebraic group”, Proceedings of the XVIth Latin American Algebra Colloquium (Spanish), Bibl. Rev. Mat. Iberoamericana, Rev. Mat. Iberoamericana, Madrid, 2007, 87–97
V. L. Popov, “Birationally nonequivalent linear actions. Cayley degrees of simple algebraic groups. Singularities of two-dimensional quotients”, Affine Algebraic Geometry (Oberwolfach, January 7–14, 2007), Oberwolfach Reports, 4, no. 1, Europ. Math. Soc., 2007, 75–78http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=4&iss=1&rank=1
94.
V. L. Popov, “Finite linear groups, lattices, and products of elliptic curves”, International Algebraic Conference Dedicated to the 100th Anniversary of D. K. Faddeev (St. Petersburg, September 24–29, 2007), St. Petersburg State University, St. Petersburg Department of the V. A. Steklov Institute of Mathematics RAS, 2007, 148–149
2006
95.
V. L. Popov, Yu. G. Zarhin, “Finite linear groups, lattices, and products of elliptic curves”, J. Algebra, 305:1 (2006), 562–576
G. Freudenburg, Algebraic Theory of Locally Nilpotent Derivations, Encyclopaedia of Mathematical Sciences, Series Invariant Theory and Algebraic Transformation Groups, VII, 136, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2006 , 261 pp.
2005
99.
V. L. Popov, “Projective duality and principal nilpotent elements of symmetric pairs”, Lie groups and invariant theory, Amer. Math. Soc. Transl. Ser. 2, 213, Amer. Math. Soc., Providence, RI, 2005, 215–222
100.
V. L. Popov, “Roots of the affine Cremona group; Rationality of homogeneous spaces; Two locally nilpotent derivations”, Affine algebraic geometry, Contemp. Math., 369, Amer. Math. Soc., Providence, RI, 2005, 12–16
101.
E. Tevelev, Projective duality and homogeneous spaces, Encyclopaedia of Mathematical Sciences, Subseries Invariant Theory and Algebraic Transformation Groups, IV, 133, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2005 , 250 pp.
102.
M. Lorenz, Multiplicative invariant theory, Encyclopaedia of Mathematical Sciences, Subseries Invariant Theory and Algebraic Transformation Groups, VI, 135, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2005 , 177 pp.
103.
L. E. Renner, Linear algebraic monoids, Encyclopaedia of Mathematical Sciences, Subseries Invariant Theory and Algebraic Transformation Groups, V, 134, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2005 , 246 pp.
2004
104.
V. L. Popov, E. A. Tevelev, “Self-dual projective algebraic varieties associated with symmetric spaces”, Algebraic transformation groups and algebraic varieties, Proceedings of the International conference “Interesting Algebraic Varieties Arising in Algebraic Transformation Groups Theory” (the Erwin Schrödinger Institute, Vienna, October 22–26, 2001), Invariant Theory and Algebraic Transformation Groups, III, Encyclopaedia of Mathematical Sciences, 132, eds. V. L. Popov, Springer, Heidelberg, Berlin, 2004, 131–167
V. L. Popov, “Moment polytopes of nilpotent orbit closures; Dimension and isomorphism of simple modules; and Variations on the theme of J. Chipalkatti”, Invariant theory in all characteristics, CRM Proc. Lecture Notes, 35, Amer. Math. Soc., Providence, RI, 2004, 193–198
106.
N. A'Campo, V. L. Popov, The computer algebra package HNC (Hilbert Null Cone), http://www.geometrie.ch/, Mathematisches Institut Universität Basel, Basel, 2004 , 12 pp.
107.
V. L. Popov (ed.), Algebraic transformation groups and algebraic varieties, Proceedings of the International conference “Interesting Algebraic Varieties Arising in Algebraic Transformation Groups Theory” held at the Erwin Schrödinger Institute (Vienna, October 22–26, 2001), Invariant Theory and Algebraic Transformation Groups, v. III, Encyclopaedia of Mathematical Sciences, 132, Springer, Berlin, Heidelberg, 2004 , xii+238 pp.
