  We use the Lorentzian AdS/CFT prescription to find the poles of the retarded
thermal Green's functions of ${\cal N=4}$ SU(N) SYM theory in the limit of
large N and large 't Hooft coupling. In the process, we propose a natural
definition for quasinormal modes in an asymptotically AdS spacetime, with
boundary conditions dictated by the AdS/CFT correspondence. The corresponding
frequencies determine the dispersion laws for the quasiparticle excitations in
the dual finite-temperature gauge theory. Correlation functions of operators
dual to massive scalar, vector and gravitational perturbations in a
five-dimensional AdS-Schwarzschild background are considered. We find
asymptotic formulas for quasinormal frequencies in the massive scalar and
tensor cases, and an exact expression for vector perturbations. In the
long-distance, low-frequency limit we recover results of the hydrodynamic
approximation to thermal Yang-Mills theory.
