  QNMs govern the linear response to perturbations of BHs, D-branes and
fuzzballs and the gravitational wave signals in the ring-down phase of binary
mergers. A remarkable connection between QNMs of neutral BHs in 4d and quantum
SW geometries describing the dynamics of ${\cal N}=2$ SYM theories has been
recently put forward. We extend the gauge/gravity dictionary to a large class
of gravity backgrounds including charged and rotating BHs of Einstein-Maxwell
theory in $d=4,5$ dimensions, D3-branes, D1D5 `circular' fuzzballs and smooth
horizonless geometries; all related to ${\cal N}=2$ SYM with a single $SU(2)$
gauge group and fundamental matter. We find that photon-spheres, a common
feature of all examples, are associated to degenerations of the classical
elliptic SW geometry whereby a cycle pinches to zero size. Quantum effects
resolve the singular geometry and lead to a spectrum of quantized energies,
labeled by the overtone number $n$. We compute the spectrum of QNMs using exact
WKB quantization, geodetic motion and numerical simulations and show excellent
agreement between the three methods. We explicitly illustrate our findings for
the case D3-brane QNMs.
