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Popov Vladimir Leonidovich

Statistics Math-Net.Ru
Total publications: 141
Scientific articles: 113
Cited articles: 70
Citations in Math-Net.Ru: 303
Citations in Web of Science: 241
Citations in Scopus: 113
Citations in MathSciNet: 525
Presentations: 72

Number of views:
This page:10877
Abstract pages:9110
Full texts:2760
References:528
Popov Vladimir Leonidovich
Professor
Doctor of physico-mathematical sciences (1984)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 3.09.1946
Phone: +7 (499) 135 25 49
Fax: +7 (499) 135 05 55
E-mail: ,
Website: http://scholar.google.com/citations?user=Qcve-A0AAAAJ&hl=ru http://researchgate.net/profile/Vladimir_Popov12
Keywords: Algebraic group, Lie group, Lie algebra, algebraic variety, action, representation, algebra, invariant, covariant, orbit, homogeneous space, automorphism group of algebraic variety, Cremona group, discrete reflection group, lattice.
UDC: 512.7, 512.745, 512.745.4, 512.743, 512.747, 512.76, 512.77, 512.71, 512.812, 512.813, 512, 519.4
MSC: 14l30, 14l24, 14l35, 15a72, 14l40, 14l10, 14l15, 14l17, 14m17, 14m20, 20G05, 15A72

Subject:

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). Leading Research Fellow at the Steklov Mathematical Institute, Russian Academy of Sciences (main place of work; January 2002–present).

Executive Managing Editor of the journal "Transformation Groups" published by Birkhäuser Boston (1996–present). Member of the Editorial Boards of the journals: "Izvestiya: Mathematics" (2006–present) and "Mathematical Notes" (2003–present) published by Russian Academy of Sciences, "Journal of Mathematical Sciences" published by Springer (2001–present), "Geometriae Dedicata" published by Kluwer (1989–1999). Founder and Title Editor of the series "Invariant Theory and Algebraic Transformation Groups" of Encyclopaedia of Mathematical Sciences published by Springer (1998–present).

Invited speaker at the International Congress of Mathematicians, Berkeley, USA (1986). The results of 1982–1983 are the subject of J. Dixmier's talk at Séminaire N. Bourbaki (J. Dixmier, Quelques résults de finitude en théorie des invariants (d'après 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 (November 2012), see http://www.ams.org/profession/fellows-list-institution

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 l'honneur 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).

Executive Managing Editor of the journal Transformation Groups (1996--present), Birkhäuser Boston. Member of the Editorial Boards of Izvestiya Mathematics (2006--present), Mathematical Notes (2003--present), Journal of Mathematical Sciences (2001--present), Springer, European Mathematical Society Newsletter (since January 2015), EMS, Geometriae Dedicata (1989--1999), Kl\"uwer. Founder and title Editor of the subseries "Invariant Theory and Algebraic Transformation Groups" of Encyclopaedia of Mathematical Sciences, Springer (1998--present).

Member, Board of Moscow Mathematical Society (1998–2000).

More than 135 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 l'Academie 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).

Principal Investigator of the fSU–USA cooperative CRDF project "Algebraic Transformation Groups and Applications" (1996–1998). Team Leader of the joint Swiss-Franco-fSU INTAS project "Algebraic Transformation Groups with Application in Representation Theory and Algebraic Geometry" (1998–2000).

First Prize, graduate students research competition, Department of Mathematics, Moscow State University Lomonosov (1969).

======================================

Among the results obtained are:

● 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.

● 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 Gel'fand–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).

● Classification of infinite discrete groups generated by complex affine unitary reflections and exploring their remarkable connections with number theory, combinatorics, coding theory, algebraic geometry and singularity theory (1980–82, 2005).

===================================

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. Popov's 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 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 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, Hilbert's 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 l'algèbre 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).

   
Main publications:
  1. N. Lemire, V. L. Popov, Z. Reichstein, “Cayley groups”, J. Amer. Math. Soc., 19:4 (2006), 921–967  crossref  mathscinet  zmath  isi  elib  scopus
  2. N. L. Gordeev, V. L. Popov, “Automorphism groups of finite dimensional simple algebras”, Ann. of Math. (2), 158:3 (2003), 1041–1065  crossref  mathscinet  zmath  isi  elib  scopus
  3. V. L. Popov, Groups, generators, syzygies, and orbits in invariant theory, Translations of Mathematical Monographs, 100, Amer. Math. Soc., Providence, RI, 1992, ISBN: 0-8218-4557-8 , vi+245 pp.  mathscinet  zmath
  4. V. L. Popov, “Modern developments in invariant theory”, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, Amer. Math. Soc., Providence, RI, 1987, 394–406  mathscinet
  5. 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.  mathscinet  zmath

