Related papers: Galois Got his Gun
Leibniz's mathematical texts are a perfect example of a type of historical document that is extremely difficult to deal with in the context of an editorial enterprise: the draft. The tables in Leibniz's mathematical manuscripts are a…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
Until now, most studies carried onto social or semantic networks have considered each of these networks independently. Our goal here is to bring a formal frame for studying both networks empirically as well as to point out stylized facts…
Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…
This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. After a description of the…
We introduce and study a class of field extensions that we call pre-Galois; viz. extensions that become Galois after some linearly disjoint Galois base change. Among them are geometrically Galois extensions of k(T), with k a field:…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its…
We establish some comparison results among the different parameterized Galois theories for $q$-difference equations, completing the work by CHatzidakis, Hardouin and Singer, that addresses the problem in the case without parameters. Our…
We consider the mathematical theory of geographical maps, with an emphasis on the eighteenth century works of Euler, Lagrange and Delisle. This period is characterized by the frequent use of maps that are no more obtained by the…
Prosopography is usually used to globally describe a large population of ordinary subjects. It is thus opposed to biography, as a genre devoted to exceptional individuals. I show in this article how to use prosopography to study a single…
Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
As a simple corollary of a highly general framework for differential and difference Galois theory introduced by Y. Andre, we formulate a version of the Galois correspondence that applies over a difference field with arbitrary field of…
In this paper we deal with Grothendieck's interpretation of Artin's interpretation of Galois's Galois Theory (and its natural relation with the fundamental group and the theory of coverings) as he developed it in Expose V, section 4,…
Jarnik's identity plays a major role in classical simultaneous approximation to two real numbers. O. German [2] has shown a generalization to the weighted setting in which the identity has to be replaced by two inequalities. His methods…
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality.
Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of…
There are two purposes in this article. One is to present a criterion for the existence of a birational embedding into a projective plane with inner and outer Galois points for algebraic curves. Another is to classify plane curves of degree…
For a Galois number field $K$, the Galois group $\text{Gal}(K/\mathbb{Q})$ acts on the class group $Cl_K$ in a very natural way: $\sigma\cdot[I]=[\sigma(I)]$ for any $\sigma \in \text{Gal}(K/\mathbb{Q})$, $[I]\in Cl_K$. In this paper, we…