Edgar Knobloch University of California, Berkeley (UC Berkeley) Low Rossby number convection is studied using an asymptotically reduced system of equations valid in the limit of strong rotation. The equations describe four regimes as the Rayleigh number Ra increases: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Ra, followed for yet larger Ra by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced hear transport efficiency, and finally by geostrophic turbulence. The Nusselt number--Rayleigh number scaling in the "ultimate" regime geostrophic turbulence is predicted and confirmed using direct numerical simulations of the reduced equations. These simulations reveal that the geostrophic turbulence is unstable to the formation of large scale barotropic vortices, via a process known as spectral condensation. The details of this process are quantified and its implications explored. This is joint work with I Grooms (Courant Institute), K Julien, A Rubio, J.B. Weiss (University of Colorado, Boulder) and G Vasil (Sydney).