Homepage of

Vladimir DOTSENKO


<...> arguably the primary social function of science,
as social institution in our days, consists in stopping
the frenetic activity of post-industrial society
— Yuri I. Manin,
"Mathematics as Profession and Vocation", 1999.



I am a professor at Institut de Recherche Mathématique Avancée, UMR 7501 de l'Université de Strasbourg et du CNRS, and I am the coordinator of research masters in mathematics at that institute. I belong to the team ART: Algèbre, représentations, topologie at that institute, and I organise one of the two seminars of that team. I am also a member of the national research network GDR 2875: théorie de l'homotopie et applications and of several subdivisions of the national research network GDR 673: informatique mathématique.

I am a junior member of Institut Universitaire de France (2021-2026), the local coordinator of the project Higher Algebra, Geometry, and Topology of Agence Nationale de la Recherche (2021-2024), and the international coordinator of the Math-AmSud project HHMA (23-MATH-06) supported by CNRS, MINCYT, and ANII (2024-2025).

Rewriting
(photo credits: Face2FaceIRL)

Academic path

Research areas

My principal research area is homotopical algebra and its applications. I am also very interested in operads, Gröbner bases, combinatorics, homological algebra, representation theory and deformation theory. The following image shows some relationships between these areas: it proves that the Jacobi identity, the defining property of Lie algebras, forms a Gröbner basis of the shuffle operad corresponding to the operad controlling Lie algebras.

Rewriting

Of course, one sees some combinatorics, since the calculus of shuffle operads uses labelled rooted trees. There is also some homological algebra, since this calculation gives the shortest proof of the Koszul property of the operad of Lie algebras (this property means that the Quillen homology of this operad is well behaved). That latter property guarantees that various general methods are available to study the homotopy category of differential graded Lie algebras; these methods are central in modern deformation theory. Representation theory appears here as well: the Koszul property allows, via a computation of Euler characteristics of certain chain complexes, to describe the representations of symmetric groups in each component Lie(n), and then to describe the action of the general linear group on the free Lie algebra.

I am often asked to suggest introductory reading on the operad theory. Here are two suggestions. First, there is a remarkable recent monograph Algebraic operads by Jean-Louis Loday and Bruno Vallette. Second, in collaboration with Murray Bremner, I wrote the book Algebraic operads: an algorithmic companion which may be a bit more accessible to the reader without a steady background in homology and homotopy.

My professional online presence

Note: any other researcher profiles featuring my work that you may find online are either obsolete or maintained without my involvement or authorization.

Publications

For most of the publications listed below, clicking on the button "Details" will give you a couple of sentences containing some information about the mathematical content of that publication.

Books

  1. Vladimir Dotsenko, Sergey Shadrin, and Bruno Vallette, Maurer-Cartan methods in deformation theory: the twisting procedure, London Mathematical Society Lecture Note Series, 488, Cambridge University Press, 2023, 186 pp.
  2. Murray Bremner and Vladimir Dotsenko, Algebraic Operads: An Algorithmic Companion, Chapman and Hall / CRC Press, 2016, xviii+365 pp.

Preprints

  1. Vladimir Dotsenko, Evgeny Feigin, Piotr Kucharski, Markus Reineke, Categorification of quiver diagonalization and Koszul algebras, preprint arXiv:2402.12768.
  2. Vladimir Dotsenko, Stable homology of Lie algebras of derivations and homotopy invariants of wheeled operads, preprint arXiv:2311.18594.
  3. Yvain Bruned and Vladimir Dotsenko, Novikov algebras and multi-indices in regularity structures, preprint arXiv:2311.09091.
  4. Vladimir Dotsenko and Iryna Kashuba, The three graces in the Tits-Kantor-Koecher category, preprint arXiv:2310.20635.
  5. Vladimir Dotsenko, Nilpotence, weak nilpotence, and the nil property in the nonassociative world: computations and conjectures, preprint arXiv:2306.11362.
  6. Vladimir Dotsenko, Fine structures inside the PreLie operad revisited, preprint arXiv:2306.08425.
  7. Vladimir Dotsenko and Xabier García-Martínez, A characterisation of Lie algebras using ideals and subalgebras, preprint arXiv:2210.14550.
  8. Vladimir Dotsenko and Sergey Mozgovoy, DT invariants from vertex algebras, preprint arXiv:2108.10338.

