Research interests 

Papers, preprints, and other works

• (With Seiichi Kamada) Alexander and Markov Theorems for Graph-Braids, in progress.
• (With Simon Covez, Marco Farinati, and Dominique Manchon) Bialgebraic approach to rack cohomology, arXiv:1905.02754
• (With Leandro Vendramin) On Structure Groups of Set-Theoretic Solutions to the Yang-Baxter Equation, Proc. Edinb. Math. Soc. (2019)
• (With Scott Carter and Seung Yeop Yang) A Prismatic Classifying Space for Foam Homology, Nonassociative mathematics and its applications, Contemp. Math., 721 (2019), 43-68.
• Applications of Self-Distributivity to Yang-Baxter Operators and Their Cohomology, J. Knot Theory Ramifications 27 (2018), no. 11, 1843012, 20 pp.
  
• Plactic Monoids: a Braided Approach, arXiv:1612.05768.
• (With Leandro Vendramin) Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation, Advances Math. 304 (2017), 1219-1261.
• Cohomology of Idempotent Braidings, with Applications to Factorizable Monoids, Int. J. Algebra Comput. 421 (2017), no. 27, 421-454.

• (With Friedrich Wagemann) Representations of crossed modules and other generalized Yetter-Drinfel'd modules, Appl. Categ. Structures 25 (2017), no. 4, 455-488.
• Braided Systems: a Unified Treatment of Algebraic Structures with Several Operations, Homology, Homotopy Appl. 19 (2017), no. 2, 141-174.
• (With Leandro Vendramin) Cohomology and extensions of braces, Pacific J. Math. 284 (2016), no. 1, 191-212.
• Cohomology of Finite Monogenic Self-Distributive Structures, J. Pure Appl. Algebra 220 (2016), no. 2, 711-734.
• (With Seiichi Kamada and Kokoro Tanaka) The Shadow Nature of Positive and Twisted Quandle Cocycle Invariants of Knots, J. Knot Theory Ramifications 24 (2015), no. 10, 1540001, 15 pp.
• Qualgebras and Knotted 3-Valent Graphs, Fund. Math. 230 (2015), no. 2, 167-204.
• Knotted 3-Valent Graphs, Branched Braids, and Multiplication-Conjugation Relations in a Group, Proceedings of Intelligence of Low-Dimensional Topology 2014: 86-100. pdf
• (With Patrick Dehornoy) Two- and Three-Cocycles for Laver Tables, J. Knot Theory Ramifications  23 (2014), no. 4, 1450017, 30 pp.
• R-Matrices, Yetter-Drinfel'd Modules and Braided Systems, Axioms 2013, 2(3), 443-476. pdf
• Categorical Aspects of Virtuality and Self-Distributivity, J. Knot Theory Ramifications 22 (2013), no. 9, 1350045, 32 pp.
  
• Symmetric Categories as a Means of Virtualization for Braid Groups and Racks, arXiv:1206.3916 (an extended version of the above JKTR publication, containing in particular a chapter on free virtual shelves and quandles).
• Homologies of Algebraic Structures via Braidings and Quantum Shuffles, J. Algebra 391 (2013), 152-92.
  
• The final version (in English) and a beamer (in French) of my PhD thesis. It was completed in 2012 at Paris 7 University, under the supervision of Marc Rosso.
• Invariants d'enchevêtrements avec des connexions plates dans le complémentaire, Master's dissertation, supervisor Marc Rosso, pdf in French
• (With V.Bernik) Algebraic Points on the Plane, Journal Math. Sciences 146 (2007), 5680-5685.

