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March 23- April 3, 2009

INSTITUT D'ETUDES SCIENTIFIQUES DE CARGESE (CORSICA, FRANCE)

A one-week spring school was followed by a one-week conference focusing on algebraic and combinatorial aspects of modern quantum field theory. This meeting was aimed at enhancing the understanding of the interaction of these subjects amongst researchers from both mathematics and physics. The main topics of the school (1st week) included mathematical aspects of advanced modern quantum field theory and gauge theory, statistical physics, condensed matter physics and renormalization group theory. The conference (2nd week) focused on applications of Hopf algebras, algebraic combinatorics, local dynamical system theory and special function theory to quantum field theory in all its facets. Both the school and conference took place in the Cargese region of Corsica (France), at the Institut d'Etudes Scientifiques de Cargese. The main motivation for the school and conference was to offer the opportunity for a broad discussion and exchange of ideas among Mathematicians and Physicists.

Hopf algebraic structure of quantum field and many-body theories II

Ch Brouder, Inst. de Minéralogie et de Physique des Milieux Condensés, Univ. Pierre et Marie Curie, Paris, France

Hopf Algebras, Theory and Applications to QFT

P. Cartier, IHES, Bures-sur-Yvette, France

Basics of perturbative QCD

Y. Dokshitzer, LPTHE, Univ. Pierre et Marie Curie, France

Noncommutative Quantum Field Theory

V. Rivasseau, Labo. de Physique théorique, Univ. Paris Sud-XI, France

Renormalization Group: an introduction

J. Zinn-Justin, DAPNIA, Saclay, France

Combinatorial Applications of Matrix Integrals and Topological Expansions I

Combinatorial Applications of Matrix Integrals and Topological Expansions II

J.-B. Zuber, LPTHE, Univ. Pierre et Marie Curie, Paris, France

Round Table Sessions

R. Flume, Department of Physics, Bonn University, Germany

Batalin-Vilkovisky Gauge Fixing via Homological Perturbation Theory

Reference for the lecture: BV Integrals

C. Albert (Zurich)

High Order Solution of a non-linear Schwinger-Dyson Equation

M. Bellon (Paris)

Operadic Point of View on the Hopf Algebra of Rooted Trees.

Reference 1 for the Lecture: (with M. Livernet) : Relating two Hopf algebras built from an operad, International Math. Research Notices (2007) no 24

Reference 2 for the Lecture: (with M. Livernet) : Pre-Lie algebras and the rooted trees operad, International Math. Research Notices (2001) no 8, pages 395-408.

F. Chapoton (Lyon)

B. Delamotte (Paris)

B. Duplantier (Saclay)

L. Foissy (Reims)

A. Frabetti (Lyon)

Perturbative quantum field theory and vertex algebras

S. Hollands (Cardiff)

J. M. Gracia-Bondia (Zaragoza)

Euclidean Epstein-Glaser Renormalization

Reference 1 for the Lecture: (by R. Brunetti, M. Duetsch, K. Fredenhagen): Perturbative Algebraic Quantum Field Theory and the Renormalization Groups

Reference 2 for the lecture: Euclidean Epstein-Glaser Renormalization

K. J. Keller (Hamburg)

T. Krajewski (Paris and Marseille)

Large-N Matrix Models : Some Algebraic Aspects

G. Krishnaswami (Durham)

J.-L. Loday (Strasbourg)

Two Hopf algebras of trees interacting

D. Manchon (Clermont--Ferrand)

Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces

N. Nikolov (Sofia)

D. Oriti (Utrecht)

W. v. Suijlekom (Nijmegen)

R. Verch (Leipzig)

Generalized Bollobas-Riordan polynomials and partial duality

F. Vignes-Tourneret (Vienna)