We start by pointing out that certain Riemann surfaces appear
rather naturally in the context of wave equations in the black hole background.
For a given black hole there are two closely related surfaces.
One is the Riemann surface of complexified "tortoise" coordinate. The
other Riemann surface appears when the radial wave equation is interpreted
as the Fuchsian differential equation. We study these surfaces
in detail for the BTZ and Schwarzschild black holes in four and higher
dimensions. Topologically, in all cases both surfaces are a sphere with a
set of marked points; for BTZ and 4D Schwarzschild black holes there
is 3 marked points. In certain limits the surfaces can be characterized
very explicitly. We then show how properties of the wave equation
(quasi-normal modes) in such limits are encoded in the geometry of the
corresponding surfaces. In particular, for the Schwarzschild black hole
in the high damping limit we describe the Riemann surface in question
and use this to derive the quasi-normal mode frequencies with the log 3
as the real part. We then argue that the surfaces one finds this way signal
an appearance of an effective string. We propose that a description
of this effective string propagating in the black hole background can be
given in terms of the Liouville theory living on the corresponding Riemann
surface. We give such a stringy description for the Schwarzschild
black hole in the limit of high damping and show that the quasi-normal
modes emerge naturally as the poles in 3-point correlation function in
the effective conformal theory.