Limit law for Brownian cover time of the two-dimensional torus

Consider the time C(r) it takes a Brownian motion to come within distance r of every point in the two-dimensional torus of area one. I will discuss the key ideas in a joint work with Jay Rosen and Ofer Zeitouni, showing that as r goes to zero, the square-root of C(r), minus an explicit non-random centering m(r), converges in distribution to a randomly shifted Gumbel law.