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Fondements mathématiques entre deux formes d’égalité dans la théorie des clans et l’égalité unique de la théorie des ensembles selon Z.F. et NBG.

M’Boka Kiese

Dans la théorie des ensembles selon Zermelo Fraenkel, fondements des mathématiques officielles, le symbole d’égalité utilisé  « =» est unique pour les éléments « x=y »comme pour les ensembles « a = b ». Cette relation d’égalité est réflexive, symétrique et transitive. Lire la suite »

LECTURE NOTES

ON HEURISTIC GENERALIZATIONS OF THE JACOBIAN CONJECTURE

By Pascal Kossivi ADJAMAGBO

University Paris 6 – Institut de Mathématiques de Jussieu-UMR 7586 CNRS

Opening lecture of the International Conference at Chern Institute of Mathematics on

Affine Algebraic Geometry and the Jacobian Conjecture” on 21-25 July 2014

Tianjin, 21 July 2014

Abstract

The aim of this opening lecture is to unveil heuristic and stimulating generalizations of the Jacobians Conjecture. By lack of time, we will consider only the first level of such generalisations, concerning first polynomial endomorphisms of the algebraic affine space in any dimension and in any characteristic, secondly complex analytic endomorphisms of the complex affine space of any dimension, thirthly real analytic endomorphisms of the real affine space of any dimension, and finally real algebraic endomorphism of the real affine space of any dimension. The complete levels of generalisation could be quiety read in the complete written version of this lecture. These restrictions of the anounced three levels of generalizations will be enough to unveil the surprising and hidden vitality and fecundity in many branches of mathematics of the venerable 75 years old Jacobian Conjecture to whom we are paying homage during these memorable days in the beating heart of the more venerable multi-millennary alive chinese civilisation and empire. Lire la suite »