Abstract : In representation theory, Nakayama algebras are a nice, combinatorially described class of algebras that are often used as examples. We study when these algebras have small homological dimension (i.e. are shod). This can be done completely combinatorially, by
Résumé : La théorie de Yang-Mills est une théorie quantique des champs (QFT) qui vise à décrire les interactions entre les particules élémentaires. Comme toute QFT, elle peut s'exprimer à l'aide d'intégrales de chemins de Feynman : des intégrales par
Let k be an algebraically closed field. In characteristic 2, the isolated wild quotient singularities arising from an action of the cyclic group Z/2Z on the power series ring in two variables k], were completely described by Artin as an
Reinterpreting finite sets as vector spaces over F1 (the nonexistent field with one element) yields a combinatorial degeneration of linear algebra. Representation theory over these new vector spaces turns out to be closely related to graph theory. We will introduce
Un problème central en théorie des nombres est de déterminer si un système d’équations polynômiales à coefficients rationnels ou entiers a des solutions rationnelles ou entières. Pour traiter ce problème, une approche historique et puissante est le principe local-global, ou
Consider the variety Comm_n of pairs of commuting n by n matrices, it is invariant under the action of GL_n on the space of pairs of all matrices, by simultaneous conjunction. The natural algebraic structure to associate with is equivariant
Quiver representation theory is a fundamental tool in modern representation theory of associative algebras. A cornerstone of this field is Gabriel’s theorem, which characterizes quivers with finitely many indecomposable representations as precisely those arising from Dynkin diagrams of type ADE.
Résumé : We study A_g, the moduli space of principally polarized abelian varieties of dimension g. The subring generated by the Chern classes of the Hodge bundle is called the tautological ring, and it was fully determined by Gerard van
La prochaine séance du séminaire des jeunes aura lieu le mardi 8 Avril de 16h30 à 17h30 dans la salle de séminaires du laboratoire. L'orateur sera Davide Ricci, doctorant en première année de thése dans l'équipe Algèbre et Géometrie. Some
One of the hardest and most fundamental problems in topology is computing homotopy groups of spheres. One can simplify it a little by restricting to the stable range. This reveals a lot more structure: stable homotopy groups form a graded