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https://www.researchgate.net/profile/Vladimir_Popov12

Full list of publications:
1. Vladimir L. Popov, “Birational splitting and algebraic group actions”, Eur. J. Math., 2:1 (2016), 283–290 , Published online: 16 May 2015 https://www.math.uni-bielefeld.de/LAG/man/552.pdf, arXiv: 1502.02167  mathnet  crossref  mathscinet  zmath  scopus
2. Vladimir L. Popov, “Bass' triangulability problem”, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, 2016 (to appear) https://www.math.uni-bielefeld.de/LAG/man/553.pdf, arXiv: 1504.03867
3. V. L. Popov, G. V. Sukhotskii, Analiticheskaya geometriya. Uchebnik i praktikum, Bakalavr. Akademicheskii kurs, 2-e izd., per. i dop., Yurait, Moskva, 2016, ISBN: 978-5-9916-6395-3 , 232 pp. http://urait.ru/catalog/388730
4. V. L. Popov, “Algebras of General Type: Rational Parametrization and Normal Forms”, Proc. Steklov Inst. Math., 292:1 (2016), 202–215  mathnet  crossref  crossref  elib
5. V. L. Popov, “Podgruppy grupp Kremony: problema Bassa”, Dokl. RAN, 468:5 (2016) (to appear)  crossref
6. Vladimir L. Popov, “Around the Abhyankar–Sathaye conjecture”, Doc. Math., 2015, Extra Volume:Alexander S. Merkurjev's Sixtieth Birthday (The Book Series, Vol. 7), 513–528 https://www.math.uni-bielefeld.de/documenta/vol-merkurjev/popov.html, arXiv: 1409.6330  mathnet  mathscinet
7. V. L. Popov, “Finite subgroups of diffeomorphism groups”, Proc. Steklov Inst. Math., 289 (2015), 221–226 , arXiv: 1310.6548v2  mathnet  crossref  crossref  isi  elib  elib  scopus
8. 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, 83–87, ISBN: 978-5-98419-062-6 http://www.mathnet.ru/ConfLogos/604/thesis-Koryazhma.pdf
9. V. L. Popov, “Number of components of the nullcone”, Proc. Steklov Inst. of Math., 290 (2015), 84–90 , arXiv: 1503.08303  mathnet  crossref  crossref  isi  elib  elib  scopus
10. Vladimir L. Popov, “On the equations defining affine algebraic groups”, Pacific J. Math., 279:1-2, Special issue. In memoriam: Robert Steinberg (2015), 423–446 http://msp.org/pjm/2015/279-1/p19.xhtml, arXiv: 1508.02860  mathnet  crossref  mathscinet  isi  scopus
11. 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
12. V. L. Popov, “On infinite dimensional algebraic transformation groups”, Transform. Groups, 19:2, special issue dedicated to E. B. Dynkin's 90th anniversary (2014), 549–568 https://www.math.uni-bielefeld.de/LAG/man/523.pdf, arXiv: 1401.0278  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 1)
13. 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, 185–213 https://www.math.uni-bielefeld.de/LAG/man/508.pdf, arXiv: 1307.5522  crossref  scopus (cited: 1)
14. 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
15. V. L. Popov, “Tori in the Cremona groups”, Izv. Math., 77:4, special issue on the occasion of I. R. Shafarevich's 90th anniversary (2013), 742–771 https://www.math.uni-bielefeld.de/LAG/man/474.pdf  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)
16. 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, 213–242 https://www.math.uni-bielefeld.de/LAG/man/448.pdf  crossref  isi (cited: 2)
17. 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
18. V. L. Popov, “Rationality and the FML invariant”, Journal of the Ramanujan Mathematical Society, 28A (2013), 409–415 http://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)  mathscinet (cited: 1)  zmath  isi (cited: 1)
19. 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
20. 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  crossref  mathscinet (cited: 9)  zmath  isi (cited: 7)  scopus (cited: 5)
21. 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  crossref  mathscinet (cited: 3)  zmath  isi (cited: 4)  elib (cited: 3)  scopus (cited: 4)
22. 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, 289–311 https://www.math.uni-bielefeld.de/LAG/man/375.pdf  mathscinet (cited: 10)  zmath  isi (cited: 11)
23. 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
24. 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
