## Victoria LEBED

I am a Hamilton Research Fellow at Trinity College Dublin (Ireland), in the research group of Vladimir Dotsenko. In 2014-2016 I was a postdoc at Jean Leray Mathematics Institute (Nantes, France), in collaboration with Friedrich Wagemann, thanks to a fellowship of Henri Lebesgue Center of Mathematics.

Here is my CV in English, and a less regularly updated CV in French.

My husband, Arnaud Mortier, is also a mathematician.

In 2017 I am teaching Module MA3416: Group Representations.

Address: School of Mathematics,

Trinity College,

Dublin 2, Ireland

E-mail: lebed (at) maths.tcd.ie

## Research interests

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.
- Plactic monoids: a braided approach, arXiv:1612.05768.
- Cohomology of Idempotent braidings, with Applications to
Factorizable Monoids, arXiv:1607.08081.

- (With Leandro Vendramin) Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation, Advances Math. 304 (2017), 1219-1261.

- (With Friedrich Wagemann) Representations of crossed modules and other generalized Yetter-Drinfel'd modules, arXiv:1509.03497, to appear in Appl. Categ. Structures.
- (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,
(an extended version of the above JKTR publication, containing in particular a chapter on free virtual shelves and quandles).*arXiv:1206.3916* - 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*

*Upcoming talks*- March 15, 2017. MathSoc, TCD, Ireland: Mathematics of Origami. Poster
- June 12-16, 2017. Self-distributive system and quandle
(co)homology theory in algebra and low

dimensional topology. Busan, South Korea.

- June 18-24, 2017. Groups, Rings and the Yang-Baxter Equation. Spa, Belgium.
- July 29 - August 5, 2017. 4th Mile High Conference on Nonassociative Mathematics. Denver, USA.
- September 4 - 8, 2017. Advances in Group Theory and Applications.
Lecce, Italy.

- September 25 - 29, 2017. Categories in Homotopy and Rewriting. CIRM, France.

## Past talks

- December 2008. Conference Algebraic Geometry and Representation Theory, Minsk, Belarus. Introductory talks for students: Knot theory; Hopf algebras
- October 2009. Working group Quantum Algebra and Topology, IMJ (Institut Mathématique de Jussieu), Paris: 2-categories associated with quantum sl(2). Notes
- December 2009. Mathematical conference, Minsk, Belarus. Introductory talk for students: Introduction to abelian categorification
- February 2010. Working group Quantum Algebra and Topology, IMJ: Diagrammatic categorification of quantum sl(n). Notes
- October 2010. A talk Who is who in the family of Homologies at the informal PhD student seminar, IMJ
- November-december 2010. Co-organizing the working group Quantum Groups, IMJ; two talks Quantum knot invariants. Notes
- January-may 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
- September-december 2011. Working group
__Geometric Representation Theory__, IMJ: Category O: the action of the center. Notes - December 2011.
__PhD Student Seminar__, IMJ: Forget the group multiplication to get a weak universal knot invariant. Notes - December 2011. A talk Topological complexity of algorithms at the informal PhD student seminar, IMJ. Notes
- March 2012.
__PhD Students' Day__, IMJ: Braidings, algebraic structures and homologies: an entangled story - June 2012.
__Working group Semantics__, laboratory PPS (Preuves, Programmes, Systèmes), IMJ: Homologies of Algebraic Structures via Braidings. Notes - October 2012. A talk Billiards: a set of balls rounding down the number pi at the informal PhD student seminar, IMJ. Notes
- November 2012. Algebra Seminar, IHP (Institut Henri Poincaré), Paris: Braided systems: generalities and applications to Hopf theory. Notes
- November 2012. Young Mathematicians' Forum, IHP: Homologies of algebraic structures: a unifying "braided" approach. Notes
- December 2012.Topology Seminar, GWU, Washington DC: Self- and multi-distributivity with a braided flavor. Notes
- December 2012. Knots in Washington XXXV: Hochschild, Chevalley-Eilenberg and quandle homologies are braided homologies
- December 2012. Algebra Seminar, University Lyon 1: Braided systems: generalities and applications to Hopf theory
- January 2013. Algebraic Topology Seminar, University Paris 13: Koszul, Hochschild, Leibniz and quandle homologies are braided homologies

- January 2013. Colloque tournant du GDR TLAG, University of Cergy-Pontoise: A unifying study of algebraic structures using "braided" tools. Notes
- February 2013. Algebra, Topology and Geometry Seminar, University of Nice: Koszul, Hochschild, Leibniz and quandle homologies are braided homologies
- March 2013. Topology Seminar, University Montpellier 2: Categorical aspects of virtuality. Notes
- March 2013. TQFT
and Categorification Seminar, IMJ: Categorical
aspects of virtuality

