CRM: Centro De Giorgi
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Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation

Four recent advances in resummation and resurgence theory

speaker: Jean Ecalle ( CNRS (France) +Orsay University (France))

abstract: 1 The so-called acceleration transforms (of use in multicritical resummation) factor into a "transparent" and an "innocuous" part, both with surprisingly explicit integral kernels.

2 Divergent expansions in a singular parameter give rise to a specific type of resurgence with an unexpectedly rich algebraic-combinatorial underpinning.

3 (with S. Sharma) Many divergent power series (e.g. in knot theory), despite verifying no useful differential or functional equations, nonetheless yield to resummation and display remarkable resurgence properties, which have to be derived directly from the syntax (sum-product concatenations) of their Taylor coefficients.

4 (with B. Vallet) Although, more than 50 years after Kolmogorov's trailblazing paper, the convergence of Lindstedt series in KAM theory still carries a waft of the mysterious, the fact is that this convergence results from a rather simple, purely combinatorial mechanism that inhibits the occurrence of "super-multiple resonances

Wed 14 Oct, 10:20 - 11:20, Aula Dini
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