Geometric Flows

This summer graduate school is a collabroation between MSRI and the FORTH-IACM Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations. This is an area of geometric analysis that lies at the interface of differential geometry and partial differential equations. The lectures will begin with an introduction to nonlinear diffusion equations and continue with classical results on the Ricci Flow, the Mean curvature flow and other fully non-linear extrinsic flows such as the Gauss curvature flow. The lectures will also include geometric applications such as isoperimetric inequalities, topological applications such as the Poincar? onjecture, as well as recent important developments related to the study of singularities and ancient solutions.