Victoria LEBED
Address: School of Mathematics, Trinity College, Dublin 2, Ireland
Email: 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 2327 2017. Registration is now open. All are welcome!
Research interests
My interests travel
around the
vast notions of structure and braiding, in particular their
homological, categorical, and topological
aspects. This includes the YangBaxter equation, braid
groups, knots and their generalized versions (virtual, welded, twisted,
handlebody, 2dimensional), knotted graphs, quantum invariants,
coloring (e.g., quandle) invariants,
quantum (quasi)shuffle algebras, braided systems, self and
mutidistributivity, Laver tables, cycle sets, Young tableaux,
categorification
of algebraic structures, Hopf
algebras and Hopf bimodules, YetterDrinfel'd modules,
RotaBaxter algebras, operads, etc. This small video
introduces some of these notions for nonmathematicians. 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 coorganized 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 GraphBraids, in progress.
 (With Scott Carter and Seung Yeop Yang) A prismatic classifying space for foam homology, in progress.
 (With Leandro Vendramin) On structure groups of settheoretic solutions to the YangBaxter 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, 421454.
 (With Leandro Vendramin) Homology of left nondegenerate settheoretic solutions to the YangBaxter equation, Advances Math. 304 (2017), 12191261.
 (With Friedrich Wagemann) Representations of crossed modules and other generalized YetterDrinfel'd modules, Appl. Categ. Structures), no. 4, 455488.
 (With Leandro Vendramin) Cohomology and extensions of braces, Pacific J. Math. 284 (2016), no. 1, 191212.
 Braided Systems: a Unified Treatment of Algebraic Structures with Several Operations, arXiv:1305.0944, to appear in Homology, Homotopy Appl.
 Cohomology of Finite Monogenic SelfDistributive Structures, J. Pure Appl. Algebra 220 (2016), no. 2, 711734.
 (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 3Valent Graphs, Fund. Math. 230 (2015), no. 2, 167204.
 Knotted 3Valent Graphs, Branched Braids, and MultiplicationConjugation Relations in a Group, Proceedings of Intelligence of LowDimensional Topology 2014: 86100. pdf
 (With Patrick Dehornoy) Two and ThreeCocycles for Laver Tables, J. Knot Theory Ramifications 23 (2014), no. 4, 1450017, 30 pp.
 RMatrices, YetterDrinfel'd Modules and Braided Systems, Axioms 2013, 2(3), 443476. pdf
 Categorical Aspects of Virtuality and SelfDistributivity, 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), 15292.
 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), 56805685.
Upcoming talks
 September 2529, 2017. Categories in Homotopy and Rewriting, CIRM, France: YangBaxter equation up to homotopy
 October 12, 2017. Algebra and Number Theory seminar, University College Dublin, Ireland
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: 2categories 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
 Coorganizing the working group Quantum Groups, IMJ; two talks Quantum knot invariants. Notes 2011
 Coorganizing 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 multidistributivity with a braided flavor. Notes
 Knots in Washington XXXV: Hochschild, ChevalleyEilenberg 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 CergyPontoise: 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 Gdistributivity with a braided flavor. Beamer
 Knots in Washington XXXVII: Qualgebras and knotted 3valent graphs. Beamer
 Logic and topology seminar, GWU, Washington DC: Towards topological applications of Laver tables. Notes
 Intelligence of lowdimensional topology, Kyoto: Knotted 3valent graphs, branched braids, and multiplicationconjugation 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 braidtheoretic applications of Laver tables. Notes and handouts
 TAPUKOOK 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 settheoretic 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 YangBaxter equation. Beamer
 Working group Algebraic topology, University of Nantes: Braid groups and free groups. Notes
 Algebra and geometry seminar, University of Caen: Laver tables: settheoretic, algebraic and topological aspects. Beamer
 Topology seminar, University of Montpellier: Braids and homology of algebraic structures: a round trip 2015
 Knots in Dallas: Twisted multidistributivity and Lawrence representations of braid groups. Beamer
 Algebra and topology seminar, University of Strasbourg: Lawrence representations of braid groups via selfdistributivity. Notes
 Joint topology seminar of Paris 7 and Paris 13 Universities: Lawrence representations of braid groups via selfdistributivity
 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 SelfDistributive Structures. Notes
 New trends in
Hopf algebras and tensor categories, Bruxelles: On braidings, YetterDrinfel’d modules,
crossed modules, and selfdistributivity
 Lens topology and geometry meeting, Lens: Braided aspects of the YangBaxter equation. Beamer
 Talks for the working group LawrenceKrammerBigelow representations of braid groups, Nantes. Notes
 Workshop Applied Representation Theory, Amiens: Representations of braid groups: homological and selfdistributivity approaches
 Geometry and Algebra, Geometry and Analysis, Utrecht, Netherlands: Unexpected facets of the YangBaxter equation. Beamer
 Algebra and geometry seminar, University of Caen: On the settheoretic solutions to the YangBaxter equation. Notes
 Algebra and Group Theory, Mulhouse: On settheoretic solutions to the YangBaxter equation. Beamer
 Mathematics Club, Nantes: Origamics, or 折り紙. Notes
 Mathematics
seminar, Vannes: Representations of braid groups via
selfdistributivity
 University of Nantes: A decomposition theorem for skew cubical homology. Notes 2016
 Workshop on Hopf algebras, Turin, Italy: On settheoretic solutions to the YangBaxter equation. Beamer
 Topology Seminar, Grenoble: Representations of braid groups via selfdistributivity
 Seminar of mathematical physics and algebraic topology, Angers: On settheoretic solutions to the YangBaxter 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 settheoretic solutions to the YangBaxter equation. Beamer
 Algebra seminar, Buenos Aires, Argentina: Cohomology of idempotent solutions to the YangBaxter 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 YangBaxter equation. Beamer
 La réunion annuelle du GDR topologie algébrique et applications, Amiens, France: Équation de YangBaxter, 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
 CINVESTAV, Mexico:
 How forgetting group laws leads to a universal knot invariant (Colloquium). Beamer
 YangBaxter equation, Young tableaux, and group factorizations (Algebra Seminar)
 Selfdistributive system and quandle (co)homology theory in algebra and low dimensional topology. Busan, South Korea: Applications of selfdistributivity to YangBaxter operators and their cohomology. Beamer
 Groups, Rings and the YangBaxter Equation, Spa, Belgium: Structure groups of YBE solutions: new properties, and cohomological applications. Beamer
 4th Mile High Conference on Nonassociative Mathematics, Denver, USA:
Self,
multi and $G$distributivity with a braided flavor.  See
more at:
http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_ss17.html#sthash.GhK3Nyh3.dpuf