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A Minicourse on Resurgence Theory
Ecalle's averaging operators for real summation (and commented bibliography).
Ecalle's averaging operators for real summation (and commented bibliography).
Organizers
Speaker
Frederic Fauvet
Time
Friday, December 12, 2025 10:30 AM - 11:30 AM
Venue
A7-201
Online
Zoom 388 528 9728
(BIMSA)
Abstract
We address the question of the real summation of divergent series of natural origin, with real coefficients; this involves subtle compensation mechanisms for the various branches of resurgent functions over the real axis, achieved through averaging procedures which respect tight constraints.
Speaker Intro
Frédéric Fauvet is a French mathematician working in analysis and dynamical systems. He is a Maître de conférences at IRMA (Institut de Recherche Mathématique Avancée), Université de Strasbourg, and a CNRS researcher. His work sits at the crossroads of resurgent analysis, dynamical systems, and algebraic/combinatorial structures such as Hopf algebras and operads, often using Jean Écalle’s mould calculus to study divergent series, linearization problems, and analytic classification in one- and several-dimensional dynamics.
In mathematical physics, Fauvet has applied resurgence techniques to quantum field–theoretic toy models, for instance in joint work on the ϕ^{2k} model in zero dimension. He has also co-edited research volumes such as From Combinatorics to Dynamical Systems and Asymptotics in Dynamics, Geometry and PDEs, helping to build bridges between combinatorics, asymptotic analysis, geometry, and PDEs.