Refereed journal papers

  1. Vladimir Dotsenko, Adam Keilthy, and Denis Lyskov, Reconnectads, to appear in Algebraic Combinatorics.
  2. Vladimir Dotsenko, Sergey Shadrin, Arkady Vaintrob, and Bruno Vallette, Deformation theory of cohomological field theories, Journal für die reine und angewandte Mathematik, online version on the publisher's website.
  3. Vladimir Dotsenko and Pedro Tamaroff, Tangent complexes and the Diamond Lemma, Bulletin of Mathematical Sciences, online version on the publisher's website.
  4. Vladimir Dotsenko and Anton Khoroshkin, Homotopical rigidity of the pre-Lie operad, Proceedings of the American Mathematical Society, Volume 152, Number 4, April 2024, Pages 1355–1371, online version on the publisher's website.
  5. Vladimir Dotsenko, Identities for deformation quantizations of almost Poisson algebras, Letters in Mathematical Physics, 114, 4, (2024), online version on the publisher's website. See also a free view-only version available as a part of "Springer Nature Content Sharing Initiative".
  6. Vladimir Dotsenko and Oisín Flynn-Connolly, Three Schur functors related to pre-Lie algebras, Mathematical Proceedings of Cambridge Philosophical Society, Volume 176, Issue 2, March 2024, Pages 441-458, online version on the publisher's website.
  7. Vladimir Dotsenko and Ualbai Umirbaev, An effective criterion for Nielsen-Schreier varieties, International Mathematics Research Notices, Volume 2023, Issue 23, December 2023, Pages 20385–20432, online version on the publisher's website.
  8. Appendix to: Anton Khoroshkin, Pedro Tamaroff, Derived Poincaré-Birkhoff-Witt theorems, Letters in Mathematical Physics, 113, 15 (2023), online version on the publisher's website.
  9. Vladimir Dotsenko, Nurlan Ismailov, and Ualbai Umirbaev, Polynomial identities in Novikov algebras, Mathematische Zeitschrift, 303, 60 (2023), online version on the publisher's website. See also a free view-only version available as a part of "Springer Nature Content Sharing Initiative".
  10. Vladimir Dotsenko, Vincent Gélinas, and Pedro Tamaroff, Finite generation for Hochschild cohomology of Gorenstein monomial algebras, Selecta Mathematica, 29, 14 (2023), online version on the publisher's website. See also a free view-only version available as a part of "Springer Nature Content Sharing Initiative".
  11. Vladimir Dotsenko, Sergey Shadrin, and Pedro Tamaroff, Generalized cohomological field theories in the higher order formalism, Communications in Mathematical Physics, 399 (2023), 1439-1500, online version on the publisher's website. See also a free view-only version available as a part of "Springer Nature Content Sharing Initiative".
  12. Murray Bremner and Vladimir Dotsenko, Associator dependent algebras and Koszul duality, Annali di Matematica Pura et Applicata (1923-), 202 (2023), 1233-1254, online version on the publisher's website. See also a free view-only version available as a part of "Springer Nature Content Sharing Initiative".
  13. Vladimir Dotsenko, Evgeny Feigin, and Markus Reineke, Koszul algebras and Donaldson-Thomas invariants, Letters in Mathematical Physics, 112, 106 (2022), online version on the publisher's website. See also a free view-only version available as a part of "Springer Nature Content Sharing Initiative".
  14. Vladimir Dotsenko and Loïc Foissy, Operads of enriched pre-Lie algebras and freeness theorems, Journal of Combinatorial Algebra, 6 (2022), 23-44, online version on the publisher's website.
  15. Vladimir Dotsenko, Homotopy invariants for M0,n via Koszul duality, Inventiones Mathematicae, 228 (2022), 77-106, online version on the publisher's website. See also a free view-only version available as a part of "Springer Nature Content Sharing Initiative".
  16. Vladimir Dotsenko and Pedro Tamaroff, Endofunctors and Poincaré-Birkhoff-Witt theorems, International Mathematics Research Notices, Volume 2021, Issue 16, Pages 12670–12690, online version on the publisher's website.
  17. Murray Bremner and Vladimir Dotsenko, Distributive laws between the operads Lie and Com, International Journal of Algebra and Computation, 30 (2020), no. 8, 1565-1576, online version on the publisher's website.
  18. Vladimir Dotsenko, Martin Markl, and Elisabeth Remm, Veronese powers of operads and pure homotopy algebras, European Journal of Mathematics, 6 (2020), 829-863, online version on the publisher's website.
  19. Vladimir Dotsenko, Martin Markl, and Elisabeth Remm, Non-Koszulness of operads and positivity of Poincaré series, Documenta Mathematica 25 (2020), 309-328, online version on the publisher's website.
  20. Vladimir Dotsenko, Word operads and admissible orderings, Applied Categorical Structures, 28 (2020), 595-600, online version on the publisher's website.
  21. Vladimir Dotsenko, Functorial PBW theorems for post-Lie algebras, Communications in Algebra, 48 (2020), no. 5, 2072-2080, online version on the publisher's website.
  22. Murray Bremner and Vladimir Dotsenko, Boardman-Vogt tensor products of absolutely free operads, Proceedings of the Royal Society of Edinburgh Section A, 150 (2020), no. 1, 367-385, online version on the publisher's website.