M. Losik, P. W. Michor, V. L. Popov, “Invariant tensor fields and orbit varieties for finite algebraic transformation groups”, A Tribute to C. S. Seshadri: Perspectives in Geometry and Representation Theory (Chennai, 2002), Hindustan Book Agency (India), Chennai, 2003, 346–378
V. L. Popov, “The Cone of Hilbert nullforms”, Proc. Steklov Inst. Math., 241 (2003), 177–194
111.
V. L. Popov, “Greetings to Seshadri on his 70th birthday”, A Tribute to C. S. Seshadri: Perspectives in Geometry and Representation Theory, Hindustan Book Agency (India), Chennai, 2003, xix
2002
112.
V. L. Popov, “Self-dual algebraic varieties and nilpotent orbits”, Proceedings of the international conference “Algebra, Arithmetic and Geometry”, Part II (Mumbai, 2000), Tata Institute of Fundamental Research, 16, Narosa Publishing House, intern. distrib. by American Mathematical Society, New Delhi, 2002, 509–533
113.
V. L. Popov, “Constructive invariant theory”, Collection of Papers Commemorating 40th Anniversary of MGIEM, MIEM Publ., Moscow, 2002, 103–106
114.
H. Derksen, G. Kemper, Computational Invariant Theory, Encyclopaedia of Mathematical Sciences, Series Invariant Theory and Algebraic Transformation Groups, 1, 130, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2002 , 268 pp.
115.
A. Białynicki-Birula, J. B. Carrell, W. M. McGovern, Algebraic quotients. Torus actions and cohomology. The adjoint representation and the adjoint action, Encyclopaedia of Mathematical Sciences, Subseries Invariant Theory and Algebraic Transformation Groups, II, 131, eds. R. V. Gamkrelidze, V. L. Popov, Springer, Berlin, 2002 , 242 pp.
2001
116.
V. L. Popov, “On polynomial automorphisms of affine spaces”, Izv. Math., 65:3 (2001), 569–587
117.
V. Popov, “Modern developments in invariant theory”, Plenary Address at Österreichische Mathematische Gesellschaft – 15 Kongress, Jahrestagung der Deutschen Mathematikervereinigung (Vienna, 16–22 September), Deutsche Mathematikervereinigung, Österreichische Mathematische Gesellschaft, 2001, 48
118.
V. L. Popov, “Preface to the Russian translation of talks at the Séminaire Bourbaki, 1992”, Mathematics. News in Foreign Science, 50, Mir, Moscow, 2001
2000
119.
P. I. Katsylo, V. L. Popov, “On Fixed Points of Algebraic Actions on $\mathbb{C}^n$”, Funct. Anal. Appl., 34:1 (2000), 33–40
120.
V. L. Popov, Editor's preface to the Russian translation of the book: D. Cox, J. Little, D. O'Shea, Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra (2nd edition, Springer, 1998), ed. V. L. Popov, Mir, Moscow, 2000, 6
121.
V. L. Popov, Generators and relations of the affine coordinate rings of connected semisimple algebraic groups, preprint ESI, no. 972, The Erwin Schrödinger Institute for Mathematical Physics, Vienna, 2000 , 12 pp.
1999
122.
V. L. Popov, G. V. Sukhotsky, Analytic Geometry. Lectures and Exercises, MGIEM, SITMO Publ., Moscow, 1999 , ii+232 pp.
123.
Vladimir Popov, “Algebraic groups of automorphisms of polynomial rings”, Colloque International “Théorie des Groupes”. Journées Solstice d'été 1999 (Institut de Mathématiques de Jussieu, 75005 Paris, France, 17, 18, 19 juin 1999), l'Université Paris 7–Denis Diderot, 1999, 15https://www.imj-prg.fr/grg/archives/Colloques/1999Solstice/
1998
124.
V. L. Popov, Discrete complex reflection groups, Workshop on Reflection Groups, January 13–21, SISSA, Trieste, Italy, 1998 , 23 pp.
125.
V. L. Popov, “Comments to the papers by D. Hilbert “Über die Theorie der algebraischen Formen” and “Über die vollen Invariantensysteme””: D. Hilbert, Selected Works, Factorial Publ., Moscow, 1998, 490–517
126.
