CRM: Centro De Giorgi
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Mould Calculus, Resurgence and Combinatorial Hopf Algebras

14 November 2011 - 18 November 2011


In recent years, many examples of graded Hopf algebras based on combinatorial structures have been discovered and investigated. There are several sources of such objects. In combinatorics, they arise as generalizations of symmetric functions and are used to work algebraically with the objects themselves instead of their generating series. In mathematical physics, they provide elegant mathematical formulations of some renormalization schemes in quantum field theory, the best known example being the Connes-Kreimer Hopf algebras of trees and Feynman graphs. They also arise naturally in the theory of operads, to quote only a few of their recent application domains.

Very recently, it has been observed that such algebras play a hidden role in resurgence theory and other fields of dynamical systems. For example, noncommutative symmetric functions arise in Ecalle's mould calculus and encode the so-called alien derivations on spaces of resurgent functions. Mould calculus is itself concerned with the classification of local dynamical systems but also with the study of multizeta values.

These connections are far-reaching and meaningful to the various corresponding mathematical communities, especially the ones of algebraic combinatorics and dynamical systems. However, they require to be deepened exchanges between experts of very different backgrounds - a notoriously challenging process.

This mini-workshop, gathering a few leading experts in each of these various aspects of the theory, together with junior researchers and PhD students, will provide ample space for discussions through informal sessions.

Anyone interested in the topics of the workshop, may send an email to Dr. Sauzin