Category Archives: Uncategorized

Number theory over function fields 1. The classical theory Let us start with classical stuff. Theorem 1 (Dirichlet) a positive integer, an integer. There exist infinitely many prime numbers such that if and only if . A more precise statement … Continue reading →

Sphere packings This lecture has been designed for an audience of 150 master’s students in Orsay, Universite Paris-Saclay. 1. The sphere packing problem 1.1. Density In Euclidean space, one tries to pack equal balls as densely as possible. Pack means … Continue reading →

Parabolic dynamics 1. Survey 1.1. What does hyperbolic, elliptic mean in dynamics? Let be a dynamical system. Even if deterministic, it can exhibit a chaotic behaviour. This has several characteristics. One of them is the Butterfly effect: sensitive dependence on … Continue reading →

Algebraic representations of ergodic actions Based on joint work with Alex Furman, and earlier litterature. Thanks to Sami Douba for his help with notetaking. Today, we start with basics on measure spaces and algebraic varieties. Later on, we shall merge … Continue reading →

Journee francilienne d’accueil des post-doctorants en mathematiques 1. Eleonora di Nezza: Special metrics in Kähler geometry I work in Kähler geometry. It has to do with complex manifolds. Let us start with the uniformization theorem. It implies that compact Riemann … Continue reading →

Slides of Pansu’s 2 lectures on Lp cohomology and large scale conformal maps. lille_15oct14_beamer

Here is the completed set of slides CIRMsep14_beamer If you want to know more about the construction of horizontal submanifolds and how Gromov uses it to bound Hausdorff dimensions from below, see Pansu’s Trento notes (2005).

Here are Pansu’s slides (version sept. 3rd, 00:13) CIRMsep14_beamer