# Vladimir Popov

- Professor: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE) / School of Applied Mathematics

- Vladimir Popov has been at HSE University since 2012.

## Education, Degrees and Academic Titles

Thesis Title: Groups, Generators, Syzygies, and Orbits in Invariant Theory

Thesis Title: Stability of Action of Algebraic Groups and Arithmetic of Quasihomogeneous Varieties

Lomonosov Moscow State University, Mechanics and Mathematics

Lomonosov Moscow State University

According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.

A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.

## Awards and Accomplishments

Best Teacher — 2016–2020, 2014

## Courses (2024/2025)

- Mathematical Logic and Theory of Alghorithms (Specialist; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 2 year, 3, 4 module)Rus
- Methods of Algebraic Geometry in Cryptography (Specialist; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 5 year, 1, 2 module)Rus
- Past Courses

## Courses (2023/2024)

- Mathematical Logic and Theory of Alghorithms (Specialist; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 2 year, 3, 4 module)Rus
- Methods of Algebraic Geometry in Cryptography (Specialist; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 5 year, 1, 2 module)Rus

## Courses (2022/2023)

- Mathematical Logic and Theory of Alghorithms (Specialist; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 2 year, 3, 4 module)Rus
- Methods of Algebraic Geometry in Cryptography (Specialist; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 5 year, 1, 2 module)Rus

## Courses (2021/2022)

## Courses (2020/2021)

## Editorial board membership

Since March 2021, "The European Mathematical Society Newsletter" has been renamed to "EMS Magazine".

*Transformation Groups*.

*Труды Московского математического общества*(

*Transactions of the Moscow Mathematical Society*).

*Известия Российской академии наук. Серия математическая*.

*Математические заметки*(

*Mathematical notes*).

*The European Mathematical Society Newsletter*.

*Journal of Mathematical Sciences*(

*Journal of Mathematical Sciences*).

*Geometriae Dedicata*.

## Conferences

- 2013
Algebraic Groups (Oberwolfach). Presentation: Algebraic groups and the Cremona group

Международная конференция, посвященная 90-летию академика И. Р. Шафаревича (Москва). Presentation: Вопросы Гротендика о действиях полупростых групп на себе сопряжениями

Научная сессия МИАН, посвященная подведению итогов 2013 г. (Москва). Presentation: Строение алгебраических подгрупп групп автоморфизмов алгебраических многообразий и, в частности, группы Кремоны Cr(n)

Семинар отдела алгебры и теории чисел и отдела алгебраической геометрии (семинар И. Р. Шафаревича) (Москва). Presentation: Жордановы группы и группы автоморфизмов алгебраических многообразий

## Main affiliation

The Steklov Mathematical Institute, Russian Academy of Sciences, Leading Research Fellow

## Personal web-page at the Steklov Mathematical Institute that contains the details of scientific career, complete list of publications, titles and video recordings of some talks

## Editorial appointments

- Transformation Groups (Birkhäuser), 1996--present (Editor-in-Chief);
- Izvestiya, Mathematics [Известия РАН, серия математическая] (Russian Academy of Sciences), 2006--present;
- Invariant Theory and Algebraic Transformation Groups, Subseries of Encyclopaedia of Mathematical Sciences (Springer), 1998--present;
- Mathematical Notes [Математические заметки] (Russian Academy of Sciences), 2003--present;
- Journal of Mathematical Sciences (Springer), 2008--present; Editorial Board of JMS.pdf
- Geometriae Dedicata (Klüwer), 1989--1999.

## Honors

- 2013: A series of papers on the structure of algebraic subgroups of automorphism groups of algebraic varieties and, in particular, of the Cremona group Cr(n) is recognized as one of the best in the Steklov Mathematical Institute. 1307.5522v5.pdf tori.pdf Cremona.pdf rationality.pdf
- Elected in November 2012: Fellow of the American Mathematical Society Fellow of the AMS.pdf (see on the site of AMS the list of Fellows sorted by country and institution)

- 2008--2010: Core member of the panel for Section 2, "Algebra", International Congress of Mathematicians 2010.

- 2010: The paper 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?, Compositio Mathematica, 147:2 (2011), 428–466 is recognized as one of the best in the Steklov Mathematical Institute. FF_p1.pdf

- 2008: John-von-Neumann-Gastprofessur, Technische Universität München, Germany. JvN_p.pdf

- 2005: The paper N. Lemire, V. L. Popov, Z. Reichstein, Cayley groups, Journal of the American Mathematical Society, 19:4 (2006), 921–967 is recognized as one of the best in the Russian Academy of Sciences. CG_p1.pdf

- 2002: The paper N. L. Gordeev, V. L. Popov, Automorphism groups of finite dimensional simple algebras, Annals of Mathematics (2), 158:3 (2003), 1041–1065 is recognized as one of the best in the Steklov Mathematical Institute. AG_p1.pdf

- 2001: Invited plenary address, XV Kongress, Österreichische Mathematische Gesellschaft, Vienna, Austria ( http://www.oemg.ac.at/Tagungen/2001/ ).