25. V. L. Popov, “Two orbits: When is one in the closure of the other?”, Proc. Steklov Inst. Math., 264 (2009), 146–158  mathnet  crossref  mathscinet  isi (cited: 3)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 4)
26. V. L. Popov, “Algebraic Cones”, Math. Notes, 86:6 (2009), 892–894  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
27. 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  crossref  mathscinet (cited: 6)  zmath  isi (cited: 5)  elib (cited: 6)  scopus (cited: 7)
28. 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  mathscinet (cited: 13)  zmath
29. V. L. Popov, “Tensor product decompositions and open orbits in multiple flag varieties”, J. Algebra, 313:1 (2007), 392–416  crossref  mathscinet (cited: 5)  zmath  isi (cited: 4)  elib (cited: 6)  scopus (cited: 4)
30. 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  mathscinet  zmath
31. V. L. Popov, “Quasihomogeneous affine threefolds”, Affine algebraic geometry (Oberwolfach, January 7–14, 2007), Oberwolfach Reports, 4, no. 1, Europ. Math. Soc., 2007, 13–16 http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=4&iss=1&rank=1
32. 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, 75–78 http://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=4&iss=1&rank=1
33. 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
34. V. L. Popov, Yu. G. Zarhin, “Finite linear groups, lattices, and products of elliptic curves”, J. Algebra, 305:1 (2006), 562–576  crossref  mathscinet (cited: 1)  zmath  isi (cited: 1)  elib (cited: 1)  scopus (cited: 1)
35. M. Losik, P. W. Michor, V. L. Popov, “On polarizations in invariant theory”, J. Algebra, 301:1 (2006), 406–424  crossref  mathscinet (cited: 6)  zmath  isi (cited: 7)  elib (cited: 7)  scopus (cited: 7)
36. N. Lemire, V. L. Popov, Z. Reichstein, “Cayley groups”, J. Amer. Math. Soc., 19:4 (2006), 921–967  crossref  mathscinet (cited: 9)  zmath  isi (cited: 8)  elib (cited: 8)  scopus (cited: 7)
37. 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  mathscinet (cited: 1)  zmath
38. 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
39. 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  mathscinet (cited: 6)  zmath  isi (cited: 6)
40. 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  mathscinet (cited: 2)  zmath
41. 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.
42. N. L. Gordeev, V. L. Popov, “Automorphism groups of finite dimensional simple algebras”, Ann. of Math. (2), 158:3 (2003), 1041–1065  crossref  mathscinet (cited: 4)  zmath  isi (cited: 6)  elib (cited: 5)  scopus (cited: 5)
43. 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  mathscinet (cited: 3)  zmath
44. V. L. Popov, “The Cone of Hilbert nullforms”, Proc. Steklov Inst. Math., 241 (2003), 177–194  mathnet  mathscinet  zmath
45. 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  mathscinet (cited: 5)  zmath
46. V. L. Popov, “Constructive invariant theory”, Collection of Papers Commemorating 40th Anniversary of MGIEM, MIEM Publ., Moscow, 2002, 103–106
47. V. L. Popov, “On polynomial automorphisms of affine spaces”, Izv. Math., 65:3 (2001), 569–587  mathnet  crossref  crossref  mathscinet  zmath  elib  scopus
48. 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
49. P. I. Katsylo, V. L. Popov, “On Fixed Points of Algebraic Actions on $\mathbb{C}^n$”, Funct. Anal. Appl., 34:1 (2000), 33–40  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
50. 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.
51. V. L. Popov, G. V. Sukhotsky, Analytic Geometry. Lectures and Exercises, MGIEM, SITMO Publ., Moscow, 1999, ISBN: 5-230-16264-3 , ii+232 pp.
52. V. L. Popov, Discrete complex reflection groups, Workshop on Reflection Groups, January 13–21, SISSA, Trieste, Italy, 1998 , 23 pp.
53. 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
54. 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  mathscinet (cited: 15)  zmath
