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.
In collaboration with Murray Bremner, I wrote a book "Algebraic Operads: An Algorithmic Companion".
Papers and preprints
Various recent and forthcoming activities
- I am one of the organisers of the conference "Hochschild (co)homology and derived categories" which is an official satellite event of the International Congress of Mathematicians; it will take place in Saint-Petersburg on June 20-26, 2022.
- I organised (together with Frederic Chapoton) the annual meeting of the French national research network of algebraic topology and its applications; it took place in Strasbourg on October 26-29, 2021.
- I organised (together with Eduardo Marcos) the thematic section Homological methods" at XXIII Latin American Algebra Colloquium which took place in Mexico City on August 5-9, 2019.
- I organised (together with Vincent Gélinas and Andrea Solotar) the workshop "Homotopy meets homology"; it took place in Dublin on May 27-31, 2019.
- I was one of the local organisers of "The 14th William Rowan Hamilton Geometry and Topology Workshop" "Group actions and ergodic theory in geometry and topology"; it took place in Dublin on July 30-August 3, 2018.
- I organised (together with Victoria Lebed) the workshop "Geometry and combinatorics of associativity"; it took place in Dublin on October 23-27, 2017.
- I was one of the organisers of the third edition of the conference "Non-associative algebras and Lie theory"; it took place in Mexico City on February 27 - March 3, 2017.
- I was one of the local organisers of "The 12th William Rowan Hamilton Geometry and Topology Workshop" "Low-dimensional topology, complex and symplectic geometry"; it took place in Dublin on August 22-26, 2016.
- I was on the program committee of the workshop Higher-Dimensional Rewriting and Applications; it took take place in Oporto, Portugal, on June 25-26, 2016.
- I was one of the local organisers of "The 11th William Rowan Hamilton Geometry and Topology Workshop" "Connections between three and four manifolds"; it took place in Dublin on August 25-29, 2015.
- I was on the program committee of the workshop Higher-Dimensional Rewriting and Applications, to take place in Warsaw, Poland, on June 28, 2015.
- I was one of the local organisers of "The 10th William Rowan Hamilton Geometry and Topology Workshop" "Homological invariants in low-dimensional topology and geometry"; it took place in Dublin on August 26-30, 2014.
- I organised (together with Uli Kraehmer) a mini-workshop Batalin-Vilkovisky algebras, operads, and Hopf algebroids, it took place in Mathematisches Forschungsinstitut Oberwolfach on February 24-28, 2014.
- I was one of the organisers of a conference dedicated to Borya Feigin on the occasion of his 60th anniversary, it took place in Moscow on December 13-19, 2013. Video recordings of talks at that conference are available here.
- I was one of the local organisers of "The 9th William Rowan Hamilton Geometry and Topology Workshop" "Geometry and Groups after Thurston"; it took place in Dublin on August 27-31, 2013.
- I organised (together with Norbert Poncin) a workshop "Higher algebras and Lie-infinity homotopy theory" at the University of Luxembourg, it took place on June 25-28, 2013.
- In February 2013 I gave a mini-course "Operads, shuffles, and Gröbner bases" at the meeting Associative and Nonassociative Algebras and Dialgebras: Theory and Algorithms (in honour of Jean-Louis Loday), at CIMAT, Guanajuato, México.
- In February 2012 I gave a mini-course "Rewriting methods for associative algebras and operads" at Algebra and computation, one of the workshops of the thematic programme "Logic and interactions 2012" held at CIRM Luminy, Marseille.
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, 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.