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Geometric Flows

Geometric Flows

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Organized by Simon Brendle, Xiuxiong Chen, Simon Donaldson, and Yuanqi Wang
October 13 – December 19, 2014

Since its invention in 1982, Hamilton’s Ricci flow has become a central tool in global differential geometry. In particular, the Ricci flow has played a central role in Perelman’s proof of the Poincare conjecture, as well as in the proof of the Differentiable Sphere Theorem. Other geometric flows like mean curvature flow, inverse mean curvature flow have shed light on deep problems in the geometry of hypersurfaces.

In recent years, there has been exciting progress in many directions. In particular, there have been major advances in our understanding of singularity formation and soliton solutions. Furthermore, geometric flows in the Kahler setting, including Kahler-Ricci flow on manifolds of general type and the Calabi flow, have led to substantial progress on core problems in complex geometry.

In this program, we will bring together researchers in the area of elliptic and parabolic partial differential equations in Riemannian geometry, Kahler Geometry and Topology.