  23. Vladimir Dotsenko, Sergey Shadrin, and Bruno Vallette, Toric varieties of Loday's associahedra and noncommutative cohomological field theories, Journal of Topology 12 (2019), 463-535, online version on the publisher's website.
  24. Vladimir Dotsenko, Algebraic structures of F-manifolds via pre-Lie algebras, Annali di Matematica Pura et Applicata (1923-), 198 (2019), no. 2, 517-527, online version on the publisher's website.
  25. Vladimir Dotsenko, A Quillen adjunction between algebras and operads, Koszul duality, and the Lagrange inversion formula, International Mathematics Research Notices, Vol. 2017: article ID rnx257, 21 pages, online version on the publisher's website.
  26. Murray Bremner and Vladimir Dotsenko, Classification of regular parametrised one-relation operads, Canadian Journal of Mathematics, 69 (2017), no. 5, 992-1035, online version on the publisher's website. Online addendum to the article showing the relevant symbolic calculations: PDF version, text version.
  27. Vladimir Dotsenko and Soutrik Roy Chowdhury, Anick resolution and Koszul algebras of finite global dimension, Communications in Algebra, 45 (2017), no. 12, 5380-5383, online version on the publisher's website.
  28. Vladimir Dotsenko, Sergey Shadrin, and Bruno Vallette, Pre-Lie deformation theory, Moscow Mathematical Journal, 16 (2016), no. 3, 505-543, online version on the publisher's website.
  29. Vladimir Dotsenko and Norbert Poncin, A tale of three homotopies, Applied Categorical Structures, 24 (2016), Issue 6, 845-873, online version on the publisher's website.
  30. Vladimir Dotsenko, Sergey Shadrin, and Bruno Vallette, Givental action and trivialisation of circle action, Journal of École Polytechnique - Mathematiques, 2 (2015), 213-246, online version on the publisher's website.
  31. Vladimir Dotsenko, Sergey Shadrin, and Bruno Vallette, De Rham cohomology and homotopy Frobenius manifolds, Journal of European Mathematical Society, 17 (2015), 535-547, online version on the publisher's website.
  32. Vladimir Dotsenko and James Griffin, Cacti and filtered distributive laws, Algebraic and Geometric Topology, 14 (2014), issue 6, 3185-3225, online version on the publisher's website.
  33. Vladimir Dotsenko, Dual alternative algebras in characteristic three, Communications in Algebra, 42 (2014), Issue 5, 1911-1920, online version on the publisher's website.
  34. Vladimir Dotsenko and Anton Khoroshkin, Quillen homology for operads via Gröbner bases, Documenta Mathematica, 18 (2013), 707-747, online version on the publisher's website.
  35. Vladimir Dotsenko and Bruno Vallette, Higher Koszul duality for associative algebras, Glasgow Mathematical Journal, 55 (2013), issue A, 55-74, online version on the publisher's website.
  36. Vladimir Dotsenko, Sergey Shadrin, and Bruno Vallette, Givental group action on topological field theories and homotopy Batalin-Vilkovisky algebras. Advances in Mathematics 236 (2013) 224–256, online version on the publisher's website.
  37. Vladimir Dotsenko and Anton Khoroshkin, Shuffle algebras, homology, and consecutive pattern avoidance, Algebra & Number Theory, 7 (2013), No. 3, 673–700, online version on the publisher's website.
  38. Vladimir Dotsenko, Pattern avoidance in labelled trees, Séminaire Lotharingien de Combinatoire, B67b (2012), 27 pp., online version on the publisher's website.
  39. Vladimir Dotsenko and Anton Khoroshkin, Gröbner bases for operads, Duke Mathematics Journal, Volume 153, Number 2 (2010), 363-396, online version on the publisher's website.
  40. Sergey Cherkis, Vladimir Dotsenko, and Christian Saemann, Superspace Actions for Multiple M2-Branes, Metric 3-Algebras and their Classification, Physical Review D, 79, 086002 (2009), 11 pp., online version on the publisher's website.
  41. Vladimir Dotsenko, Parking functions and vertex operators, Selecta Mathematica, 14: 2 (2009), 229-245, online version on the publisher's website.
  42. Vladimir Dotsenko, Compatible associative products and trees, Algebra & Number Theory, 3 (2009), no. 5, 567-586, online version on the publisher's website.
  43. Vladimir Dotsenko, An operadic approach to deformation quantization of compatible Poisson brackets, I, Journal of Generalised Lie Theory and Applications, 1 (2007), No. 2, 107-115, online version on the publisher's website.
  44. Mikhail Bershtein, Vladimir Dotsenko, and Anton Khoroshkin, Quadratic algebras related to the bihamiltonian operad, International Mathematics Research Notices Vol. 2007: article ID rnm122, 30 pages, online version on the publisher's website.
  45. Vladimir Dotsenko and Anton Khoroshkin, Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad, Functional Analysis and Its Applications, 41 (2007), no.1, 1-17, online version on the publisher's website.
  46. Vladimir Dotsenko, Homology of the Lie algebra of vector fields on a line with coefficients in symmetric powers of its adjoint representation, Functional analysis and its applications, 40 (2006), no.2, 13-19, online version on the publisher's website.
  47. V.Dotsenko, N.Iyudu, and D.Korytin, An analogue of the Magnus problem for associative algebras, Journal of Mathematical Sciences (New York), 131, no. 6 (2005), 6023-6026, online version on the publisher's website.

