In this talk, we present a new method (PisCES) for finding time-varying community structure in dynamic networks. The method implements degree-corrected spectral clustering, with a smoothing term to promote similarity across time periods. We prove that this method converges to the global solution of a nonconvex optimization problem, which can be interpreted as the spectral relaxation of a smoothed K-means clustering objective. We also show that smoothing is applied in a time-varying and data-dependent manner; for example, when a drastic change point exists in the data, smoothing is automatically suppressed at the time of the change point. Finally, we show that the detected time-varying communities can be effectively visualized through the use of sankey plots.