V. L. Popov, “Reductive subgroups of $Aut(A^3)$ and $Aut(A^4)$”, Tagungsbericht 14/1998, Algebraische Gruppen, 05.04–11.04.1998 (Mathematisches Forschungsinstitut Oberwolfach, 05.04–11.04,1998), v. 14, Mathematisches Forschungsinstitut Oberwolfach, 1998, 13–14https://www.mfo.de/occasion/9815/www_view
1997
127.
V. Popov, G. Röhrle, “On the number of orbits of a parabolic subgroup on its unipotent radical”, Algebraic Groups and Lie Groups, Australian Mathematical Society Lecture Series, 9, Cambridge University Press, Cambridge, 1997, 297–320
128.
V. L. Popov, “A finiteness theorem for parabolic subgroups of fixed modality”, Indag. Math. (N.S.), 8:1 (1997), 125–132
V. L. Popov, “On the Closedness of Some Orbits of Algebraic Groups”, Funct. Anal. Appl., 31:4 (1997), 286–289
130.
Vladimir Popov, “Orbits of parabolic subgroups acting on its unipotent radicals”, Tagungsbericht 42/1997. Einh"ullende Algebren und Darstellungstheorie. 02.11–08.11.1997 (Mathematisches Forschungsinstitut Oberwolfach. 02.11–08.11.1997), v. 42, Mathematisches Forschungsinstitut Oberwolfach, 1997, 13http://oda.mfo.de/bsz325095604.html
131.
D. V. Alekseevskii, V. O. Bugaenko, G. I. Olshanskii, V. L. Popov, O. V. Schwarzman, “Érnest Borisovich Vinberg (on his 60th birthday)”, Russian Math. Surveys, 52:6 (1997), 1335–1343
1995
132.
V. L. Popov, “An analogue of M. Artin's conjecture on invariants for nonassociative algebras”, Lie Groups and Lie Algebras: E. B. Dynkin's Seminar, American Mathematical Society Translations Ser. 2, 169, Amer. Math. Soc., Providence, RI, 1995, 121–143
V. Popov, “Sections in invariant theory”, Proceedings of The Sophus Lie Memorial Conference (Oslo, 1992), Scandinavian University Press, Oslo, 1994, 315–361
134.
V. L. Popov, “Divisor class groups of the semigroups of the highest weights”, J. Algebra, 168:3 (1994), 773–779
135.
V. L. Popov, E. B. Vinberg, “Invariant theory”, Encyclopaedia of Mathematical Sciences, 55, Algebraic Geometry IV, Springer-Verlag, Berlin, Heidelberg, New York, 1994, 123–284
V. L. Popov, “Singularities of closures of orbits”, Quantum Deformations of Algebras and Their Representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992), Israel Math. Conference Proceedings, 7, Bar-Ilan University, Ramat Gan, 1993, 133–141
137.
V. L. Popov, Predislovie k russkomu perevodu knigi: V. Kats, Beskonechnomernye algebry Li, eds. V. L. Popov, Mir, M., 1993, 5–6 , 425 pp.
1992
138.
V. L. Popov, “On the “lemma of Seshadri””, Arithmetic and Geometry of Varieties, Samara State Univ., Samara, 1992, 133–139
139.
V. L. Popov, È. B. Vinberg, “Some open problems in invariant theory”, Proc. Internat. Conf. in Algebra, Part 3 (Novosibirsk, 1989), Contemporary Mathematics, 131, Part 3, American Mathematical Society, Providence, RI, 1992, 485–497
V. L. Popov, Groups, Generators, Syzygies, and Orbits in Invariant Theory, Translations of Mathematical Monographs, 100, Amer. Math. Soc., Providence, RI, 1992 , vi+245 pp.
141.
V. L. Popov, “On the “lemma of Seshadri””, Lie Groups, Their Discrete Subgroups, and Invariant Theory, Advances in Soviet Mathematics, 8, Amer. Math. Soc., Providence, RI, 1992, 167–172
1991
142.
