Braids and invariant metrics on groups of area-preserving diffeomorphisms of surfaces

In this talk I will survey results on the large-scale metric
properties of groups area-preserving diffeomorphisms of surfaces endowed with the hydrodynamic L^2-metric (or more generally the L^p-metric). I will prove that every finite dimensional vector space admits a quasi-isometric embedding into these groups, and in particular these groups are unbounded w.r.t. these metrics. The methots used involvequasi-morphisms on braid groups and configuration space integrals.

No previous knowledge of the subject will be assumed.