Speaker：

Philippe G. LeFloch (Sorbonne University and CNRS)

Title：

The initial value problem for the Einstein equations for massive fields

Abstract:

This series of lectures is devoted to recent advances on nonlinear PDE

systems of coupled wave and Klein-Gordon equations, especially on the

initial value problem for the Einstein equations of general

relativity, describing the evolution of a self-gravitating massive

field. I will present material on the structure of the Einstein

equations and the stability of their solutions, together with the

Euclidian-Hyperboloidal Foliation Method introduced by the speaker in

collaboration with Yue Ma (Xi'an Jiatong Univ). The latter is a novel

and versatile method of analysis which applies to a variety of

nonlinear wave-Klein-Gordon systems. For the convenience of the

audience, the lectures will be relatively independent from each other.

The first part of the course will provide a general overview of the

most important problems and results in the field, while in the final

lectures an outline of the technical elements of the

Euclidian-Hyperboloidal Foliation Method will be given. The course

will be accessible to graduate students. Some related papers can be

found at the link: https://philippelefloch.org

Note: The lecture will be given in a hybrid format

(only NLPDE seminar members may attend in person).

Date/Time：

(1) October 6, 2022 15：00 -- 16：15

(2) October 11, 2022 15：00 -- 16：15

(3) October 18, 2022 15：00 -- 16：15

(4) October 25, 2022 14：00 -- 15：15

*In Japan time (GMT+9)