55. V. L. Popov, “A finiteness theorem for parabolic subgroups of fixed modality”, Indag. Math. (N.S.), 8:1 (1997), 125–132  crossref  mathscinet (cited: 7)  zmath  isi (cited: 10)  elib (cited: 9)  scopus (cited: 9)
56. V. L. Popov, “On the Closedness of Some Orbits of Algebraic Groups”, Funct. Anal. Appl., 31:4 (1997), 286–289  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
57. 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  mathscinet (cited: 4)  zmath  isi (cited: 22)
58. V. Popov, “Sections in invariant theory”, Proceedings of The Sophus Lie Memorial Conference (Oslo, 1992), Scandinavian University Press, Oslo, 1994, 315–361  mathscinet (cited: 26)
59. V. L. Popov, “Divisor class groups of the semigroups of the highest weights”, J. Algebra, 168:3 (1994), 773–779  crossref  mathscinet  zmath  isi  elib  scopus
60. 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, ISBN: 3-540-54682-0
61. 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  mathscinet (cited: 1)  zmath
62. V. L. Popov, “On the “lemma of Seshadri””, Arithmetic and Geometry of Varieties, Samara State Univ., Samara, 1992, 133–139  mathscinet  zmath
63. 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  crossref  mathscinet (cited: 1)  isi (cited: 51)
64. V. L. Popov, Groups, generators, syzygies, and orbits in invariant theory, Translations of Mathematical Monographs, 100, Amer. Math. Soc., Providence, RI, 1992, ISBN: 0-8218-4557-8 , vi+245 pp.  mathscinet (cited: 12)  zmath
65. 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  mathscinet (cited: 3)
66. 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  mathscinet (cited: 3)
67. 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  mathscinet (cited: 1)  isi (cited: 45)
68. 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  mathscinet
69. V. L. Popov, “Automorphism groups of polynomial algebras”, Problems in Algebra (Gomel'), v. 4, Universitetskoe, Minsk, 1989, 4–16  mathscinet
70. E. B. Vinberg, V. L. Popov, “Invariant theory”, Algebraicheskaya geometriya–4, Itogi nauki i tekhn., Ser. Sovrem. probl. mat., Fundam. napravleniya, 55, VINITI, M., 1989, 137–309  mathnet (cited: 70)  mathscinet (cited: 110)  zmath [V.. L. Popov, È. B. Vinberg, “Invariant theory”, Algebraic Geometry–4, Encyclopaedia of Mathematical Sciences, 55, Springer-Verlag, Berlin, Heidelberg, 1994, 123–284]
71. 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
72. 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  mathscinet
73. V. L. Popov, “Closed orbits of Borel subgroups”, Matem. sb., 135(177):3 (1988), 385–402  mathnet (cited: 3)  mathscinet (cited: 2)  zmath; V. L. Popov, “Closed orbits of Borel subgroups”, Math. USSR-Sb., 63:2 (1989), 375–392  crossref  mathscinet  zmath
74. 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  mathscinet
75. V. L. Popov, “Modern developments in invariant theory”, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, Amer. Math. Soc., Providence, RI, 1987, 394–406  mathscinet (cited: 1)
76. 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  crossref  mathscinet (cited: 8)  isi (cited: 9)
77. 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
78. V. L. Popov, “Contractions of the actions of reductive algebraic groups”, Matem. sb., 130(172):3(7) (1986), 310–334  mathnet (cited: 29)  mathscinet (cited: 30)  zmath; V. L. Popov, “Contractions of the actions of reductive algebraic groups”, Math. USSR-Sb., 58:2 (1987), 311–335  crossref  mathscinet  zmath
79. 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
80. H. Kraft, V. L. Popov, “Semisimple group actions on the three-dimensional affine space are linear”, Comment. Math. Helv., 60:3 (1985), 466–479  crossref  mathscinet (cited: 17)  zmath  isi (cited: 24)  elib (cited: 7)  scopus (cited: 21)
81. 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  mathscinet
82. V. L. Popov, “Homological dimension of algebras of invariants”, J. Reine Angew. Math., 341 (1983), 157–173  crossref  mathscinet (cited: 3)  zmath  isi (cited: 10)  scopus (cited: 7)