- 1998--1999: Invited Noted Scholar, Heidelberg, Germany.

- 1996: Invited Noted Scholar, the University of British Columbia, Vancouver, Canada.

- 1992: Habilitation is published by AMS as the monograph V. L. Popov, Groups, Generators, Syzygies, and Orbits in Invariant Theory, Translations of Mathematical Monographs, 100, American Mathematical Society, Providence, RI, 1992, ISBN: 0-8218-4557-8, vi+245 pp.

- 1986: Invited sectional address, the International Congress of Mathematicians, Algebra Section, Berkeley, USA. MDIT_p1.pdf

- 1986: J. Dixmier's talk at Séminaire Bourbaki Quelques résults de finitude en théorie des invariants (d'après V. L Popov), 38ème année 1985-86, no. 659, pp. 163-175. apres Popov.pdf

- 1972: PhD Thesis with Distinguished Honors (summa cum laude).

## Membership in Dissertation Council

Member of Dissertation Council D 002.022.03 at the Steklov Mathematical Institute of the Russina Academy of Sciences (specialities 01.01.04 and 01.01.06).

## Seminar and conference talks in 2007--2015

2015

1. Vladimir L. Popov, 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.

2014

1. Vladimir L. Popov, Simple algebras and invariants of linear actions, Joint seminar of Department of algebra and number theory and Department of algebraic geometry (Shafarevich seminar), Steklov Mathematical Institute, Russian Academy of Sciences, November 18, 2014, 15:00

2. Vladimir L. Popov, 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, 12:50-13:30

3. Vladimir L. Popov, Orbit closures, International conference ``Geometric Complexity Theory'', September 15--20, 2014, Simons Institute for Theoretical Computing, Berkeley University of California, USA, September 16, 2014, 9:00-9:50

4. V. L. Popov, Quotients by conjugation action, cross-sections, singularities, and representation rings, Workshop ID: 1404, Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras, Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras, The Mathematisches Forschungsinstitut Oberwolfach, Germany, 19.01.2014--25.01.2014

5. V. L. Popov, Automorphism groups of algebraic varieties, Steklov Mathematical Institute Seminar, March 27, 2014, 16:00.

6. Vladimir L. Popov, Finite group actions on algebraic varieties: a "social" approach, Kyoto Workshop on Algebraic Varieties and Automorphism Groups, July 7--11, 2014, Research Institute for Mathematical Sciences, Kyoto University, Japan, July 10, 2014, 10:00-11:00

7. Vladimir L. Popov, Infinite dimensional automorphism groups of algebraic varieties, multiple transitivity, and unirationality, Workshop ``Frontiers of rationality'', July 14--18, 2014, The University Centre in Svalbard, Longyearbyen (Spitsbergen), Norway, July 17, 2014, 14:00-15:00

2013

1. V. L. Popov, Structure of algebraic subgroups of automorphism groups of algebraic varieties and, in particular, the Cremona groups Cr(*n*), Scientific Session of Steklov Mathematical Institute devoted to the results of 2013, Steklov Mathematical Institute, Russian Academy of Sciences, November 20, 2013, 10:20

2. V. L. Popov, Jordan groups and automorphism groups of algebraic varieties, Joint seminar of Department of algebra and number theory and Department of algebraic geometry (Shafarevich seminar), Steklov Mathematical Institute, Russian Academy of Sciences, September 10, 2013, 15:00

3. V. L. Popov, Questions by Grothendieck on actions of semisimple groups on itself by conjugation, International conference dedicated to 90th birthday of aademician Igor Rostislavovich Shafarevich,

Steklov Mathematical institute RAS, June 5, 2013, 14:30.

4. V. L. Popov, Algebraic groups and the Cremona group, Workshop ID: 1315, Algebraic Groups, The Mathematisches Forschungsinstitut Oberwolfach, Germany, 07.04.2013--13.04.2013

5. V. L. Popov, Orbit closures, Research Workshop of Israel Science Foundation on Orbits, Primitive Ideals and Quantum Groups, The Weitsmann institute of Science, The University of Haifa, Israel, 24.02.2013--07.03.2013

6. V. L. Popov, Rational functions on semisimple Lie algebras and the Gelfand--Kirillov conjecture, International Conference in Memory of Tonny A. Springer "Algebraic Groups and Representation Theory", Hong Kong, 04.01.2013--09.01.2013

2012

1. V. L. Popov, Tori in the Cremona groups, Second one-day conference in memory of V. A. Iskovskikh, Steklov Mathematical Institute, Russian Academy of Sciences, 27.12.2012 - 27.12.2012

2. V. L. Popov, Simple algebras and the analogue of classical invariant theory for nonclassical groups, International conference* Arithmetic as Geometry: Parshin Fest*, Steklov Mathematical Institute, Russian Academy of Sciences, 26.11.2012 - 29.11.2012

