Passionate with algebraic geometry and intelligent computing. CV

# Curriculum Vitae

## General info

## Career

- 2017-present: Associate Professor at MIPT, Department of Discrete Mathematics.
- 2017-present: Editor of the educational magazine for children “Kvantik”
- 2016-present: Researcher at Kharkevich Institute, Laboratory 13 for Algebra and Number Theory.
- 2014-2015: Postdoc at Saint-Petersburg State University, Chair of Higher Algebra and Number Theory, Scientific Supervisor N.A. Vavilov.

## Education

- 2010-2013: PhD in Co-Tutorship at the Moscow State University, Chair of Higher Algebra, Scientific Supervisor I.V. Arzhantsev, and University of Grenoble, Institut Fourier, Scientific Supervisor M.G. Zaidenberg.
- 2005-2010: Student at the Moscow State University, Chair of Higher Algebra, Scientific Supervisor I.V. Arzhantsev.
- 1995-2005: Lyceum-school 130, Novosibirsk.

Competitions:

- 2003, 2004: (twice) Second prize at the All-Russian Mathematical Olympiad.
- 2003, 2004: (twice) Winner of the International Tournament of Towns.
- 2004: Diploma of the 16th Summer Conference of the Tournament of Towns.
- 2007,2009: (twice) First prize at the International Mathematical Competition for University Students
- 2008, 2009: MIPT Math Olympiad for Undergraduate Students, Second prize at 2008, First prize at 2009
- Olympiads at the Faculty of Mechanics and Mathematics, Moscow State University:
- 2006: Second prize at the Faculty Olympiad
- 2007: Third prize at the Probability Theory Olympiad
- 2007: First prize at the Ordinary Differential Equations Olympiad
- 2008: First prize at the Partial Differential Equations Olympiad
- 2009: First prize at the Discrete Mathematics Olympiad

## Languages

- Russian: native
- English: advanced
- French: intermediate

## Research

## Mathematical interests

- Algebraic groups and monoids
- Lie algebras and their representations
- Invariant theory
- Spherical varieties.
- Automorphisms of finite-dimensional algebras
- Locally nilpotent derivations
- Flexibility of affine varieties
- Automorphism groups of affine varieties
- Actions of ind-groups
- T-varieties

## Publications

*Affine algebraic monoids as endomorphisms’ monoids of finite-dimensional algebras*,**Proceedings of the American Mathematical Society 137**(2009), 3227–3233.*Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5*,**Functional Analysis and Applications 47**(2013), no. 4, 45–52.*On solvability of the automorphism group of a finite-dimensional algebra*,**Journal of Algebra 403**(2014), 445–458.- (with Ivan Arzhantsev and Hendrik Süß)
*Infinite transitivity on universal torsors*,**Journal of the London Mathematical Society 89**(2014), no. 3, 762–778. - (with Kevin Langlois)
*Demazure roots and spherical varieties: the example of horizontal SL(2)-actions*, preprint; arXiv:1406.5744. - (with Sergei Kovalenko and Mikhail Zaidenberg)
*On automorphism groups of affine surfaces*,**Advanced Studies in Pure Mathematics 75**(2017), Algebraic Varieties and Automorphism Groups, 207–286; arXiv:1511.09051. - (with Mateusz Michałek and Hendrik Süß)
*Flexible affine cones and flexible coverings*,**Mathematische Zeitschrift 290**(2018), no. 3-4, 1457-1478, http://doi.org/10.1007/s00209-018-2069-2 - (with Nikolay Bogachev)
*Vinberg’s Algorithm for Hyperbolic Lattices*,**Mathematical Notes 103**(2018), no. 5-6, 836-840, http://doi.org/10.1134/S0001434618050164 - (with Andriy Regeta)
*When is the automorphism group of an affine variety nested?*, preprint, arXiv:1903.07699 - (with Vsevolod Gubarev)
*Injective Rota-Baxter operators of weight zero on F[x]*, preprint, arXiv:2005.14030 *Affine cones over cubic surfaces are flexible in codimension one*,**Forum Mathematicum 33**(2021), no. 2, 339–348 DOI:10.1515/forum-2020-0191

Alternatively, see my Publons profile. There are also abstracts in Schools-Conferences on Lie Algebras, Algebraic Groups and Invariant Theory.

## Talks

- Talk
*Affine algebraic monoids as endomorphisms’ monoids of finite-dimensional algebras*at- June 2009: Summer School
*Lie Algebras, Algebraic Groups and Invariant Theory*, Samara. - May 2010: Conference
*Malt’sev meeting*, Novosibirsk.

