Resurgence, Physics and Numbers

Description

This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years – a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues. Front Matter ....Pages i-xi Asymptotics, ambiguities and resurgence (Inês Aniceto)....Pages 1-66 Nonlinear eigenvalue problems (Carl M. Bender, Javad Komijani, Qing-hai Wang)....Pages 67-89 Feynman diagrams and their algebraic lattices (Michael Borinsky, Dirk Kreimer)....Pages 91-107 Invariants of identity-tangent diffeomorphisms expanded as series of multitangents and multizetas (Olivier Bouillot, Jean Ecalle)....Pages 109-232 The resurgent approach to topological string theory (Ricardo Couso-Santamaría)....Pages 233-248 WKB and resurgence in the Mathieu equation (Gerald V. Dunne, Mithat Ünsal)....Pages 249-298 Renormalised conical zeta values (Li Guo, Sylvie Paycha, Bin Zhang)....Pages 299-327 Combinatorics of Poincaré’s and Schröder’s equations (Frédéric Menous, Jean-Christophe Novelli, Jean-Yves Thibon)....Pages 329-378 Back Matter ....Pages 379-381