- March 2013. British Mathematical Colloquium, Sheffield, UK: Associative Algebras, Bialgebras and Leibniz Algebras as Braided Objects. Beamer
- April 2013. Algebra and Topology Seminar, University of Strasbourg: Associative algebras, bialgebras and Leibniz algebras as braided objects
- September 2013. Knots,
Manifolds and Group Actions, Słubice, Poland:
*Distributive homology is a braided homology*. Notes - September 2013. Topology Seminar, University of Grenoble: Braids and homology of algebraic structures: a round trip
- December 2013. KOOK Seminar, Osaka: Braids and homology of algebraic structures: a round trip. Notes
- January 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
- January 2014. Knots in Washington XXXVII: Qualgebras and knotted 3-valent graphs. Beamer
- January 2014. Logic and topology seminar, GWU, Washington DC: Towards topological applications of Laver tables. Notes
- May 2014. Intelligence of low-dimensional topology, Kyoto: Knotted 3-valent graphs, branched braids, and multiplication-conjugation relations in a group. Beamer
- June 2014. Topology Seminar, Tsukuba University, Japan: A bridge between knotted graphs and axiomatizations of groups. Beamer
- July 2014. Friday Seminar, Osaka City University: Towards braid-theoretic applications of Laver tables. Notes and hand-outs
- July 2014. TAPU-KOOK Seminar, Daejeon, Korea: Categorical aspects of virtuality. Beamer
- July 2014. Topology Symposium, Tohoku University, Japan: Laver Tables: from Set Theory to Braid Theory. Beamer and (very) extended abstract
- August 2014. Knots and Low Dimensional Manifolds, Busan, Korea: Laver tables: topological applications of set-theoretic constructions. Beamer
- September 2014. FMSP Lectures, University of Tokyo: A bridge between knotted graphs and axiomatizations of groups. Beamer

- October 2014. Topology, geometry and algebra seminar, University of Nantes: Braids and homology of algebraic structures: a round trip. Notes
- October 2014. Topology and geometry seminar, University of Geneva: Braids and homology of algebraic structures: a round trip
- November 2014. Symposium on Mathematical Physics, University of Zürich: New aspects of the Yang-Baxter equation. Beamer
- November 2014. Working group Algebraic topology, University of Nantes: Braid groups and free groups. Notes
- November 2014. Algebra and geometry seminar, University of Caen: Laver tables: set-theoretic, algebraic and topological aspects. Beamer
- December 2014. Topology seminar, University of Montpellier: Braids and homology of algebraic structures: a round trip
- January 2015. Knots in Dallas: Twisted multi-distributivity and Lawrence representations of braid groups. Beamer
- January 2015. Algebra and topology seminar, University of Strasbourg: Lawrence representations of braid groups via self-distributivity. Notes
- February 2015. Joint topology seminar of Paris 7 and Paris 13 Universities: Lawrence representations of braid groups via self-distributivity
- March 2015. Algebraic topology seminar, Université catholique de Louvain, Belgium: Braided diagrams as a unifying tool in homology theory. Notes
- April 2015. University of Nantes: Cohomology of Finite Monogenic Self-Distributive Structures. Notes
- June 2015. New trends in
Hopf algebras and tensor categories, Bruxelles: On braidings, Yetter-Drinfel’d modules,
crossed modules, and self-distributivity

- June 2015. Lens topology and geometry meeting, Lens: Braided aspects of the Yang-Baxter equation. Beamer
- June 2015. Talks for the working group Lawrence-Krammer-Bigelow representations of braid groups, Nantes. Notes
- July 2015. Workshop Applied Representation Theory, Amiens: Representations of braid groups: homological and self-distributivity approaches
- September 2015. Geometry and Algebra, Geometry and Analysis, Utrecht, Netherlands: Unexpected facets of the Yang-Baxter equation. Beamer
- October 2015. Algebra and geometry seminar, University of Caen: On the set-theoretic solutions to the Yang-Baxter equation. Notes
- October 2015. Algebra and Group Theory, Mulhouse: On set-theoretic solutions to the Yang-Baxter equation. Beamer
- November 2015. Mathematics Club, Nantes: Origamics, or 折り紙. Notes
- November 2015. Mathematics
seminar, Vannes:
*Representations of braid groups via self-distributivity*

- December 2015. University of Nantes: A decomposition theorem for skew cubical homology. Notes
- January 2016. Workshop on Hopf algebras, Turin, Italy: On set-theoretic solutions to the Yang-Baxter equation. Beamer
- January 2016. Topology
Seminar, Grenoble:
*Representations of braid groups via self-distributivity* - February 2016. Seminar of mathematical physics and algebraic topology, Angers: On set-theoretic solutions to the Yang-Baxter equation
- February 2016. Mathematics Club, Nantes: Billiard as a tool for computing the digits of the number π. Notes
- April 2016. Mathematics Club, Nantes: Erdős distinct distances problem, or Vote for diversity!
- July 2016. 3+1 dimensional topological phases of matter, Leeds, UK:
- July 2016. XXI Coloquio Latinoamericano de Álgebra, Buenos Aires, Argentina: On set-theoretic solutions to the Yang-Baxter equation. Beamer
- July 2016. Algebra seminar, Buenos Aires, Argentina: Cohomology of idempotent solutions to the Yang-Baxter equation, with applications
- Septembe 2016. Mathematics, Statistics and Applied Mathematics Seminar, Galway, Ireland: How forgetting group laws leads to a universal knot invariant. Notes
- October 2016. Mathematics Colloquium, TCD, Dublin, Ireland: Unexpected facets of the Yang-Baxter equation. Beamer
- October 2016. La réunion annuelle du GDR topologie algébrique et applications, Amiens, France: Équation de Yang-Baxter, tableaux de Young, factorisations de groupes. Beamer
- December 2016. Semantics seminar, Paris: What do braids know about Young tableaux? Beamer
- February 2017. Cohomological Methods in Geometry, Freiburg, Germany: How braids can help to compute Hochschild cohomology. Beamer
- February, 2017. Marburg, Germany: What do braids know about Young tableaux? Beamer
- March, 2017. Algebra days 2017 in honour of Patrick Dehornoy, Caen, France: A journey into the green book. Beamer

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*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