- June 2009: Summer School
- Talk
*Flexibility of affine cones over del Pezzo surfaces of degree 5 and 4*- March 2011: Seminar “Lie Groups and Invariant Theory” Moscow, Russia
- February 2012:
*Swiss-French workshop on algebraic geometry*Enney, Switzerland. - June 2012: International Conference dedicated to the 65-th anniversary of Askold G. Khovanskii Moscow, Russia
- June 2012: Third Summer School
*Lie Algebras, Algebraic Groups and Invariant Theory*Togliatti, Russia

- April 2013: Talk
*Flexibility of universal torsors*at the Seminar of Algebra and Geometry Basel, Switzerland - January 2014: Talk
*Flexibility of affine varieties*at the Fourth School*Lie Algebras, Algebraic Groups and Invariant Theory*, Moscow, Russia - Talk
*Flexible varieties covered by toric charts*:- July 2014: Kyoto Workshop on Algebraic Varieties and Automorphism Groups Kyoto, Japan
- July 2014: International Short-School/Conference
*Affine Algebraic Geometry & the Jacobian Conjecture*, Tianjin, China

- December 2014: Talk
*Flexibility of affine cones and total coordinate spaces*at the Algebraic Geometry Seminar at IBS Center for Geometry and Physics, Pohang, Korea - June 2015: Talk
*Automorphism groups of affine surfaces*at the conference*Meeting of generations*by Dynasty Foundation Mosow, Russia - Talk
*Automorphism groups of affine surfaces without additive actions*:- June 2015 Fifth School
*Lie Algebras, Algebraic Groups and Invariant Theory*Samara, Russia - August 2015 School (and Workshop) on Finite Subgroups of Cremona Groups Trento, Italy

- June 2015 Fifth School
- Talk
*Automorphism groups of affine varieties consisting of algebraic elements*- January 2017 Christmas meetings Moscow, Russia
- January 2017 Sixth School
*Lie Algebras, Algebraic Groups and Invariant Theory*Moscow, Russia - January 2018 Conference “Polynomial Rings and Affine Algebraic Geometry”, Tokyo, Japan

- Talk
*Nested automorphism groups*- May 2018 Conference “Algebraic Geometry - Mariusz Koras in memoriam”, Warsaw, Poland
- November 2018 59th MIPT Scientific Conference, Moscow, Russia
- April 2019 Vinberg’s Seminar on Lie Groups and Invariant Theory, Moscow, Russia
- September 2019 Conference “Emerging Research in Algebraic Groups, Motives, and K-Theory”, St.Petersburg, Russia

Mini-courses:

- May 2011: Mini-course on a flexibility of affine toric varieties at Sobolev Institute of Mathematics Novosibirsk, Russia In the context of the project 14.740.11.0346,
*Actual problems of modern algebra*, supported by the Ministry of education and science of Russian Federation

Also participated in conferences (not an exhaustive list):

- April 2009: Workshop
*Hamiltonian actions: invariants and classification*, Luminy, France - August 2009: Summer School
*Structures in Lie Representation Theory*, Bremen, Germany - November 2010: Workshop
*Automorphismes des Espaces Affines*, Dijon, France - January 2011: Workshop
*Torsors: Theory and Applications*, Edinburgh, UK - February 2011: Winter School
*Lie Algebras, Algebraic Groups and Invariant Theory*, Moscow, Russia - September 2011: Autumn School
*Geometric Invariant Theory, old and new*, Lukecin, Poland - February 2012: Winter School
*Homogeneous Spaces and Geometric Representation Theory*, Bochum, Germany - April 2012: Conference
*Birational and affine geometry*, Moscow, Russia - September 2012: Autumn School
*Subgroups of Cremona groups*, Lukecin, Poland - November 2012: Conference in algebraic geometry
*Birpol3*, Basel, Switzerland - February 2013:
*2nd Swiss-French workshop on algebraic geometry*, Enney, Switzerland - September 2013 Autumn School
*Power sum decompositions and apolarity, a geometric approach*, Lukecin, Poland

## Scholarships

- 2008: Moscow Government Scholarship
- 2012: Russian Government Scholarship
- 2010–2013: French Government Scholarship
- 2013: Simons Scholarship
- 2015: Dynasty Scholarship

## Projects

- 2012–2013:
*Infinitely transitive action of automorphism groups and locally nilpotent derivations*, project 12–01–31342 supported by RFBR. - 2012–2013:
*Algebraic transformation groups, equvariant symplectic geometry and representation theory*, project 12–01–00704–a supported by RFBR. - 2012–2013:
*Automorphisms, derivations, and additive structures on algebraic varieties*, project 8214 supported by the Ministry of education and science of Russian Federation. - December 2013: Collaboration project in context of *Réseau franco-russe de formation et de recherche en mathématiques} supported by GDRI, France.
- others…