Past talks

2008
•  Conference Algebraic Geometry and Representation Theory, Minsk, Belarus. Introductory talks for students: Knot theory; Hopf algebras
 2009

• Working group Quantum Algebra and Topology, IMJ (Institut Mathématique de Jussieu), Paris: 2-categories associated with quantum sl(2). Notes
• Mathematical conference, Minsk, Belarus. Introductory talk for students: Introduction to abelian categorification
 2010

• Working group Quantum Algebra and Topology, IMJ: Diagrammatic categorification of quantum sl(n). Notes
• A talk Who is who in the family of Homologies at the informal PhD student seminar, IMJ
• Co-organizing the working group Quantum Groups, IMJ; two talks Quantum knot invariants. Notes
2011
•  Co-organizing the working group Canonical Bases, IMJ; two talks Canonical bases in the gl(n) case and their connection to Young diagrams. Notes, notes 2
• Working group Geometric Representation Theory, IMJ: Category O: the action of the center. Notes
• PhD Student Seminar, IMJ: Forget the group multiplication to get a weak universal knot invariant. Notes
• A talk Topological complexity of algorithms at the informal PhD student seminar, IMJ. Notes
2012
• PhD Students' Day, IMJ: Braidings, algebraic structures and homologies: an entangled story
• Working group Semantics, laboratory PPS (Preuves, Programmes, Systèmes), IMJ: Homologies of Algebraic Structures via Braidings. Notes
• A talk Billiards: a set of balls rounding down the number pi  at the informal PhD student seminar, IMJ. Notes
• Algebra Seminar, IHP (Institut Henri Poincaré), Paris: Braided systems: generalities and applications to Hopf theory. Notes
• Young Mathematicians' Forum, IHP: Homologies of algebraic structures: a unifying "braided" approach.  Notes
• Topology Seminar, GWU, Washington DC: Self- and multi-distributivity with a braided flavor. Notes
• Knots in Washington XXXV: Hochschild, Chevalley-Eilenberg and quandle homologies are braided homologies
• Algebra Seminar, University Lyon 1: Braided systems: generalities and applications to Hopf theory
2013
•  Algebraic Topology Seminar, University Paris 13: Koszul, Hochschild, Leibniz and quandle homologies are braided homologies

• Colloque tournant du GDR TLAG, University of Cergy-Pontoise: A unifying study of algebraic structures using "braided" tools. Notes
• Algebra, Topology and Geometry Seminar, University of Nice: Koszul, Hochschild, Leibniz and quandle homologies are braided homologies
• Topology Seminar, University Montpellier 2: Categorical aspects of virtuality. Notes
• TQFT and Categorification Seminar, IMJ: Categorical aspects of virtuality
  
• British Mathematical Colloquium, Sheffield, UK: Associative Algebras, Bialgebras and Leibniz Algebras as Braided Objects. Beamer
• Algebra and Topology Seminar, University of Strasbourg: Associative algebras, bialgebras and Leibniz algebras as braided objects
• Knots, Manifolds and Group Actions, Słubice, Poland: Distributive homology is a braided homology. Notes
• Topology Seminar, University of Grenoble: Braids and homology of algebraic structures: a round trip
•  KOOK Seminar, Osaka: Braids and homology of algebraic structures: a round trip. Notes
2014

• Joint Mathematics Meetings AMS, Special Session on Algebraic Structures Motivated by Knot Theory, Baltimore, USA: Self-, multi- and G-distributivity with a braided flavor. Beamer
• Knots in Washington XXXVII: Qualgebras and knotted 3-valent graphs. Beamer
• Logic and topology seminar, GWU, Washington DC: Towards topological applications of Laver tables. Notes
• Intelligence of low-dimensional topology, Kyoto: Knotted 3-valent graphs, branched braids, and multiplication-conjugation relations in a group. Beamer
• Topology Seminar, Tsukuba University, Japan: A bridge between knotted graphs and axiomatizations of groups. Beamer
• Friday Seminar, Osaka City University: Towards braid-theoretic applications of Laver tables. Notes and hand-outs
• TAPU-KOOK Seminar, Daejeon, Korea: Categorical aspects of virtuality. Beamer
• Topology Symposium, Tohoku University, Japan: Laver Tables: from Set Theory to Braid Theory. Beamer and (very) extended abstract
• Knots and Low Dimensional Manifolds, Busan, Korea: Laver tables: topological applications of set-theoretic constructions. Beamer
•  FMSP Lectures, University of Tokyo: A bridge between knotted graphs and axiomatizations of groups. Beamer

