In this talk, I will consider three models of statistical mechanics: the classical XY model in arbitrary dimension, the lattice Coulomb gas in dimension two, and the square well model in arbitrary dimension. For …

We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn …

The Becker-Döring equations describe the dynamics of cluster formation and have long been known to exhibit metastable behaviour near the critical monomer concentration. In the linear setting, where the monomer …

Given a group G, it is natural to ask whether or not it is linear, i.e., if G is isomorphic to a subgroup of GLN(R) for some N and some ring R. In this seminar, we will answer this question for the group G = Bn, the …

Soit X un objet géométrique (variété complexe, algébrique, symplecique,...). Un problème énumératif consiste à compter les sous-objets satisfaisant des contraintes fixées. Une idée naturelle consiste à dégénérer X, …

La dimension de Kodaira est un invariant biméromorphe discret fondamental des variétés kählériennes compactes. D'après le théorème d'uniformisation, deux surfaces de Riemann compactes ont la même dimension de …

Entanglement distillation is a fundamental task in quantum information theory. In this work, we prove that Werner states in arbitrary dimension are 2-copy distillable if and only if they are 1-copy distillable and …

The Ginzburg-Landau energy is studied in a specific geometry: an infinite strip with Neumann boundary conditions and under symmetry properties related to very experiments in Bose Einstein condensates. We show that …