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
Abstract : The RSA algorithm is one of the oldest widely used public-key encryption algorithm. It relies on the difficulty of factorizing primes, with the best-known classical algorithms performing in sub-exponential time. Shor's algorithm, which relies on the laws of
Let A be a gentle algebra. It is given by a quiver (directed graph) and 0-relations (non-admissible directed paths). The indecomposable modules of A are determined by the combinatorics of undirected walks on the quiver. So every module admits a
In 1966, Mark Kac famously asked: “Can one hear the shape of a drum?” — that is, can the geometry of a domain $\Omega \in \RR^d$ be determined from the spectrum of the Dirichlet Laplacian on $\Omega$? The answer, known
Let A be a gentle algebra. It is given by a quiver (directed graph) and 0-relations (non-admissible directed paths). The indecomposable modules of A are determined by the combinatorics of undirected walks on the quiver. So every module admits a
Abstract: The dimer model is a statistical mechanics model that studies random perfect matchings on graphs. It was introduced in the 1960s, when the partition functions and correlations were exactly computed by Kasteleyn, Temperley, and Fisher. Over the past few
Mon lemme de topologie est vrai dans les espaces métriques, les espaces compacts ou même les groupes topologiques, mais je ne souhaite pas le démontrer plusieurs fois. Je souhaite travailler avec des fonctions méromorphes, et pourtant, j'ai encore du mal
Résumé : Dans les années 90, Serre a initié un programme de recherche autour de la probabilité qu'une équation choisie aléatoirement au sein d'une famille possède une solution rationnelle. Par exemple, il démontra que 0% des coniques diagonales possèdent un
