Modul: MAT772 Geometrie-Seminar

## Volumes of random 3-manifolds

Gabriele Viaggi talk

**Date:** 13.11.19 **Time:** 15.45 - 16.45 **Room:** ETH HG G 43

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).