83. V. L. Popov, “Syzygies in the theory of invariants”, Izv. AN SSSR. Ser. matem., 47:3 (1983), 544–622  mathnet (cited: 5)  mathscinet (cited: 3)  zmath; V. L. Popov, “Syzygies in the theory of invariants”, Math. USSR-Izv., 22:3 (1984), 507–585  crossref  mathscinet  zmath
84. 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
85. 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.  mathscinet (cited: 14)  zmath
86. V. L. Popov, “A finiteness theorem for representations with a free algebra of invariants”, Izv. AN SSSR. Ser. matem., 46:2 (1982), 347–370  mathnet (cited: 4)  mathscinet  zmath; V. L. Popov, “A finiteness theorem for representations with a free algebra of invariants”, Math. USSR-Izv., 20:2 (1983), 333–354  crossref  mathscinet  zmath
87. V. Grigor'ev, V. L. Popov, D. D. Solncev, Problems in algebra, MIEM Publ., Moscow, 1982 , 98 pp.
88. 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  mathscinet (cited: 10)
89. V. L. Popov, “The constructive theory of invariants”, Izv. AN SSSR. Ser. matem., 45:5 (1981), 1100–1120  mathnet (cited: 5)  mathscinet (cited: 4)  zmath; V. L. Popov, “The constructive theory of invariants”, Math. USSR-Izv., 19:2 (1982), 359–376  crossref  mathscinet  zmath
90. 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
91. 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
92. 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
93. V. L. Popov, “Hilbert's theorem on invariants”, Soviet Math. Dokl., 20:6 (1979), 1318–1322  mathscinet  zmath
94. 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
95. V. L. Popov, “Classification of spinors of dimension fourteen”, Trudy Mosk. matem. obschestva, 37, MMO, 1978, 173–217  mathnet (cited: 1)  mathscinet (cited: 2)  zmath; V. L. Popov, “Classification of spinors of dimension fourteen”, Trans. Mosc. Math. Soc., 1 (1980), 181–232  zmath
96. V. L. Popov, “Algebraic curves with an infinite automorphism group”, Math. Notes, 23:2 (1978), 102–108  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  scopus (cited: 1)
97. V. L. Popov, “One conjecture of Steinberg”, Funct. Anal. Appl., 11:1 (1977), 70–71  mathnet  crossref  mathscinet  zmath  scopus (cited: 1)
98. V. L. Popov, “Classification of the spinors of dimension fourteen”, Uspekhi Mat. Nauk, 32:1(193) (1977), 199–200  mathnet  mathscinet  zmath
99. 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
100. 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  mathscinet (cited: 9)
101. V. L. Popov, “Representations with a free module of covariants”, Funct. Anal. Appl., 10:3 (1976), 242–244  mathnet  crossref  mathscinet  zmath  scopus (cited: 19)
102. V. L. Popov, “The classification of representations which are exceptional in the sense of Igusa”, Funct. Anal. Appl., 9:4 (1975), 348–350  mathnet  crossref  mathscinet  zmath  scopus (cited: 2)
103. 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  mathnet  crossref  mathscinet  zmath
104. 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  mathnet  crossref  mathscinet  zmath
105. 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  mathnet  crossref  mathscinet  zmath  scopus (cited: 1)
106. 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  mathnet  crossref  mathscinet  zmath
107. V. L. Popov, “Quasihomogeneous affine algebraic varieties of the group SL(2)”, Math. USSR-Izv., 7:4 (1973), 793–831  mathnet  crossref  mathscinet  zmath
108. È. B. Vinberg, V. L. Popov, “On a class of quasihomogeneous affine varieties”, Math. USSR-Izv., 6:4 (1972), 743–758  mathnet  crossref  mathscinet  zmath
109. 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  mathnet  crossref  mathscinet  zmath
110. 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  mathnet
111. 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  mathnet  crossref  mathscinet  zmath  scopus (cited: 2)
112. 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
113. V. L. Popov, “Stability criteria for the action of a semisimple group on a factorial manifold”, Math. USSR-Izv., 4:3 (1970), 527–535  mathnet  crossref  mathscinet  zmath
