Resurgence monomials
演讲者
Frederic Fauvet
时间
2025年12月10日 10:30 至 11:30
地点
A7-201
线上
Zoom 388 528 9728
(BIMSA)
摘要
There exist families of resurgent functions with good algebraic properties, that constitute very structured building blocks, to deal in an effective way with the resurgence properties of solutions to a given problem. We discuss the ``check-lists'' and describe explicit examples of these systems of so--called resurgence monomials, with in particular a presentation of the paralogarithmic family, used in inverse problems (the quest for systems with prescribed Stokes data, formulated within the framework of alien calculus). Along the way, we \ introduce some elements of Ecalle's mould combinatorics, which are necessary to compute with resurgence monomials.
演讲者介绍
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.