Related papers: Galois Got his Gun
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own…
The paper studies the probability for a Galois group of a random polynomial to be $A_n$. We focus on the so-called large box model, where we choose the coefficients of the polynomial independently and uniformly from $\{-L,\ldots, L\}$. The…
In science and beyond, numbers are omnipresent when it comes to justifying different kinds of judgments. Which scientific author, hiring committee-member, or advisory board panelist has not been confronted with page-long "publication…
This paper was motivated by a recent paper by Krumm and Pollack investigating modulo-$p$ behaviour of quadratic twists with rational points of a given hyperelliptic curve, conditional on the abc-conjecture. We extend those results to…
We apply the concepts of classical and quantum channels to the modeling of opinion dynamics and propose a stochastic method for representing the temporal variation of individual and group opinions. In particular, we use quantum Galois noise…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
We describe in dialogue form a possible way of discovering and investigating 10-adic numbers starting from the naive question about a `largest natural number'. Among the topics we pursue are possibilities of extensions to transfinite…
The aim of this article is to study rational parallelisms of algebraic varieties by means of the transcendence of their symmetries. The nature of this transcendence is measured by a Galois group built from the Picard-Vessiot theory of…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…
The enterprise of trying to explain different social and economic phenomena using concepts and ideas drawn from physics has a long history. Statistical mechanics, in particular, has been often seen as most likely to provide the means to…
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
The stated aim of this conference is to debate the continuing evolution of IS in businesses and other organisations. This paper seeks to contribute to this debate by exploring the concept of appropriation from a number of different…
We study the basic Galois connection induced by the "satisfaction" relation between external operations $A^n\rightarrow B$ defined on a set $A$ and valued in a possibly different set $B$ on the one hand, and ordered pairs $(R,S)$ of…
The nineteenth century Russian author Leo Tolstoy based his egalitarian views on sociology and history on mathematical and probabilistic views, and he also proposed a mathematical theory of waging war.
The choice of priors may become an insoluble problem if priors and Bayes' rule are not seen and accepted in the framework of subjectivism. Therefore, the meaning and the role of subjectivity in science is considered and defended from the…
This article reflects on the life and mathematical contributions of Pierre Cartier, a distinguished figure in 20th- and 21st-century mathematics. As a key member of the Bourbaki collective, Cartier played a pivotal role in the formalization…
This paper collects many results on galoisian ideals and Galois theory.
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the…