114. 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, Encyclopaedia of Mathematical Sciences, 130, Subseries “Invariant Theory and Algebraic Transformation Groups”, no. VIII, 2nd Enlarged Ed. with two Appendices by V. L. Popov, and an Addendum by N. A. Campo and V. L. Popov, Springer, Berlin, 2015, 309–322, ISBN: 978-3-662-48420-3 DOI:10.1007/978-3-662-48422-7
115. Vladimir L. Popov, “Stratification of the nullcone”, Appendix C in: H. Derksen, G. Kemper, Computational Invariant Theory, Encyclopaedia of Mathematical Sciences, 130, Subseries “Invariant Theory and Algebraic Transformation Groups”, no. VIII, 2nd Enlarged Ed. with two Appendices by V. L. Popov, and an Addendum by N. A. Campo and V. L. Popov, Springer, Berlin, 2015, 323–344, ISBN: 978-3-662-48420-3 DOI:10.1007/978-3-662-48422-7
116. Norbert A'Campo, Vladimir L. Popov, “The source code of HNC”, Addendum to Appendix C in: H. Derksen, G. Kemper, Computational Invariant Theory, Encyclopaedia of Mathematical Sciences, 130, Subseries “Invariant Theory and Algebraic Transformation Groups”, no. VIII, 2nd Enlarged Ed. with two Appendices by V. L. Popov, and an Addendum by N. A. Campo and V. L. Popov, Springer, Berlin, 2015, 345–358, ISBN: 978-3-662-48420-3 DOI:10.1007/978-3-662-48422-7
117. 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, ISBN: 978-3-662-48420-3 , 387 pp. DOI:10.1007/978-3-662-48422-7
118. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
119. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
120. 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, ISBN: 978-5-4439-0206-7
121. 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, ISBN: 978-3-642-18398-0 , 253 pp.  crossref  mathscinet (cited: 22)  zmath
122. 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, ISBN: 978-3-642-17403-2 , 233 pp.  crossref  mathscinet (cited: 13)
123. 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, ISBN: 978-3-540-76756-5 , 265 pp.  crossref  mathscinet (cited: 10)  zmath
124. 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, ISBN: 3-540-29521-6 , 261 pp.  mathscinet (cited: 69)  zmath
125. 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, ISBN: 3-540-22898-5 , 250 pp.  mathscinet (cited: 19)  zmath
126. 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, ISBN: 3-540-24323-2 , 177 pp.  mathscinet (cited: 26)  zmath
127. 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, ISBN: 3-540-24241-4 , 246 pp.  mathscinet (cited: 59)  zmath
128. 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, ISBN: 3-540-20838-0 , xii+238 pp.  mathscinet (cited: 5)
129. 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
130. 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, ISBN: 3-540-43476-3 , 268 pp.  mathscinet (cited: 143)  zmath
131. 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, ISBN: 3-540-43211-6 , 242 pp.  mathscinet (cited: 7)  zmath
132. V. L. Popov, “Preface to the Russian translation of talks at the Séminaire Bourbaki, 1992”, Mathematics. News in Foreign Science, 50, Mir, Moscow, 2001
133. 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
134. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)
135. V. L. Popov, Predislovie k russkomu perevodu knigi: V. Kats, Beskonechnomernye algebry Li, eds. V. L. Popov, Mir, M., 1993, 5–6, ISBN: 5-03-002574-X , 425 pp.  mathscinet (cited: 16)
136. V. L. Popov, Basic algebraic structures, MIEM Publ., Moscow, 1989 , 42 pp.
137. V. L. Popov, Analytic Geometry, MIEM Publ., Moscow, 1988 , 44 pp.
138. V. L. Popov, Linear Algebra, MIEM Publ., Moscow, 1988 , 45 pp.
139. 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  mathscinet  zmath
140. V. L. Popov, Preface to the Russian translation of: T. Springer, Invariant theory, Mir, Moscow, 1981, 5–8
141. V. L. Popov, 86 papers, v. 1–5, Matematicheskaya entsiklopediya, Sov. entsikl., M., 1977–1985  hlocal; V. L. Popov, 86 papers, Encyclopaedia of Mathematics, Kluwer Academic Publishers, 1987–2002

