Liouville Correlation Functions from Four-Dimensional Gauge Theories

We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2{mathcal{N}=2} SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0, 1.