The asymptotic dimension of the mapping class group (exposé commun avec le thème topologie)

We will show that the mapping class group has finite asymptotic dimension. A key piece of the proof is the construction of a quasi-tree that mapping class acts on. This construction works in a quite general setting for groups that have some aspect of negative curvature. We will describe this construction and explain how it relates to the asymptotic dimension of the mapping class group. This is joint work with K. Fujiwara and M. Bestvina.