Presentations in Math-Net.Ru
1. On the equations defining affine algebraic groups
The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics
May 14, 2016 12:10   
2. The equations defining algebraic groups
Talk delivered at the Chebyshev Laboratory, St. Petersburg State University
December 24, 2015 11:00
3. Simple algebras and algebraic groups
September 16, 2015 13:30   
4. Bass' problem on triangulable subgroups of the Cremona group
May 22, 2015 10:00
5. Invariant Theory
May 21, 2015 18:00   
6. Algebraic subgroups of the Cremona groups
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
7. About Grothendieck
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
8. Jordan groups
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
December 18, 2014 14:00   
9. Closures of orbits
St. Petersburg Seminar on Representation Theory and Dynamical Systems
December 17, 2014 17:00
10. Simple algebras and invariants of linear actions
Seminar of the Department of Algebra and Number Theory and of the Department of Algebraic Geometry (Shafarevich Seminar)
November 18, 2014 15:00
11. Orbit closures of algebraic group actions
International conference "Geometry, Topology and Integrability", October 20-25, 2014, Skolkovo Institute of Science and Technology, Moscow
October 23, 2014 12:50
12. Orbit closures
September 16, 2014 09:00   
13. Infinite dimensional automorphism groups of algebraic varieties, multiple transitivity, and unirationality
July 17, 2014 14:00
14. Finite group actions on algebraic varieties: a “social” approach
July 10, 2014 10:00
15. Automorphism groups of algebraic varieties
Steklov Mathematical Institute Seminar
March 27, 2014 16:00   
16. Quotients by conjugation action, cross-sections, singularities, and representation rings
January 20, 2014 15:00
17. Строение алгебраических подгрупп групп автоморфизмов алгебраических многообразий и, в частности, группы Кремоны $\mathrm{Cr}_n$
Scientific session of the Steklov Mathematical Institute dedicated to the results of 2013
November 20, 2013 10:20   
18. Жордановы группы и группы автоморфизмов алгебраических многообразий
Seminar of the Department of Algebra and Number Theory and of the Department of Algebraic Geometry (Shafarevich Seminar)
September 10, 2013 15:00
19. Grothendieck's questions on conjugating actions of semisimple groups
International conference dedicated to the 90th anniversary of academician Igor Rostislavovich Shafarevich
June 5, 2013 14:30   
20. Algebraic groups and the Cremona group
April 9, 2013 10:20
21. Orbit closures
March 6, 2013 11:30
22. Rational functions on semisimple Lie algebras and the Gelfand–Kirillov conjecture
January 4, 2013 15:10
23. Tori in Cremona groups
Second one-day conference dedicated to the memory of V. A. Iskovskikh
December 27, 2012 12:30   
24. Simple algebras and the analogue of classical invariant theory for nonclassical groups
International conference "Arithmetic as Geometry: Parshin Fest"
November 29, 2012 15:00   
25. Jordan groups and automorphism groups of algebraic varieties
November 2, 2012
26. Rational functions on semisimple Lie algebras and the Gelfand–Kirillov Conjecture
October 2, 2012   
27. 170 years of invariant theory
September 27, 2012
28. Coordinate algebras of algebraic groups: generators and relations
September 27, 2012
29. Rational functions on semisimple Lie algebras and the Gelfand–Kirillov Conjecture
September 25, 2012
30. Tori in Cremona groups
International conference "Essential Dimension and Cremona Groups", Chern Institute of Mathematics, Nankai University, Tianjin, China
June 12, 2012
31. 170 years of invariant theory
Colloquium talk at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.
June 8, 2012 16:30
32. Rational actions on affine spaces
International conference "Birational and affine geometry"
April 23, 2012 11:00   
33. On the subgroups of the Cremona group
Seminar of the Department of Algebra and Number Theory and of the Department of Algebraic Geometry (Shafarevich Seminar)
April 3, 2012 15:00
34. Invariant rational functions on semisimple Lie algebras and the Gelfand–Kirillov conjecture
International conference "Algebra and Mathematical Logic" dedicated to the 100-th birthday of Professor V. V. Morozov
September 27, 2011 11:20
35. Cross-sections, quotients, and representation rings of semisimple algebraic groups
Colloque International, Journées Solstice d'été 2011, Institut de Mathématiques de Jussieu, Université Paris-7 Denis Diderot, Paris
June 23, 2011 09:00
36. Discrete groups generated by complex reflections
International conference "GEOMETRY, TOPOLOGY, ALGEBRA and NUMBER THEORY, APPLICATIONS" dedicated to the 120th anniversary of Boris Delone (1890–1980)
August 17, 2010 14:00
37. Cross-sections, quotients, and representation rings of semisimple algebraic groups
International Algebraic Conference dedicated to the 70th birthday of Anatoly Yakovlev, June 19–24, 2010, St. Petersburg, Russia
June 19, 2010 09:30
38. Cayley groups
International Workshop Non-Archimedean Analysis, Lie Groups and Dynamical Systems February 8-12, 2010, Paderborn, Germany
February 8, 2010 14:50
39. Cross-sections, quotients, and representation rings of semisimple algebraic groups