V. L. Popov, “Invariant theory”, Algebra and Analysis (Kemerovo, 1988), Amer. Math. Soc. Transl. Ser. 2, 148, Amer. Math. Soc., Providence, RI, 1991, 99–112
1990
143.
V. L. Popov, “When are the stabilizers of all nonzero semisimple points finite?”, Operator algebras, unitary representations, nveloping algebras, and invariant theory (Paris, 1989), Progress in Mathematics, 92, Birkhäuser Boston, Boston, MA, 1990, 541–559
1989
144.
V. L. Popov, “Some applications of algebra of functions on $G/U$”, Group Actions and Invariant Theory (Montreal, PQ, 1988), CMS Conference Proceedings, 10, Amer. Math. Soc., Providence, RI, 1989, 157–166
145.
V. L. Popov, “Automorphism groups of polynomial algebras”, Problems in Algebra (Gomel'), v. 4, Universitetskoe, Minsk, 1989, 4–16
1994
146.
V.. L. Popov, È. B. Vinberg, “Invariant theory”, Algebraic Geometry–4, Encyclopaedia of Mathematical Sciences, 55, Springer-Verlag, Berlin, Heidelberg, 1994, 123–284
1989
147.
V. L. Popov, “Modules with finite stabilizers of nonzero semisimple elements”, Proc. Intern. Conference commemorating A. I. Mal'cev (Novosibirsk), Math. Inst. Sib. Branch Acad. Sci., Novosibirsk, 1989, 108
148.
V. L. Popov, Basic algebraic structures, MIEM Publ., Moscow, 1989 , 42 pp.
1988
149.
V. L. Popov, “On the actions of ${\mathbf G}_a$ on ${\mathbf A}^n$”, Arithmetic and geometry of varieties, Kuibyshev. Gos. Univ., Kuybyshev, 1988, 93–98
1989
150.
V. L. Popov, “Closed orbits of Borel subgroups”, Math. USSR-Sb., 63:2 (1989), 375–392
1988
151.
V. L. Popov, Analytic Geometry, MIEM Publ., Moscow, 1988 , 44 pp.
152.
V. L. Popov, Linear Algebra, MIEM Publ., Moscow, 1988 , 45 pp.
1987
153.
V. L. Popov, “One and a half centuries in the theory of invariants”, Methodological analysis of mathematical theories, Akad. Nauk SSSR Prezid., Tsentral. Sovet Filos. (Metod.) Sem., Moscow, 1987, 235–256
V. L. Popov, “On actions of ${\mathbf G}_a$ on ${\mathbf A}^n$”, Algebraic groups (Utrecht, 1986), Lecture Notes in Math., 1271, Springer, Berlin, 1987, 237–242
V. L. Popov, Editor's preface to the Russian translation of the book: H. Kraft, Geometrische Methoden in der Invariantentheorie, eds. V. L. Popov, Mir, Moscow, 1987, 5–7
157.
V. L. Popov, “Stability of actions of Borel subgroups”, Proc. of the XIX-th All Union Algebraic Conference (L'vov), v. 1, Steklov Math. Inst. Acad. Sci. USSR, Moscow, 1987, 48
158.
V. L. Popov, “Contractions of the actions of reductive algebraic groups”, Math. USSR-Sb., 58:2 (1987), 311–335
1986
159.
V. L. Popov, “On one-dimensional unipotent subgroups of the automorphism group of a polynomial algebra”, Proc. of the X-th All Union Symposium on Groups Theory (Minsk), Math. Isnt. Belorus. Acad. Sci., 1986, 182
1985
160.
H. Kraft, V. L. Popov, “Semisimple group actions on the three-dimensional affine space are linear”, Comment. Math. Helv., 60:3 (1985), 466–479
V. L. Popov, “Comments to the papers by H. Weyl “Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare TYransformationen”, "Spinors in $n$ dimensions" and “Eine für die Valenztheorie geeignete Basis der binären vektorinvarianten””, H. Weyl, Selected Works, Nauka, Moscow, 1984, 471–478; 461–467
1983
162.
V. L. Popov, “Homological dimension of algebras of invariants”, J. Reine Angew. Math., 341 (1983), 157–173
V. L. Popov, “Syzygies in the theory of invariants”, Math. USSR-Izv., 22:3 (1984), 507–585
1983
164.
