Summer Graduate School
|Location:||Stavros Niarchos Foundation Cultural Center, Athens, Greece|
[The image on this vase from Minoan Crete, dated on 1500-2000 BC, resembles an ancient solution to the Curve shortening flow - one of the most basic geometric flows. The vase is at Heraklion Archaeological Museum]
The purpose of the workshop 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 Poincaré onjecture, as well as recent important developments related to the study of singularities and ancient solutions.
Students are expected to have a basic (advanced undergraduate or beginning graduate) background on elliptic and parabolic partial equations and Classical Riemannian Geometry. More precisely the students are expected to have the following background:
1. A basic course on Partial Differential Equations such as: L.C. Evans, Partial Differential Equations, Chapters 2 and 5-7
2. A basic course on Riemannian Geometry such as: Manfredo do Carmo, Riemannian Geometry, Chapters 1-8 or John Lee, Riemannian Manifolds.
For eligibility and how to apply, see the Summer Graduate Schools homepage
Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.
This summer graduate school is supported by the Stavros Niarchos Foundation
parabolic partial differential equations
mean curvature flow