Geometric flows are powerful tools for tackling important problems across diverse areas in geometry and topology, and beyond. Spectacular successes go back at least to Donaldson’s work on the Hitchin-Kobayashi correspondence, and continue to the present, with the proofs of the Poincare and Geometrization Conjectures, the Differentiable Sphere Theorem, the proof the Anderson-Cheeger-Colding-Tian conjecture in dimension three, and the Generalized Smale Conjecture. There are still many key open problems in a range of areas for which geometric flows provide a natural approach.

To realize the large number of striking potential applications of geometric flows one needs two major inputs. On the one hand, major breakthroughs in the analysis of the nonlinear partial differential equations arising in geometric flows are clearly required. On the other hand, essential input is needed from the particular geometric or topological situation under consideration. The main objective of this workshop was to bring together a range of researchers in geometry and topology, whose research interests were closely aligned to topics where geometric flows either already or are expected to play a key role, with experts in the analysis of geometric flows.