Sobolev-subcritical fast diffusion with vanishing boundary condition leads to

finite-time extinction, with a vanishing profile selected by the initial datum. In a joint

work with R. McCann and C. Seis, we quantify the rate of convergence to this profile for

general smooth bounded domains. In rescaled time variable, the solution either converges

exponentially fast or algebraically slow. In the first case, the nonlinear dynamics are

well-approximated by exponentially decaying eigenmodes, giving a higher order

asymptotics. We also improve on a result of Bonforte and Figalli, by providing a new and

simpler approach which is able to accommodate the presence of zero modes.