Conference proceedings

  1. Vladimir Dotsenko, The cohomology of M0,n+1 is Koszul (a proof of a conjecture of Manin), Oberwolfach Reports, 18 (2021), no. 1, 239-241, online version on the publisher's website.
  2. Murray Bremner and Vladimir Dotsenko, Distributive laws between the operads Lie and Com: extended abstract. In: Maple in Mathematics Education and Research. MC 2019. Communications in Computer and Information Science, vol. 1125, 349-352, online version on the publisher's website.
  3. Vladimir Dotsenko, Operads, Oberwolfach Reports, 11 (2014), no. 1, 601-604, online version on the publisher's website.
  4. Vladimir Dotsenko and Mikael Vejdemo Johansson, Implementing Gröbner bases for operads, arXiv:0909.4950, Séminaires et Congrès, Volume 26 (2011), 77-98, online version on the publisher's website.
  5. Vladimir Dotsenko, Freeness theorems for operads via Gröbner bases, arXiv:0907.4958, Séminaires et Congrès, Volume 26 (2011), 61-76, online version on the publisher's website.
  6. Vladimir Dotsenko and Mikael Vejdemo Johansson, Operadic Gröbner bases: an implementation, Lecture Notes in Computer Science 6327 (2010), 249-252, online version on the publisher's website.

