  We explain how equivariant localization may be applied to AdS/CFT to compute
various BPS observables in gravity, such as central charges and conformal
dimensions of chiral primary operators, without solving the supergravity
equations. The key ingredient is that supersymmetric AdS solutions with an
R-symmetry are equipped with a set of equivariantly closed forms. These may in
turn be used to impose flux quantization and compute observables for
supergravity solutions, using only topological information and the
Berline--Vergne--Atiyah--Bott fixed point formula. We illustrate the formalism
by considering $AdS_5\times M_6$ and $AdS_3\times M_8$ solutions of $D=11$
supergravity. As well as recovering results for many classes of well-known
supergravity solutions, without using any knowledge of their explicit form, we
also compute central charges for which explicit supergravity solutions have not
been constructed.
