Séminaires : Séminaire Géométrie et Topologie

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ

We discuss a law of large numbers for the volumes of random 3-manifolds. Such objects, introduced by Dunfield and Thurston, come from the observation that certain families of 3-manifolds, such as Heegaard splittings of a fixed genus, are naturally parametrized by the elements of the mapping class group of a closed orientable surface. We can sample a random Heegaard splitting simply by picking at random the gluing map that defines it. In order to do this systematically, we make a random walk on the mapping class group of the Heegaard surface. We will see that the (simplicial) volumes of the associated 3-manifolds grow linearly in the step of the walk (with an exact asymptotic).