3. V. L. Popov, Jordan groups and automorphism groups of algebraic varieties, International conference *Groups of Automorphisms in Birational and Affine Geometry*, Italy, Levico Terme, 29.10.2012--3.11.2012

4. V. L. Popov, Rational functions on semisimple Lie algebras and the Gelfand–-Kirillov Conjecture, International conference *Lie Algebras, Torsors and Cohomological Invariants*, Canada, Banff, 30.09.2012--5.10.2012

5. V. L. Popov, Coordinate algebras of algebraic groups: generators and relations, *Algebra & Number Theory Seminar* of the Pennsylvania State University, USA, 27.09.2012

6. V. L. Popov, 170 years of invariant theory, Colloquium talk at the Pennsylvania State University, USA, 27.09.2012

7. V. L. Popov, Rational functions on semisimple Lie algebras and the Gelfand–-Kirillov Conjecture, *GAP Semina*r of the Pennsylvania State University, USA, 25.09.2012

8. V. L. Popov, Tori in the Cremona Groups, International conference *Essential dimension and Cremona groups*, Chern Institute of Mathematics, Nankai University, Tianjin, China, 11.06.2012--15.06.2012

9. V. L. Popov, 170 years of invariant theory, Colloquium talk at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, 8.06.2012

10. V. L. Popov, Rational actions on affine spaces, International conference Birational and affine geometry, Steklov Mathematical Institute, Russian Academy of Sciences and HSE, 23.04.2012--27.04.2012

11. V. L. Popov, On subgroups of the Cremona groups, seminar talk at the *Shafarevich seminar*, Steklov Mathematical Institute, Russian Academy of Sciences, 3.04.2012

2011

1. V. L. Popov, *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, Kazan, September 27, 2011, 11:20.

2. V. L. Popov, Cross-sections, quotients, and representation rings of semisimple algebraic groups, plenary talk, Colloque International Journées Solstice d'été 2011, Institut de Mathématiques de Jussieu, Université Paris-7 Denis Diderot, Paris, France (June 23--25, 2011), June 23, 2011, 9:30.

**2010**

1. V. L. Popov, Cayley groups, International Workshop Non-Archimedean Analysis, Lie Groups and Dynamical Systems, Paderborn, Germany (February 8-12, 2010), February 8, 2010, 14:50.

2. V. L. Popov, Cross-sections, quotients, and representation rings of semisimple algebraic groups, International algebraic conference dedicated to the 70th birthday of Anatoly Yakovlev, St. Petersburg, Russia (June 19-24, 2010), June 19, 2010, 9:30.

3. V. L. Popov, Discrete groups generated by complex reflections, International conference "Geometry, Topology, Algebra, and Number Theory" dedicated to the 120th anniversary of Boris Delone, Moscow, Russia (16-20 August 16--20, 2010), August 17, 2010, 14:00.

**2009**

1. V. L. Popov, 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.

2. В. Л. Попов, Две орбиты: когда одна лежит в замыкании другой? Семинар отдела алгебры МИАН, 28 апреля 2009 г. 15:00.

3. V. L. Popov, *Algebraic groups and singularities, *Three lectures at the Summer school-conference on algebraic geometry and complex analysis for young Russian scientists, Yaroslavl, May 2009.

4. V. L. Popov, 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 13-18, 2009), September 16, 2009, 9:50.

5. V. L. Popov,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 1--5, 2009), June 5, 15:00.

**2008**

1. V. L. Popov, 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.

2. V. L. Popov, 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 19-25, 2008), May 23, 14:30.

3. V. L. Popov, One and a half centuries of invariant theory Steklov Mathematical Institute Seminar, February 28, 2008, 16:00.

4. V. L. Popov, Describing the Hilbert cone of unstable points, International Conference Geometric Invariant Theory, Mathematisches Institut Georg-August-Universität Göttingen, Göttingen, Germany (June 2-6, 2008), June 2, 9:30.

5. V. L. Popov, Rationality of extensions of invariant fields, Seminar of the Department of Algebra, Steklov Mathematical Institute, January 29, 2008, 15:00.

**2007**

1. V. L. Popov, Discrete groups generated by complex reflections, Seminar of the Department of Algebra, Steklov Mathematical Institute, March 27, 2007, 15:00.

2. V. L. Popov, One and a half centuries of Invariant Theory, The 2007 Collingwood Lecture, Durham University, Great Britain, November 23, 2007, 13:15. Cl.pdf

3. 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 Department of V. A. Steklov Mathematical Institute St. Petersburg (September 24--29, 2007), September 24, 2007, 11:00.

4. V. L. Popov, Quasihomogeneous affine threefolds, International Conference Affine Algebraic Geometry , Oberwolfach, Germany (January 7--13, 2007).

## HSE Researchers Become Members of the Russian Academy of Sciences

On October 28, the Russian Academy of Sciences (RAS) held a meeting to announce the results of elections of new members: 176 scholars were selected as academicians, and 323 scholars as corresponding members. HSE researchers are among the new RAS members.