A number of interesting problems in physics can be phrased in terms of connection problems of ordinary differential equations. These are deeply connected to a class of Riemann-Hilbert problem which was recently solved using techniques from conformal field theory. In this talk, I'll summarize a procedure which uses c=1 conformal blocks to compute scalar and vector quasinormal modes of black holes in anti-de Sitter spaces in five dimensions. After discussing instabilities and physical implications, I'll outline a similar method for quasinormal modes of the four-dimensional Kerr black holes, based on irregular conformal blocks at c=1.