Asymptotics in dynamics, geometry and PDEs; generalized Borel summation [electronic resource] : proceedings of the conference held in CRM Pisa, 12-16 October 2009, vol. II /
Costin, Ovidiu.editor.
Fauvet, Frédéric.editor.
Menous, Frédéric.editor.
Sauzin, David.editor.
These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
Description based upon print version of record.
Title Page; Copyright Page; Table of Contents; Introduction; Authors' affiliations; Feynman graphs in perturbative quantum field theory; 1 Introduction; 2 Perturbation theory; 3 Multi-loop integrals; 4 Periods; 5 A theorem on Feynman integrals; 6 Sector decomposition; 7 Hironaka's polyhedra game; 8 Shuffle algebras; 9 Multiple polylogarithms; 10 From Feynman integrals to multiple polylogarithms; 11 Conclusions; References; The flexion structure and dimorphy: flexion units, singulators, generators, and the enumeration of multizeta irreducibles; 1 Introduction and reminders
1.1 Multizetas and dimorphy1.2 From scalars to generating series; 1.3 ARI//GARI and its dimorphic substructures; 1.4 Flexion units, singulators, double symmetries; 1.5 Enumeration of multizeta irreducibles; 1.6 Canonical irreducibles and perinomal algebra; 1.7 Purpose of the present survey; 2 Basic dimorphic algebras; 2.1 Basic operations; 2.2 The algebra ARI and its group GARI; 2.3 Action of the basic involution swap; 2.4 Straight symmetries and subsymmetries; 2.5 Main subalgebras; 2.6 Main subgroups; 2.7 The dimorphic algebra ARIal/al C ARIal/al .
2.8 The dimorphic group GARIas/as C GARIas/as3 Flexion units and twisted symmetries; 3.1 The free monogenous flexion algebra Flex(E); 3.2 Flexion units; 3.3 Unit-generated algebras Flex(E); 3.4 Twisted symmetries and subsymmetries in universal mode; 3.5 Twisted symmetries and subsymmetries in polar mode; 4 Flexion units and dimorphic bimoulds; 4.1 Remarkable substructures of Flex(E); 4.2 The secondary bimoulds ess and esz; 4.3 The related primary bimoulds es and ez; 4.4 Some basic bimould identities; 4.5 Trigonometric and bitrigonometric bimoulds
4.6 Dimorphic isomorphisms in universal mode4.7 Dimorphic isomorphisms in polar mode; 5 Singulators, singulands, singulates; 5.1 Some heuristics. Double symmetries and imparity; 5.2 Universal singulators senk(ess) and seng(es); 5.3 Properties of the universal singulators; 5.4 Polar singulators: description and properties; 5.5 Simple polar singulators; 5.6 Composite polar singulators; 5.7 From al/al to al/il. Nature of the singularities; 6 Anatural basisfor ALIL C ARIal/il; 6.1 Singulation-desingulation: the general scheme; 6.2 Singulation-desingulation up to length 2
6.3 Singulation-desingulation up to length 46.5 The basis lama/lami.; 6.6 The basis loma/lomi; 6.7 The basis luma/lumi; 6.8 Arithmetical vs analytic smoothness; 6.9 Singulator kernels and "wandering" bialternals; 7 A conjectural basis for ALAL C ARIal/al . The three series of bialternals; 7.1 Basic bialternals: the enumeration problem; 7.2 The regular bialternals: ekma, doma; 7.3 The irregular bialternals: carma; 7.4 Main differences between regular and irregular bialternals; 7.5 The pre-doma potentials; 7.6 The pre-carma potentials; 7.7 Construction of the carma bialternals
7.8 Alternative approach
Includes bibliographical references and indexes.
These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
Mathematical analysis.
Analysis (Mathematics).
Mathematical physics.
Analysis.
Theoretical, Mathematical and Computational Physics.