• Topology, geometry and algebra seminar, University of Nantes: Braids and homology of algebraic structures: a round trip. Notes
• Topology and geometry seminar, University of Geneva: Braids and homology of algebraic structures: a round trip
• Symposium on Mathematical Physics, University of Zürich: New aspects of the Yang-Baxter equation. Beamer
• Working group Algebraic topology, University of Nantes: Braid groups and free groups. Notes
• Algebra and geometry seminar, University of Caen: Laver tables: set-theoretic, algebraic and topological aspects. Beamer
• Topology seminar, University of Montpellier: Braids and homology of algebraic structures: a round trip
2015

• Knots in Dallas: Twisted multi-distributivity and Lawrence representations of braid groups. Beamer
• Algebra and topology seminar, University of Strasbourg: Lawrence representations of braid groups via self-distributivity. Notes
• Joint topology seminar of Paris 7 and Paris 13 Universities: Lawrence representations of braid groups via self-distributivity
• Algebraic topology seminar, Université catholique de Louvain, Belgium: Braided diagrams as a unifying tool in homology theory. Notes
• University of Nantes: Cohomology of Finite Monogenic Self-Distributive Structures. Notes
• New trends in Hopf algebras and tensor categories, Bruxelles: On braidings, Yetter-Drinfel’d modules, crossed modules, and self-distributivity
  
• Lens topology and geometry meeting, Lens: Braided aspects of the Yang-Baxter equation. Beamer
• Talks for the working group Lawrence-Krammer-Bigelow representations of braid groups, Nantes. Notes
• Workshop Applied Representation Theory, Amiens: Representations of braid groups: homological and self-distributivity approaches
• Geometry and Algebra, Geometry and Analysis, Utrecht, Netherlands: Unexpected facets of the Yang-Baxter equation. Beamer
• Algebra and geometry seminar, Caen: On the set-theoretic solutions to the Yang-Baxter equation. Notes
• Algebra and Group Theory, Mulhouse: On set-theoretic solutions to the Yang-Baxter equation. Beamer
• Mathematics Club, Nantes: Origamics, or 折り紙. Notes
• Mathematics seminar, Vannes: Representations of braid groups via self-distributivity
  
• University of Nantes: A decomposition theorem for skew cubical homology. Notes
2016

• Workshop on Hopf algebras, Turin, Italy: On set-theoretic solutions to the Yang-Baxter equation. Beamer
• Topology Seminar, Grenoble: Representations of braid groups via self-distributivity
• Seminar of mathematical physics and algebraic topology, Angers: On set-theoretic solutions to the Yang-Baxter equation
• Mathematics Club, Nantes: Billiard as a tool for computing the digits of the number π. Notes
• Mathematics Club, Nantes: Erdős distinct distances problem, or Vote for diversity!
• 3+1 dimensional topological phases of matter, Leeds, UK: Crossed modules and beyond. Beamer
  
• XXI Coloquio Latinoamericano de Álgebra, Buenos Aires, Argentina: On set-theoretic solutions to the Yang-Baxter equation. Beamer
• Algebra seminar, Buenos Aires, Argentina: Cohomology of idempotent solutions to the Yang-Baxter equation, with applications
• Mathematics, Statistics and Applied Mathematics Seminar, Galway, Ireland: How forgetting group laws leads to a universal knot invariant. Notes
• Mathematics Colloquium, TCD, Dublin, Ireland: Unexpected facets of the Yang-Baxter equation. Beamer
• La réunion annuelle du GDR topologie algébrique et applications, Amiens, France: Équation de Yang-Baxter, tableaux de Young, factorisations de groupes. Beamer
• Semantics seminar, Paris: What do braids know about Young tableaux? Beamer
2017

• Cohomological Methods in Geometry, Freiburg, Germany: How braids can help to compute Hochschild cohomology. Beamer
• Marburg, Germany: What do braids know about Young tableaux? Beamer
• Algebra days 2017 in honour of Patrick Dehornoy, Caen, France: A journey into the green book. Beamer
• MathSoc, TCD, Ireland: Mathematics of Origami. Poster