3d Gravity, Universality and Poincare Series

Modular invariance plays an important role in the AdS3/CFT2 correspondence. Using modular invariance, I discuss under what conditions a 2d CFT shows a Hawking-Page phase transition in the largec limit, and what this implies for the range of validity of the Cardy formula and the universality of its spectrum. I will also discuss partition functions obtained by summing over the modular group, how their properties are compatible with their gravity interpretation, and briefly touch on implications for the existence of pure gravity.