  We propose a program for counting microstates of four-dimensional BPS black
holes in N >= 2 supergravities with symmetric-space valued scalars by
exploiting the symmetries of timelike reduction to three dimensions. Inspired
by the equivalence between the four dimensional attractor flow and geodesic
flow on the three-dimensional scalar manifold, we radially quantize stationary,
spherically symmetric BPS geometries. Connections between the topological
string amplitude, attractor wave function, the Ooguri-Strominger-Vafa
conjecture and the theory of automorphic forms suggest that black hole
degeneracies are counted by Fourier coefficients of modular forms for the
three-dimensional U-duality group, associated to special "unipotent"
representations which appear in the supersymmetric Hilbert space of the quantum
attractor flow.
