LEADER 03352nam 22004455a 450 001 9910151932803321 005 20091109150325.0 010 $a3-03719-573-8 024 70$a10.4171/073 035 $a(CKB)3710000000953847 035 $a(CH-001817-3)106-091109 035 $a(PPN)178155675 035 $a(EXLCZ)993710000000953847 100 $a20091109j20090924 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRenormalization and Galois Theories$b[electronic resource] /$fAlain Connes, Fre?de?ric Fauvet, Jean-Pierre Ramis 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2009 215 $a1 online resource (279 pages) 225 0 $aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;$x2523-5133 ;$v15 327 $tNoncommutative geometry and motives (a? quoi servent les endomotifs?) /$rCaterina Consani --$tRenormalisation of non-commutative field theories /$rVincent Rivasseau, Fabien Vignes-Tourneret --$tMould expansions for the saddle-node and resurgence monomials /$rDavid Sauzin --$tGalois theory, motives and transcendental numbers /$rYves Andre? --$tThe combinatorics of Bogoliubov's recursion in renormalization /$rKurusch Ebrahimi-Fard, Dominique Manchon --$t(Non)commutative Hopf algebras of trees and (quasi)symmetric functions /$rMichael E. Hoffman --$tFormal differential equations and renormalization /$rFre?de?ric Menous --$tFeynman integrals and multiple polylogarithms /$rStefan Weinzierl. 330 $aThis volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both reseachers and graduate students in mathematics and physics. 606 $aAlgebraic geometry$2bicssc 606 $aAlgebraic geometry$2msc 606 $aQuantum theory$2msc 615 07$aAlgebraic geometry 615 07$aAlgebraic geometry 615 07$aQuantum theory 686 $a14-xx$a81-xx$2msc 702 $aConnes$b Alain 702 $aFauvet$b Fre?de?ric 702 $aRamis$b Jean-Pierre 801 0$bch0018173 906 $aBOOK 912 $a9910151932803321 996 $aRenormalization and Galois Theories$92565665 997 $aUNINA