MGR Programmatic Seminar: Numerically evolving the Ricci Flow on S^3

REULA, O.; PARISI, FLORENCIA; GOMEZ, SANTIAGO; BEDERIAN, CARLOS

Berkeley

Otro; MSRI Program in Mathematical General Relativity; 2013

Mathematical Sciences Research Institute

In this talk I will discuss some attempts to evolve a Ricci Flows in S^3. I will focus in different types of problems that arise in this activity: Some analytical ones, among them, which are the convenient gauge choices, which are the questions one would like to answer (hopping on getting some feedback from the audience), and the way to extract relevant global information from the numerical solution. On the other hand, evolving numerically partial differential equations on manifolds with non-trivial topology implies the use of multiple grids, each one representing a coordinate patch, and the union of them, a chart for the underlying manifold. So numerical techniques to deal with these situations have to be properly implemented so that information from one of the grids can be carried to the others, and how to prevent spurious solutions to appear and dominate the evolution. https://www.msri.org/seminars/20381