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Summer Graduate School

Geometric Flows (Athens, Greece) June 15, 2020 - June 26, 2020
Parent Program: --
Location: Stavros Niarchos Foundation Cultural Center, Athens, Greece
Organizers Nicholas Alikakos (National and Kapodistrian University of Athens (University of Athens)), Panagiota Daskalopoulos (Columbia University)
Description
Image
photo courtesy of Panagiota Daskalopoulos

[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]

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 Poincaré onjecture,  as well as recent important developments related to the study of singularities and ancient solutions.

Suggested Prerequisites

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