I will describe work in progress with Ooguri on the singularities of the two point function at finite temperature in a conformal field theory in more than two dimensions. At weak coupling the only singularity is on the light cone, but in the large N, large lambda regime a new singularity emerges. This new singularity corresponds to a null geodesic in the AdS/Schwarzschild black hole, which may wrap the photon sphere many times. After deriving this result, I will provide some preliminary evidence that these singularities are resolved by stringy effects at finite lambda. The basic tool I will use is to take the Penrose limit around a given null geodesic, and then use the solubility of the string theory in this background.