Opérateurs différentiels et courbes elliptiques
La détermination projective
Progrès récents sur l’hypothèse du continu
Les travaux récents de Woodin ont considérablement renouvelé la théorie des ensembles en lui apportant une intelligibilité globale et en restaurant son unité. Pour la première fois, ses résultats ouvrent une perspective réaliste de résoudre le problème du continu, et, à tout le moins, ils établissent le caractère irréfutablement signifiant et précis de celui-ci.
Groupes de Garside
Left-Garside categories, self-distributivity, and braids
In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the relationship between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy, Braids and...
Multiple left distributive systems
We describe the free objects in the variety of algebras involving several mutually distributive binary operations. Also, we show how an associative operation can be constructed on such systems in good cases, thus obtaining a two way correspondence between LD-monoids (sets with a left self-distributive and a compatible associative operation) and multi-LD-systems (sets with a family of mutually distributive operations).
An associative operation on monogenic left distributive systems
Term substitution induces an associative operation on the free objects of any equational variety. In the case of left distributivity, the construction can be extended to any monogenic structure.
Homology of gaussian groups
We describe new combinatorial methods for constructing explicit free resolutions of by -modules when is a group of fractions of a monoid where enough lest common multiples exist (“locally Gaussian monoid”), and therefore, for computing the homology of . Our constructions apply in particular to all Artin-Tits groups of finite Coexter type. Technically, the proofs rely on the properties of least common multiples in a monoid.
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