Historically, the first systematic approaches to finding optimal geometric structures have made use of variational approaches and/or elliptic PDEs. Ever since the work of Eells–Sampson and Hamilton, however, geometers have also embraced flows or parabolic methods, which are more dynamic in nature. Over the last thirty years, the mean curvature flow and the Ricci flow have become tremendously active areas of research. Highlights include Perelman’s spectacular proof of the Poincare and geometrization conjecture, the proof of the differentiable sphere theorem, and the analytic minimal model program. This workshop will feature some of the most exciting new developments in the field, such as progress on flows with surgery, various proposed notions of Ricci flow through singularities, and the classification of hypersurfaces with small entropy.