Related papers: Groupes, courbes et croissance
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…
In this summary of Habilitation Thesis, it is outlined author's 18 years research activity on mathematical physics, geometric methods in particle physics and gravity, modifications and applications (after defending his PhD thesis in 1994).…
This paper, in French, is a celebration of Max Dehn, and an essay of describing some of his results published in the beginning of the 1910's, and their offspring. It has been written up for a winter school in Les Diablerets, March 7-12,…
This second issue of the French Complex Systems Roadmap is the outcome of the Entretiens de Cargese 2008, an interdisciplinary brainstorming session organized over one week in 2008, jointly by RNSC, ISC-PIF and IXXI. It capitalizes on the…
This habilitation thesis is cumulative and, therefore, is collecting and connecting research that I (together with several co-authors) have conducted over the last few years. Thus, the absolute core of the work is formed by the ten…
A partly autobiographical survey of the development of enumerative and algebraic combinatorics in the 1960's and 1970's.
In this paper we give a survey of recent methods for the asymptotic and exact enumeration of number fields with given Galois group of the Galois closure. In particular, the case of fields of degree up to 4 is now almost completely solved,…
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
The goal of our work is to use a set of reports and extract named entities, in our case the names of Industrial or Academic partners. Starting with an initial list of entities, we use a first set of documents to identify syntactic patterns…
This text was published in the Gazette de la Soci\'et\'e Math\'ematique de France in October 2023. It is an introduction to the theory of motives, from its sources to its more modern developments.
These few pages briefly present the way in which Activity Theory has been adopted for several years now by French researchers in didactics of mathematics and has been adapted to study the learning of school mathematics in relation with the…
I provide a summary of the theoretical talks in Hard Probes 2012 together with some personal thoughts about the present and the future of the field.
This thesis summarises my scientific contributions in the domain of network science, human dynamics and computational social science. These contributions are associated to computer science, physics, statistics, and applied mathematics. The…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
These notes combine material from short lecture courses given in Paris, France, in July 2001 and in Srni, the Czech Republic, in January 2003. They discuss groups of symplectomorphisms of closed symplectic manifolds (M,\om) from various…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
This article is an extended version of the article published by EDP Sciences at the occasion of the 150 years of the ``Soci\'et\'e Fran\c{c}aise de Physique'' (in French)
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects,…