Related papers: Groupes, courbes et croissance
This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic…
This is the text accompanying my Bourbaki seminar on the work of Bloom and Sisask, Croot, Lev, and Pach, and Ellenberg and Gijswijt.
This manuscript gives an overview of my research work carried out within the FEMTO-ST institute in Besan\c{c}on, more particularly in the Automatic and Micro-Mechatronic Systems (AS2M) department. It is above all the result of my…
This is a survey of the existing digital collections of French mathematical literature, run by non-profit organizations. This includes research monographs, serials, proceedings, Ph. D. theses, collected works, books and personal websites.
We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is…
Humans spend a significant part of their lives being a part of groups. In this document we propose research directions that would make it possible to computationally form productive groups. We bring to light several issues that need to be…
This is a brief introduction to the study of growth in groups of Lie type, with $SL_2(\mathbb{F}_q)$ and some of its subgroups as the key examples. They are an edited version of the notes I distributed at the Arizona Winter School in 2016.…
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…
Lecture notes of a course on birational geometry (taught at College de France, Winter 2011, with the support of Fondation Sciences Math\'ematiques de Paris). Topics covered: introduction into the subject, contractions and extremal rays,…
The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…
In this paper we provide an overview of important research works on response-adaptive randomization completed in the past decades.
Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit…
Lectures presented at the Les Houches 2016 Summer School "Integrability: from Statistical Systems to Gauge Theory".
We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.
We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.
We describe the links between group theory and psychology, in particular through the works of Piaget. We show that groups appear universally in his description of children's intelligence, and that the notion of groupoid, which was little…
These proceedings are gathering twelve different research papers developping the theory of recognizability for various kinds of discrete objects: words. terms, graphs, etc...
This is a survey of old and new problems and results in additive number theory.
Generating series are crucial in enumerative combinatorics, analytic combinatorics, and combinatorics on words. Though it might seem at first view that generating Dirichlet series are less used in these fields than ordinary and exponential…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…