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Titlebook: Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation; Proceedings of the c Ovidiu Costin,Frédéric Fauvet,David Sauzin Co

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Ovidiu Costin,Frédéric Fauvet,David SauzinA unique effort to give an account of recent achievements in modern asymptotics, including resurgence theory and mould calculus.Applications to topics as diverse as mathematical physics, local dynamic
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Feynman graphs in perturbative quantum field theory,field theory. The mathematical structures — apart from being of interest in their own right — allow to derive algorithms for the computation of these graphs. Topics covered are the relations of Feynman integrals to periods, shuffle algebras and multiple polylogarithms.
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On the parametric resurgence for a certain singularly perturbed linear differential equation of secr the example P(.) . x.. − 1).. Based on a global study of its actual solutions, especially their Stokes phenomena, we present an analytic proof of the resurgence of its formal solutions. Many details are given, but the complete proof will be presented in a future article.
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Characterization in the Integral Casetaker equation (Theorem 3 and Theorem 5), whose Borel transformed Voros coefficient can be concretely given (Theorem 2). These results give a tangible description of the alien derivative of WKB solutions of an MPPT equation (Theorem 6). The details are given in [5] and [11].
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Conference proceedings 2011s 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 f
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The flexion structure and dimorphy: flexion units, singulators, generators, and the enumeration of en attempt a broad-brush overview of the whole question of canonical irreducibles and introduce the promising subject of perinomal algebra. As a recreational aside, we also state, justify, and computationally check a refinement of the standard conjectures about the enumeration of multizeta irreducibles.
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