a projection
       Address: School of Mathematics, Trinity College, Dublin 2, Ireland
         E-mail: lebed (at) maths.tcd.ie

  I am a Hamilton Research Fellow at Trinity College Dublin (Ireland), in the research group of Vladimir Dotsenko. Here is my CV in English, and a less regularly updated CV in French.
  My husband, Arnaud Mortier, is also a mathematician, working at Dublin City University (Ireland).

  In 2017 (Hilary Term) I was teaching Module MA3416: Group Representations.
  In 2017 (Michaelmas Term) I will be teaching Module MA1S11: Mathematics for Scientists.

  With Vladimir Dotsenko we are organising a Hamilton Mathematics Institute workshop Geometry and combinatorics of associativity, to be held in Dublin on October 23-27 2017. Registration is now open. All are welcome!

Research interests 

A knot in Vicenza   My interests travel around the vast notions of structure and braiding, in particular their homological, categorical, and topological aspects. This includes the Yang-Baxter equation, braid groups, knots and their generalized versions (virtual, welded, twisted, handlebody, 2-dimensional), knotted graphs, quantum invariants, coloring (e.g., quandle) invariants, quantum (quasi-)shuffle algebras, braided systems, self- and muti-distributivity, Laver tables, cycle sets, Young tableaux, categorification of algebraic structures, Hopf algebras and Hopf bimodules, Yetter-Drinfel'd modules,  Rota-Baxter algebras, operads, etc. This small video introduces some of these notions for non-mathematicians. 
  I like elegant and elucidating mathematics. Sharing it is a real pleasure. That is why I engage in outreach activities whenever possible. For instance, last year I co-organized the Mathematics Club of the University of Nantes, and took part in the 5 minutes Lebesgue adventure.

Papers, preprints, and other works

  • (With Seiichi Kamada) Alexander and Markov Theorems for Graph-Braids, in progress.
  • (With Leandro Vendramin) On structure groups of set-theoretic solutions to the Yang-Baxter equation, arXiv:1707.00633
  • Plactic monoids: a braided approach, arXiv:1612.05768.
  • Cohomology of Idempotent braidings, with Applications to Factorizable Monoids, Int. J. Algebra Comput. 421 (2017), no. 27.
  • (With Leandro Vendramin) Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation, Advances Math. 304 (2017), 1219-1261.
A knot in Ireland
  • (With Friedrich Wagemann) Representations of crossed modules and other generalized Yetter-Drinfel'd modules, Appl. Categ. Structures), no. 4, 455-488.
  • (With Leandro Vendramin) Cohomology and extensions of braces, Pacific J. Math. 284 (2016), no. 1, 191-212.
  • Braided Systems: a Unified Treatment of Algebraic Structures with Several Operations, arXiv:1305.0944, to appear in Homology, Homotopy Appl.
  • 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.

Upcoming talks

A braid in Rouen

Past talks

  •  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
  • A knot sum in KyotoWorking 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

A knotted 3-valent graph in Osaka
A braid in Washington