Thermally fluctuating superconductors in two dimensions

We describe the different regimes of finite temperature dynamics in the vicinity of a zero temperature superconductor to insulator quantum phase transition in two dimensions. New results are obtained for a low temperature phase-only hydrodynamics, and for the intermediate temperature quantum-critical region. In the latter case, we obtain a universal relationship between the frequency-dependence of the conductivity and the value of the d.c. resistance.