Related papers: Galois Got his Gun
This preprint is the extended version of a paper that will be published in the proceedings of the Oberwolfach conference "Explicit vs tacit knowledge in mathematics" (January 2012). It presents a case study on some algebraic researches at…
Classical applications of Galois theory concern algebraic numbers and algebraic functions. Still, the night before his duel, Galois wrote that his last mathematical thoughts had been directed toward applying his "theory of ambiguity to…
The Jordan measure, the Jordan curve theorem, as well as the other generic references to Camille Jordan's (1838-1922) achievements highlight that the latter can hardly be reduced to the "great algebraist" whose masterpiece, the Trait\'e des…
In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…
These notes are an exposition of Galois Theory from the original Lagrangian and Galoisian point of view. A particular effort was made here to better understand the connection between Lagrange's purely combinatorial approach and Galois…
The mathematisation of the socio-economic sphere, where mathematics actively constructs social reality, presents a challenge for studies on ethics in mathematics and its education. While existing scholarship on ethics in mathematics offers…
This paper aims to provide an overview of recent researches studies on Camille Jordan's early works (1860-1870). We especially shed new light on the relation between Galois and Jordan by discussing the collective dimensions of Jordan's…
Motivated by applications of algebraic geometry, we introduce the Galois width, a quantity characterizing the complexity of solving algebraic equations in a restricted model of computation allowing only field arithmetic and adjoining…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
The object of this paper is the study of a class of dessins d'enfants, the so-called diameter four trees. These objects, first introduced by G. Shabat, can be considered as the simplest non trivial example of etale covers of the projective…
The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of…
Counting number fields with prescribed Galois group is an enduring challenge in arithmetic statistics. Using the determinant method, we provide an upper bound for even groups, which is new in some cases.
Apart from a few remarks on lattice systems with global or gauge symmetries, most of this talk is devoted to some interesting ancient examples of symmetries and their breakdowns in elasticity theory and hydrodynamics. Since Galois Theory is…
Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see [9], and also the very helpful notes of Cardialaguet [4] on Lions' lectures, the Master Equation has attracted a lot of interest, and various…
We carry out some of Galois's work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite…
This is a introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of their interrelations.
We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the…
Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…
The present notes are the expanded and polished version of three lectures given in Stanford, concerning the analytic and arithmetic properties of weight one modular forms. The author tried to write them in a style accessible to…
We review a series of models of sociophysics introduced by Galam and Galam et al in the last 25 years. The models are divided in five different classes, which deal respectively with democratic voting in bottom up hierarchical systems,…