V. L. Popov, “On homological dimension of algebras of invariants”, Proc. of the XVII-th All Union Algebraic Conference (Minsk), Math. Inst. Belorus. Acad. Sci, 1983, 152–153
1982
165.
V. L. Popov, Discrete Somplex Reflection Groups, Lectures delivered at the Math. Institute Rijksuniversiteit Utrecht in October 1980, Commun. Math. Inst. Rijksuniv. Utrecht, 15, Rijksuniversiteit Utrecht Mathematical Institute, Utrecht, 1982 , 89 pp. www.researchgate.net/publication/261552178_Discrete_complex_reflection_groups . Second enlarged edition published in Communications in Mathematics, vol. 30 (2022), no. 3 (published August 22, 2023), 303–375, cm.episciences.org/11725
1983
166.
V. L. Popov, “A finiteness theorem for representations with a free algebra of invariants”, Math. USSR-Izv., 20:2 (1983), 333–354
1982
167.
V. Grigor'ev, V. L. Popov, D. D. Solntcev, Problems in algebra, MIEM Publ., Moscow, 1982 , 98 pp.
1981
168.
V. L. Popov, “Constructive invariant theory”, Young Tableaux and Schur Functors in Algebra and Geometry (Toruń, 1980), Astérisque, 87, Soc. Math. France, Paris, 1981, 303–334
1982
169.
V. L. Popov, “The constructive theory of invariants”, Math. USSR-Izv., 19:2 (1982), 359–376
1981
170.
V. L. Popov, Preface to the Russian translation of: T. Springer, Invariant theory, Mir, Moscow, 1981, 5–8
171.
V. L. Popov, “Appendix 3 to the Russian translation of the book”: T. A. Springer, Invariant theory”, Mathematics. News in Foreign Science, 24, eds. V. L. Popov, Mir, Moscow, 1981, 153–182
1980
172.
V. L. Popov, “Complex root systems and their Weyl groups”, Proc. of the VII All Union Symposium on Group Theory (Krasnoyarsk), Math. Inst. Sib. Branch Acad. Sci., Krasnoyarsk Univ., Krasnoyarsk, 1980, 91
173.
V. L. Popov, “Constructive invariant theory”, Proc. internat. conf. “Young Tableaux and Schur Functions in Algebra and Geometry” (Toruń, Poland), Inst. Math. Acad. Polon. Sci., 1980, 10–11
1979
174.
V. L. Popov, “Hilbert's theorem on invariants”, Soviet Math. Dokl., 20:6 (1979), 1318–1322
175.
V. L. Popov, “On Hilbert's fourteenth problem”, Proc. of the XV-th All Union Algebraic Conference (Krasnoyarsk), Math. Inst. Sib. Branch Acad. Sci., Krasnoyarsk Univ., Krasnoyarsk, 1979, 123
1980
176.
V. L. Popov, “Classification of spinors of dimension fourteen”, Trans. Mosc. Math. Soc., 1 (1980), 181–232
1978
177.
V. L. Popov, “Algebraic curves with an infinite automorphism group”, Math. Notes, 23:2 (1978), 102–108
1977
178.
V. L. Popov, “One conjecture of Steinberg”, Funct. Anal. Appl., 11:1 (1977), 70–71
179.
V. L. Popov, “Classification of the spinors of dimension fourteen”, Uspekhi Mat. Nauk, 32:1(193) (1977), 199–200
180.
V. L. Popov, “Crystallographic groups generated by affine unitary reflection”, Proc. of the XIV-th All Union Algebraic Conference (Novosibirsk), v. 1, Math. Inst. Sib. Branch Acad. Sci., Novosibirsk Univ., Novosibirsk, 1977, 55–56
1987
181.
V. L. Popov, 86 papers, Encyclopaedia of Mathematics, Kluwer Academic Publishers, 1987–2002
1976
182.
V. G. Kac, V. L. Popov, E. B. Vinberg, “Sur les groupes linéaires algébriques dont l'algèbre des invariants est libre”, C. R. Acad. Sci. Paris Sér. A-B, 283:12 (1976), A875–A878
183.