Expository publications

  1. Vladimir Dotsenko, Alexander Shen, and Mark Spivakovsky, Foreword to the special issue dedicated to Rafail Kalmanovich Gordin, Arnold Mathematical Journal, 5 (2019), 1-4, Online version on the publisher's website.
  2. Vladimir Dotsenko, Арифметика квадратичных форм, Moscow, MCCME publishers, 2015, 30 pages (in Russian).
  3. Vladimir Dotsenko, Review of the book "Alan M. Turing" by Sara Turing, Irish Math. Soc. Bulletin Number 70, Winter 2012, 54-57.
  4. Vladimir Dotsenko, Remembering Jean-Louis Loday, 2012.
  5. Vladimir Dotsenko and Constantin Shramov, Об одной хорошо забытой старой задаче, Quant, 4 (2009), 34-36 (in Russian).
  6. Vladimir Dotsenko, Rafail Gordin, Alexander Shen and Constantin Shramov, Избранные задачи вступительных экзаменов в математические классы школы 57, Quant, 4 (2009), 57-58 (in Russian).
  7. Vladimir Dotsenko, Заметки о случайных изоморфизмах, Math. Education, 12 (2008), 81-94 (in Russian).
  8. Vladimir Dotsenko (ed.), Задачи по математике, предлагавшиеся ученикам математического класса 57 школы (выпуск 2004 года, класс "Д"), MCCME publishers, 2004, 220 pages (in Russian).
  9. Vladimir Dotsenko, Задачи о метрических компактах , Math. Education, 8 (2004), 237-238 (in Russian).
  10. Vladimir Dotsenko, Числа Каталана и естественные отображения , in Saint--Petersburg Mathematical Olympiad 2003, SPb, Nevskii Dialekt publishers, 2003; 2nd edition in Collected materials of summer camps of the Tournament of Towns, MCCME publishers, 2009, 31 pages (in Russian).
  11. Vladimir Dotsenko, Об одном доказательстве теоремы Гильберта о нулях , Math. Education, 6 (2002), 116-118 (in Russian).

Translations

  1. I. M. Pak, О нескольких теоремах Файна, об Эндрюсе, Дайсоне и об упущенных возможностях , Math. Education, 7 (2003), 136–148. (Translated into Russian by V.Dotsenko).

Preprints superseded by other articles or not intended for publication

  1. Vladimir Dotsenko, Sergey Shadrin, and Bruno Vallette, The twisting procedure, arXiv:1810.02941.
  2. Vladimir Dotsenko, Free Lie algebras are not Lily bialgebras.
  3. Vladimir Dotsenko and Anton Khoroshkin, Free resolutions via Gröbner bases, arXiv:0912.4895.
  4. Vladimir Dotsenko and Anton Khoroshkin, Anick-type resolutions and consecutive pattern avoidance, arXiv:1002.2761.
  5. Vladimir Dotsenko, A remark on Frobenius characters of set representations of symmetric groups, arXiv:0802.1340.

Software: Gröbner bases for operads

This part of my webpage (which is occationally updated) contains various materials related to the implementation of Gröbner bases for operads, as defined by myself and Anton Khoroshkin in our paper (see also the arXiv version). This implementation was created by Willem Heijltjes under my guidance; it was supported by University of Luxembourg in 2012 and by Trinity College Dublin in 2014.

Let me know if you use this program for other operad-related computations; I will be very happy to add them to this list (which I shall also update with some computations of mine in due course)!

Research associates and assistants

Current

Past

Contact information

Office

My office is I-505 (building of the IRMA, 5th floor)

If you are visiting Strasbourg and need directions: from the train station of Strasbourg (Gare Centrale), take tram C to the stop Université, walk down Rue Edmond Labbé from the tram stop, continue into Rue du Général Zimmer. After about 400m of walking in total (5 minutes), the mathematics institute building will be on your left. Take the elevator to the fifth floor.

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