Jean-Louis LODAY
ANNONCES / ANNOUNCEMENTS :
Lecture on "Algebras,
Operads, Combinads" (exposé à Lille le 23 mars 2012)
Abstract. A type of
algebras is encoded by an operad. Similarly a type of operads is
encoded by a combinad. We
describe what is a combinad, and give some details on two examples:
nonsymmetric operads and permutads. We introduce circled trees and
higher operadic structures which look like opetopes. We exhibit an
attractive relationship with the canonical basis of quantum groups as
introduced by G. Lusztig and M. Kashiwara.
Operads
and Universal Algebra, Proceedings of the International Conference
held in Tianjin, China, 5-9 July 2010.
Prépublications /
Preprints :
- "Operadic construction of the renormalization group", with
Nikolay M. Nikolov, preprint 20p., (2012). pdf
- "Exponential series without denominators", preprint 13p., (2012).
pdf
- "Permutads", with M.O. Ronco, preprint 38 p., (2011). pdf
- "The YY game", preprint 7 p., (2011). pdf
- "Free loop space and homology", preprint 20 p., (2011). pdf
- "Algebraic operads",
avec
Bruno
Vallette,
Grundlehren
Math.
Wiss.
346,
Springer,
Heidelberg, 2012. Here is
version 0.99: pdf .
Comments
welcome. Leitfaden
Publications
récentes
/
Recent papers : (2008-2012):
- "Dichotomy
of
the
addition
of
natural
numbers", in "Associahedra,
Tamari Lattices and Related Structures", Tamari Memorial
Festschrift,
F. Mueller-Hoissen, J. Pallo and J. Stasheff (Eds.), Progress in
Mathematics, vol. 299, Birkhauser, 2012.
- "Some
problems in operad theory", Proc. Int. Conf., in Nankai
Series in Pure, Applied Mathematics and Theoretical Physics, Vol. 9
(World Scientific, Singapore, 2012), 139--146.
- "The symmetric
operation in a
free pre-Lie algebra is magmatic", with Nantel Bergeron,
Proc. Amer. Math. Soc. 139-5 (2011), 1585-1597.
- "Combinatorial
Hopf
Algebras" with
Maria Ronco, Quanta of maths, 347–383, Clay Math. Proc., 11,
Amer. Math. Soc., Providence, RI, 2010.
- "The diagonal of
the
Stasheff polytope", Higher structures in
geometry and physics, 269–292, Progr. Math., 287,
Birkhäuser/Springer, New York, 2011.
arXiv:0710.0572
- "On the operad of associative
algebras with derivation", Georgian
Mathematical Journal 17, no 2, (2010), 347--372.
- "Cyclic homology theory"
with M. Wodzicki, Lecture notes on noncommutative geometry and quantum
groups, European Mathematical Society Publishing House, ed. Piotr M.
Hajac, to appear. pdf
- "Parastatistics
algebras and super semi-standard
Young tableaux" with T. Popov, Proceedings of "Lie Theory
and its Applications in Physics", Varna, 2007, eds. H.-D. Doebner and
V.K. Dobrev (Heron Press, Sofia, 2008), 423-430.
- "Generalized
bialgebras
and
triples
of
operads".
Astérisque No. 320 (2008), x+116 pp.
- "Parastatistics
Algebra,
Young
Tableaux
and
the
Super
Plactic
Monoid"with T. Popov, Int. J. Geom. Methods Mod. Phys. 5
(2008),
no. 8, 1295--1314.
Publications / Papers : liste
complète / complete
list
Miscellanées
(en français, or in english)
- Dan Quillen (1940-2011),
fichier
pdf en français, 5 pages.
- 23.03.2010 KaféMaths du 22 mars 2010: "Polyèdres au coeur des arbres",
pdf
- 04.01.2010 "Comment j'ai
trouvé l'associaèdre", pdf
- 03.01.2010 "Carte de voeux à l'associaèdre",
pdf
Editeur de / Editor of :
Domaines d'intérêt / Fields
of interest:
Topologie algébrique, K-théorie, algèbre
homologique, géométrie non commutative, opérades,
props, combinatoire,
physique théorique, tresses.
Kafemath
(c'est chez Céleste, dixit François Dubois)
Images
des Mathématiques (vulgarisation)
Images (dont polytopes de Stasheff),
G.W. Zinbiel, Encyclopedia
of
types
of
algebras
2010, Proc.
Int. Conf., in Nankai Series in Pure, Applied Mathematics and
Theoretical Physics, Vol. 9 (World Scientific, Singapore, 2012),
217--298.
Dernières modifications / Last modifications : Mar 2012