V. L. Popov, “Representations with a free module of covariants”, Funct. Anal. Appl., 10:3 (1976), 242–244
1975
184.
V. L. Popov, “The classification of representations which are exceptional in the sense of Igusa”, Funct. Anal. Appl., 9:4 (1975), 348–350
185.
V. L. Popov, “Classification of three-dimensional affine algebraic varieties that are quasi-homogeneous with respect to an algebraic group”, Math. USSR-Izv., 9:3 (1975), 535–576
1974
186.
V. L. Popov, “Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles”, Math. USSR-Izv., 8:2 (1974), 301–327
187.
V. L. Popov, “Structure of the closure of orbits in spaces of finite-dimensional linear SL(2) representations”, Math. Notes, 16:6 (1974), 1159–1162
1973
188.
V. L. Popov, “Classification of affine algebraic surfaces that are quasihomogeneous with respect to an algebraic group”, Math. USSR-Izv., 7:5 (1973), 1039–1056
189.
V. L. Popov, “Quasihomogeneous affine algebraic varieties of the group SL(2)”, Math. USSR-Izv., 7:4 (1973), 793–831
1972
190.
È. B. Vinberg, V. L. Popov, “On a class of quasihomogeneous affine varieties”, Math. USSR-Izv., 6:4 (1972), 743–758
191.
V. L. Popov, “On the stability of the action of an algebraic group on an algebraic variety”, Math. USSR-Izv., 6:2 (1972), 367–379
192.
V. L. Popov, “Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles”, Uspekhi Mat. Nauk, XXVII:4 (1972), 191–192
1971
193.
E. M. Andreev, V. L. Popov, “Stationary subgroups of points of general position in the representation space of a semisimple Lie group”, Funct. Anal. Appl., 5:4 (1971), 265–271
194.
V. L. Popov, “Regular action of a semisimple algebraic group on an affine factorial algebra”, Proc. of the XI-th All Union Algebraic Colloquium (Kishinev), Math. Istitute Mold. Acad. Sci., Kishinev, 1971, 75
1970
195.
V. L. Popov, “Stability criteria for the action of a semisimple group on a factorial manifold”, Math. USSR-Izv., 4:3 (1970), 527–535
Rationality of homogeneous spaces Vladimir Popov Conference “Birational geometry and Fano varieties”
dedicated to Yu.G. Prokhorov 60th anniversary March 14, 2024 11:00
Воспоминания об Алексее Николаевиче Паршине V. L. Popov, F. A. Bogomolov, B. S. Kashin, A. G. Sergeev, M. A. Korolev, S. O. Gorchinskiy, I. A. Panin “Numbers and functions” – Memorial conference for 80th birthday of Alexey Nikolaevich Parshin December 1, 2022 16:30
Jordan groups V. L. Popov Knots and Representation Theory October 14, 2019 18:30
25.
Root systems and root lattices in number fields V. L. Popov XVII International Conference Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history dedicated to the centenary of the birth of professor N. I. Feldman and the ninetieth anniversary of the birth of professors A. I. Vinogradov, A. V. Malyshev and B. F. Skubenko, TSPU of Leo Tolstoy, Tula, September 23–28, 2019 September 24, 2019
Jordan groups V. L. Popov International Conference "Algebra and Mathematical Logic: Theory and Applications" Kazan Federal University and Tatarstan Academy of Sciences Kazan, June 24-28, 2019 June 27, 2019 09:00
Affine algebraic groups and Cremona groups V. L. Popov International conference "Affine Algebraic Groups, Motives, and Cohomological Invariants", September 16-21, 2018, Banff International Research Station for Mathematical Innovation and Discovery (BIRS), Canada September 19, 2018 09:00
35.
Cremona groups vs. algebraic groups V. L. Popov International conference Algebraic Geometry — Mariusz Koras in memoriam, May 28–June 1, 2018, Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland May 28, 2018 10:40
36.