International Workshop Linear Algebraic Groups and Related Structures, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Canada
September 16, 2009 09:50
40. Cross-sections and quotients for the actions of semisimple algebraic groups
International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh
June 30, 2009 10:00   
41. Two orbits: when is one in the closure of the other?
International conference Affine Algebraic Geometry in honour of Peter Russell, McGill University, Montreal, Canada
June 5, 2009 15:00
42. Algebraic groups and singularities
Summer School-Conference on Algebraic Geometry and Complex Analysis, Yaroslavl
May 11, 2009
43. Two orbits: when is one in the closure of the other?
Seminar of the Department of Algebra
April 28, 2009 15:00
44. Is the field of functions on the Lie algebra pure over the invariant subfield?
The second annual conference-meeting MIAN–POMI "Algebra and Algebraic Geometry"
December 24, 2008 12:15   
45. Describing the Hilbert cone of unstable points
International Conference Geometric Invariant Theory, Mathematisches Institut Georg-August-Universitat Gottingen, Gottingen, Germany
June 2, 2008 09:30
46. Tensor product decompositions and open orbits in multiple flag varieties
International Conference Lie Theory and Geometry. The Mathematical Legacy of Bertram Kostant, University of British Columbia, Vancouver, Canada
May 23, 2008 14:30
47. One and a half centuries of invariant theory
Steklov Mathematical Institute Seminar
February 28, 2008 16:00   
48. Rationality of extensions of invariant fields
Seminar of the Department of Algebra
January 29, 2008 15:00
49. One and a half centuries of Invariant Theory
The 2007 Collingwood Lecture, Durham University, Great Britain
November 23, 2007 13:15
50. Finite linear groups, lattices, and products of elliptic curves
International Algebraic Conference dedicated to the 100th anniversary of D. K. Faddeev
September 25, 2007 11:00
51. Cayley groups
International conference on algebra and number theory, dedicated to the 80th anniversary of V. E. Voskresensky, Samara
May 22, 2007
52. Discrete groups generated by complex reflections
Seminar of the Department of Algebra
March 27, 2007 15:00
53. Generically transitive algebraic group actions, open orbits in multiple flag varieties, and tensor product decompositions
Seminar of the Department of Algebra
January 23, 2007 15:00
54. Quasihomogeneous affine threefolds
International Conference Affine Algebraic Geometry, Oberwolfach, Germany
January 7, 2007
55. Generically multiple transitive algebraic group actions
International conference Algebraic Geometry: Warsaw 1960-2005, Bedlęwo, Poland
June 8, 2006
56. Finite linear groups, lattices, and products of elliptic curves
International Workshop Algebra and Geometry on the occasion of Norbert A'Campo's 65th anniversary, ETH Zurich, Switzerland
May 18, 2006
57. 13th Hilbert problem and algebraic groups
Meetings of the St. Petersburg Mathematical Society
April 18, 2006
58. Finite linear groups, lattices, and products of elliptic curves (joint work with Yu. G. Zarhin)
Seminar of the Department of Algebra
April 4, 2006
59. Projective self-dual algebraic varieties and nilpotent orbits
Buenos Aires Satellite Conference of the Lat Am Algebra Colloquium, BASCOLA, University of Buenos Aires
August 10, 2005 11:00
60. Finite dimensional simple algebras and the analogue of classicalinvariant theory for nonclassical groups
XVI Latin American Algebra Colloquium, Coloniadel Sacramento, Uruguay
August 7, 2005
61. Projective duality and nilpotent orbits
Seminar of the Department of Algebra
April 12, 2005
62. Generators and relations of algebras of regular functions of connected linear groups
Seminar of the Department of Algebra
January 18, 2005
63. Polynomial automorphisms
The University of British Columbia, Mathematics Department
November 24, 2004 15:00
64. 150 years of Invariant Theory
Red Raider Symposium 2004: Invariant Theory in Perspective Texas Technical University, Lubbock TX, USA
November 11, 2004 10:00
65. Cayley groups
International Conference Arithmetic Geometry, St. Petersburg
June 26, 2004
66. Проективно самодвойственные алгебраические многообразия и нильпотентные орбиты
Lie groups and invariant theory
May 5, 2004 16:20
67. Cayley groups
International Conference Commutative Algebra and Algebraic Geometry in honor of Professor Miyanishi, Osaka University, Japan
May 1, 2004
68. Cayley maps for algebraic groups
International Colloquium Algebraic Groups and Homogeneous Spaces, Bombay, India
January 6, 2004
69. Finite dimensional simple algebras and the analogue of classical invariant theory for nonclassical groups
International workshop on Invariant Theory, Queen's University, Kingston, ON, Canada
April 8, 2002
70. Homogeneous spaces and the problems of groups actions and algebraic geometry
International Workshop Group Actions on Rational Varieties CRM, Montreal, Canada
February 27, 2002 09:00
71. Hilbert 13th problem and algebraic groups
Moscow mathematical society
April 4, 2000
72. Kostant sections
Colloque International "Groupes et Algèbres" Journées Solstice d'été, Institut de Mathématiques de Jussieu, Université Paris-7 Denis Diderot, Paris
June 23, 1995

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