Equipe
CALIN
GDR
CNRS Renormalisation
Bures sur Yvette, le 27 Février
2012.
IHES, 35 Route de Chartres 91440 Bures-sur-Yvette, France .
Rencontre organisée par Gérard H.E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY et HOANG NGOC MINH
Combinatorics of Mathematical
Renormalization : a special day
Les algèbres de Hopf combinatoires et diagrammatiques conduisent souvent à des calculs effectifs en Renormalisation mais nous aurons également besoin de mieux comprendre ces calculs par l'intermédiaire de leurs représentations géométriques.
Pour toute réservation (train, hôtel, …), veuillez contacter Monsieur Aimé Bayonga (responsable financier du LIPN - 7030 UMR CNRS).
L'inscription est gratuite dans la mesure des places disponibles (nous avons prévu 20 personnes) et il suffit d'envoyer à Aimé Bayonga les informations suivantes
Mr/Ms
:
Nom :
Prénom :
institution :
Courriel :
Date
d'arrivée :
Date de départ :
10h30-10h30 |
Accueil des participants |
||
10h30-11h30 |
Christian Brouder |
Quantum field theory on curved spacetimes : merging Borcherds' and the causal approaches | There are two successful
approaches to renormalized quantum field theory on curved spacetimes:
i) the causal approach initiated by Brunetti and Fredenhagen [Commun.
Math. Phys. 208 (2000) 623-61] and further developed by themselves,
Hollands, Wald and Dütsch; ii) a Hopf algebraic approach recently
proposed by Borcherds [Alg. Numb. Theor. 5 (2011) 627-58]. The causal approach is analytic, it uses non-linear functionals and microlocal analysis. Borcherds' approach is more geometric and algebraic, it uses Hopf algebra bundles and a Gaussian condition for Feynman measures. A common framework will be presented to merge these two approaches. |
11h30-12h30 |
Nikolay Nikolov |
Operadic structures in the renormalization | The operads naturally appear in
the description of composition of formal power series of vector
variables. This is the intrinsic reason why operads appear related to
the renormalization group and its action. We study this relation in a
joint work with Jean-Louis Loday. On the combinatorial level our
construction gives an operadic interpretation of the group attached to
the Connes-Kreimer Hopf algebra. We can introduce also an operad
structure on the function spaces spanned by Feynman amplitudes. All
these operads, the combinatorial and the functional one, give rise to
groups that are related by morphisms induced by operadic morphisms. I
will also discuss the generalization of the Callan–Symanzik equation
that appears as a Maurer-Cartan equation on the constructed groups.
Such a generalized Callan–Symanzik equation was suggested by the author
as a recursive system of cohomological equations that determine basic
differential anomalies in the renormalization of Feynman diagrams. |
12h30-14h30 |
Lunch |
||
14h30-15h30 |
Frédéric Patras |
On the BWH factorization for non Rota-Baxter schemes | For renormalization schemes
(i.e. for given regularization +
subtraction maps) whose subtraction map satisfies the Rota-Baxter (RB)
identity, the Bogoliubov recursion yields automatically a
Birkhoff-Wiener-Hopf decomposition of Feynman rules characters in the
Hopf algebra picture. When the RB property is lost, the Bogoliubov
recursion still makes
sense. We analyse the corresponding combinatorics and show how it
relates to the recently introduced exponential renormalization method.
Based on joint works with K. Ebrahimi-Fard. |
15h30-16h30 |
Olivier
Bouillot |
Renormalization of multitangent functions and applications | After some reminders on
multizeta values, we will introduce the
multitangent functions. Then, we will see a profound link with
multizeta values: the reduction into monotangent functions. After, we
will study in details renormalization of divergent multitangent
functions and will see what will be the renormalisation contribution
relatively to multizeta values. Finally, we will introduce some
conjectures concerning the links between multizeta values and
multitangent functions. |
16h30-17h00 |
Tea/cofee Break | ||
17h00-18h00 | Vincel Hoang Ngoc Minh |
$\phi$-deformed
shuffle
bialgebras
and
bases in duality |
In order to extend the
Schützenberger factorization in the context of $\phi$-deformed shuffle
bialgebras, we give an explicite construction of bases in duality via
the convolutional CQMM theorem. |
18h00 |
Pierre Cartier |
A
few
concluding
words |
Liste des participants
Van Chiên Bui (Paris 13)
Christian Brouder (CNRS-Paris 6)
Pierre Cartier (IHES)
Viêt Dang (Paris7)
Gérard Duchamp (Paris 13)
Joachim Kock (Barcelona)
Maxim Kontsevich
(IHES)
Gleb Koshevoy (IHES)
Jean-Yves Enjalbert
(Paris 13)
Sylvia Goodenough (Paris
13)
Vincel Hoang Ngoc Minh
(Lille 2/Paris 13)
Frédéric Menous (Paris 11)
Nikolay M. Nikolov (IHES)
Nguyen Hoang (Paris 13)
Frédéric Patras (CNRS-Nice)
Karol Penson (Paris 6)
Adrian Tanasa (Paris 13)
Christophe Tollu (Paris
13)