Conductivity of thermally fluctuating superconductors in two dimensions

We review recent work on a continuum, classical theory of thermal fluctuations in two-dimensional superconductors. A functional integral over a Ginzburg-Landau free energy describes the amplitude and phase fluctuations responsible for the crossover from Gaussian fluctuations of the superconducting order at high temperatures, to the vortex physics of the Kosterlitz-Thouless transition at lower temperatures. Results on the structure of this crossover are presented, including new results for corrections to the Aslamazov-Larkin fluctuation conductivity