Page mathématique de Vladimir DOTSENKO

Journal

I am happy to advertise a new open-access journal "Higher structures" where I serve on the editorial board. Its website is accessible via the URL https://journals.mq.edu.au/index.php/higher_structures/. If your research is related to the scope of this journal, please do consider publishing a paper there.

Book

In collaboration with Murray Bremner, I wrote a book "Algebraic Operads: An Algorithmic Companion".

Table of Contents:

1. Normal forms for vectors and univariate polynomials
2. Noncommutative associative algebras
3. Nonsymmetric operads
4. Twisted associative algebras and shuffle algebras
5. Symmetric operads and shuffle operads
6. Operadic homological algebra and Gröbner bases
7. Commutative Gröbner bases
8. Linear algebra over polynomial rings
9. Case study of nonsymmetric binary cubic operads
10. Case study of nonsymmetric ternary quadratic operads
Appendix. Maple code for Buchberger's algorithm

Papers and preprints

  • A complete list of all publications, both research and expository (and electronic versions of some of them), is here
  • The arXiv collection of my papers is here.
  • My Google Scholar profile is here.
  • The MathSciNet list of my papers is here (subscription required).

Various recent and forthcoming activities

Some research talks

  • "Graded algebras and the Lagrange inversion formula", a talk at the workshop "Graded Algebras, Geometry and related Topics" celebrating the 60th birthday of Adolfo Sánchez Valenzuela, Merida, November 2016:YouTube Video.
  • "Noncommutative M0,n+1", a talk at Samuel Gitler Memorial Conference, CINVESTAV, September 2016: YouTube Video.
  • "Shuffle operads", Introductory Workshop of the GDO programme: video of the talk on the Newton Institute website.
  • "Homotopical meaning of the Givental group", Higher Structure 2013 Workshop of the GDO programme: video of the talk on the Newton Institute website.
  • "Hierarchies of identities for differential operators and moduli spaces of curves", Algebra Seminar, University Lyon 1, February 9, 2012. Beamer presentation: PDF.
  • "Filtered distributive laws", Conference "Operads and rewriting", Lyon, France, November 3, 2011. Beamer presentation: PDF.
  • "Shuffle operads", Conference "New development in noncommutative algebra and its applications", Isle of Skye, Scotland, June 30, 2011. Beamer presentation: PDF.
  • "Compatible associative products and trees", LMS--ARTIN workshop "Integrable systems: algebraic aspects", University of Glasgow, April 23, 2010. Beamer presentation: PDF.
  • "Anick resolutions, shuffle algebras, and consecutive pattern avoidance", British Mathematics Colloquium, Edinburgh, April 6, 2010. Beamer presentation: PDF

Research supervision and mentorship

In 2021-24, I am supervising the PhD thesis of Paul Laubie, who works on a homotopy invariant generalisation of the Duflo theorem.

In 2020-23, I am supervising the PhD thesis of Basile Coron, who works on some topics of homotopical algebra related to De Concini-Procesi wonderful models of subspace arrangements.

In 2017-21, I supervised the PhD thesis of Pedro Tamaroff, who works on a number of topics in homological and homotopical algebra; his thesis is available here. His homepage may be consulted via this link.

In 2018/19, I was a mentor of Vincent Gélinas during his time as a postdoc at the Hamilton Mathematics Institute. His stay in Dublin resulted in this paper written together with myself and with Pedro Tamaroff.

In 2017-19, I supervised the Masters thesis of Norah Alghamdi who worked on Gröbner bases for nonsymmetric operads and their applications; her work resulted in the thesis "The associative filtration of the dendriform operad".

In 2016-18, I was a mentor of Victoria Lebed during her time as a postdoc at the Hamilton Mathematics Institute; she is now a maître de conférences at Université de Caen - Normandie.

In 2016, I was a mentor of José Moreno during his exchange visit to Trinity College Dublin as a part of his PhD studies in Malaga. José then was a postdoc at MPIM Bonn, and in September 2019 he moved to Trinity College Dublin to start a competitive research fellowship awarded by the Irish Research Council. Since then he wrote this paper with my student Pedro Tamaroff.

In 2014/15, I supervised the Masters thesis of Soutrik Roy Chowdhury who studied an important computational method of homological algebra, the Anick's resolution. His thesis is available here.

In 2013/14, I supervised the Masters thesis of Lucas Mason-Brown who studied invariant (coordinate-independent) operations that map various differential-geometric constructions to one another. His thesis is available here.