Alexander Perepechko

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

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.
  • 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
  • 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

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…

Programming and stuff