主讲人 / Speaker

Sari Ghanem

BIMSA

时间 / Time

Wed., 11:00-12:30 & 14:00-15:30

2025 Spring Semester

(from Feb. 19, 2025)

地点 / Venue

A513, Shuangqing Complex Building A

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Dispersive estimates for non-linear waves

in mathematical General Relativity

课程介绍 / Description

This course introduces the tools of analysis for proving dispersive estimates for solutions of non-linear wave equations arising in General Relativity from the point of view of analysis and partial differential equations. The course material builds on one hand, on a previous course that I gave in the Spring 2024 on the Cauchy problem in mathematical General Relativity, and on the other hand, on a previous course that I gave in the Fall 2024 on non-linear wave equations in General Relativity. The goal of this course is to show a method to obtain dispersive estimates for solutions of tensorial coupled non-linear hyperbolic partial differential equations, provided that one exploits the non-linear structure of the wave equations. We shall exhibit how this can be applied in General Relativity for perturbations of the Minkowski space-time governed bytheEinstein-Yang-Mills system in the Lorenz gauge and in wave coordinates, by studying first the simpler case of higher dimensions.

Prerequisite:

Basic knowledge from my previous courses on “The Cauchy problem in mathematical General Relativity” and on “Non-linear wave equations in General Relativity”, graduate level knowledge in differential geometry, and in Riemannian geometry, and basic knowledge in partial differential equations and analysis.

Target Audience:

Graduate students, Postdoc, Researcher

主讲人简介 / About the Speaker

Sari Ghanem had his undergraduate education at Classe Préparatoire in Toulouse and completed his Master degree in Paris, and a second Master in the USA. Thereafter, he obtained his PhD in 2014 from the University of Paris VII (Institut de Mathématiques de Jussieu) under the supervision of Frédéric Hélein (Jussieu) and Vincent Moncrief (Yale University). He then worked as a postdoctoral fellow at the Albert Einstein Institute (Max-Planck Institute for Gravitational Physics), and at the University of Grenoble in France. Thereafter, he founded the Al-Khwarizmi-Noether Institute for mathematics (https://akn-institute.org/the-institute/about/) of which he was the creator and chair on a voluntary basis, and worked at the Universities of Hamburg and of Lübeck in Germany. Now, he is a research Visiting Assistant Professor at BIMSA in China.