Title: Anomalous superdiffusion of Brownian motion in random incompressible flowsAbstract: We study Brownian motion advected by a stationary, divergence-free random drift whose spatial correlations decay slowly. Such long-range dependence is expected to produce {it superdiffusion}: for a typical realization of the drift, the variance of the displacement of the particle grows faster than linearly in time, […]

Title: Symplectic Weyl laws and groups of area-preserving homeomorphisms. Abstract: The algebraic structure of the group of volume-preserving homeomorphisms of a manifold of dimension at least three has been well-understood since the work of Fathi from the 70s. However, the surface case has long remained a mystery. I will discuss joint work clearing up parts of […]