Evolution Equations In Geometry

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

Evolution equations are basic objects in the sciences, describing how natural phenomena change over time. For instance, modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. Other natural evolutions leads to other equations, many of parabolic type, e.g. Ricci flow, and many have common features. Broader impacts of the project are through mentoring graduate students and young researchers, organizing seminars, and the writing of textbooks and expository articles. The bulk of this project concerns evolution equations. Mean curvature flow, as well as new methods for dealing with the diffeomorphism group for non compact spaces with applications to Ricci flow, will be major topics investigated. Other natural evolution equations coming from various branches of sciences will be studied as well as part of the project. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.