Variations on the theme of Zariski's Cancellation Problem V. L. Popov International conference Polynomial Rings and Affine Algebraic Geometry (PRAAG-2018), February 12--16, 2018, Tokyo Metropolitan University, Tokyo, Japan February 14, 2018 11:50
Algebraic subgroups of the Cremona groups V. L. Popov International Scientific Session "Algebraic Geometry, Warsaw 1960-2015", on the occasion of awarding the honorary doctorate of the University of Warsaw to Professor Andrzej Szczepan Bialynicki-Birula, March 19-20, 2015, Warshaw, Poland March 20, 2015 15:00
51.
About Grothendieck V. L. Popov Meeting "Alexander Grothendieck (1928--2014) and mathematics of XXth century" of the Section of Mathematics, Central House of Scientists of the RAS February 19, 2015 18:30
52.
Jordan groups V. L. Popov General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences December 18, 2014 14:00
53.
Closures of orbits V. L. Popov St. Petersburg Seminar on Representation Theory and Dynamical Systems December 17, 2014 17:00
Orbit closures of algebraic group actions V. L. Popov International conference "Geometry, Topology and Integrability", October 20-25, 2014, Skolkovo Institute of Science and Technology, Moscow October 23, 2014 12:50
Tori in Cremona groups V. L. Popov International conference "Essential Dimension and Cremona Groups", Chern Institute of Mathematics, Nankai University, Tianjin, China June 12, 2012
75.
170 years of invariant theory V. L. Popov Colloquium talk at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China. June 8, 2012 16:30
Discrete groups generated by complex reflections V. L. Popov International conference "GEOMETRY, TOPOLOGY, ALGEBRA and NUMBER THEORY, APPLICATIONS" dedicated to the 120th anniversary of Boris Delone (1890–1980) August 17, 2010 14:00
Cayley groups V. L. Popov International Workshop Non-Archimedean Analysis, Lie Groups and Dynamical Systems February 8-12, 2010, Paderborn, Germany February 8, 2010 14:50
Describing the Hilbert cone of unstable points V. L. Popov International Conference Geometric Invariant Theory, Mathematisches Institut Georg-August-Universitat Gottingen, Gottingen, Germany June 2, 2008 09:30
Cayley groups V. L. Popov International conference on algebra and number theory, dedicated to the 80th anniversary of V. E. Voskresensky, Samara May 22, 2007
Polynomial automorphisms V. L. Popov The University of British Columbia, Mathematics Department November 24, 2004 15:00
108.
150 years of Invariant Theory V. L. Popov Red Raider Symposium 2004: Invariant Theory in Perspective Texas Technical University, Lubbock TX, USA November 11, 2004 10:00
109.
Cayley groups V. L. Popov International Conference Arithmetic Geometry, St. Petersburg June 26, 2004
Cayley groups V. L. Popov International Conference Commutative Algebra and Algebraic Geometry in honor of Professor Miyanishi, Osaka University, Japan May 1, 2004
112.
Cayley maps for algebraic groups V. L. Popov International Colloquium Algebraic Groups and Homogeneous Spaces, Bombay, India January 6, 2004
Algebraic group actions and rational singularities V. L. Popov International Workshop "Trends in Commutative Algebra", Indian Institute of Technology, Bombay, January 13–15, 2000 January 14, 2000 09:00
117.
Modern developments in invariant theory V. L. Popov International Workshop "Trends in Commutative Algebra", Indian Institute of Technology, Bombay, January 13–15, 2000 January 13, 2000 10:00
Kostant sections V. L. Popov Colloque International "Groupes et Algèbres" Journées Solstice d'été, Institut de Mathématiques de Jussieu, Université Paris-7 Denis Diderot, Paris June 23, 1995
Books in Math-Net.Ru
Algebra and Arithmetic, Algebraic, and Complex Geometry, Collected papers. In memory of Academician Alexey Nikolaevich Parshin, Trudy Mat. Inst. Steklova, 320, ed. V. L. Popov, S. O. Gorchinskiy, A. B. Zheglov, D. V. Osipov, 2023, 324 с. http://mi.mathnet.ru/book1934
Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 307, ed. A. N. Parshin, V. L. Popov, S. O. Gorchinskiy, Vik. S. Kulikov, 2019, 328 с. http://mi.mathnet.ru/book1773