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
Abstract : Last year, a major flood in the Yvette river basin caused significant damage in the area around Paris-Saclay University. Such rare, high-impact events lie in the tails of probability distributions and may not be adequately described by standard
In this talk, I will describe the moduli spaces of curves as a set and present a few key examples. I will also introduce the stable graphs associated to nodal curves.
I will present some general results on the finite-time blow-up of the mass critical gKdV equation. Then, we will focus on results concerning finite-time infinite-point blow-up. Previously, the blow-up rate of such solutions was limited with a lower bound of
Résumé : Dans cet exposé, nous donnerons un point de vue d'ensemble de la théorie des algèbres centrales simples et du groupe de Brauer d'un corps. L'exposé sera guidé par l'étude des quaternions et l'étude d'exemples issus de la théorie
Abstract: The binormal flow, which models the evolution of vortex filaments, and the cubic nonlinear Schrödinger equation are deeply connected through the Hasimoto transform, linking vortex filament dynamics with dispersive partial differential equations. In this talk, I will give an
