# In the steps of Galois. Proceedings of the Evariste Galois bicentenary meeting.

**In the steps of Galois. Proceedings of the Evariste Galois bicentenary meeting.**

Fabio Maia Bertato, Jean-Jacques Szczeciniarz, José Carlos Cifuentes.

The work of Evariste Galois, known today as Galois Theory, gave rise to modern mathematical thought with its characteristic abstraction and generality. ‘Modern thought’ makes reference to a movement whose characteristic was a break with tradition, a new self-criticism, and a trend toward abstraction and formal means of expression. Evariste Galois was involved in this movement as a mathematician, as well as by his uncompromising social and political commitments. Galois Theory is essentially a dynamical theory that has and continues to evolve because of how it penetrates throughout the entirety of mathematical thought. Its force is due to its deeply critical mind and its interdisciplinary, functoral conception of mathematics. This book offers to a wider public the proceedings of the “Evariste Galois Bicentenary Meetings”. It presents various views on GT for different domains of the mathematical corpus, both for those linked to the 19th century and those linked to the 20th century. The reader will observe that two principle orientations emerge, synchronically, from these analyses: that of algebraic geometry and that of logic. There are thus two directions in which we can look for Galois’ Legacy.

:: May 2014

:: ISBN : 9782705688523

:: EAN: 978-2705688523

**Table of Contents**

I. *The Galois Legacy*, Ubiratan D’AMBROSIO, p. 13

II. *Galois et la Symetrie*, Bruno POIZAT p. 39

III. *The Mysterious Strength of”the” Galois Theory*, Jean-Jacques SZCZECINIARZ, p. 61

IV. *Galois Extensions of Groups and Modules in the Context of Universal Algebra*, José Carlos CIFUENTES, p. 111

V. *Galois Theory and Schemes Covering Spaces in Algebraic Geometry*, André CONTIERO, p. 141

VI. *A Structuralist Perspective on Galois-Type Correspondences (and why they are interesting) *, Jairo José da SILVA, p. 161

VII. *Galois Cubic Extensions and Applications*, Trajano NETO and Tatiana RODRIGUES, p. 183

VIII. *From the Fundamental Theorem of Symmetric Polynomials to Galois Theory*, Paulo A. MARTIN, p. 191

IX. *Generalized Galois Theory*, Newton C.A. da COSTA, p. 205

X. *Expansions of Galois Theory in Algebra: infinity Galois theory and applications*, Hugo Luiz MARIANO, p. 227

XI. *Évariste Galois Bicentennary Meeting*, Fábio Maia BERTATO, p. 257