Summer Graduate School

Mathematical general relativity is the study of mathematical problems related to Einstein's theory of gravitation. There are interesting connections between the physical theory and problems in differential geometry and partial differential equations.

The purpose of the workshop is to introduce graduate students to some fundamental aspects of mathematical general relativity, with particular emphasis on the geometry of the Einstein constraint equations and the Positive Mass Theorem.  These topics will comprise a component of the upcoming semester program at MSRI in Fall 2013.

There will be mini-courses, as well as several research lectures. Students are expected to have had courses in graduate real analysis and Riemannian geometry, while a course in graduate-level partial differential equations is recommended.

Bibliography (PDF)
Intro to GR Notes (PDF)
Harmonic Function and AF metrics (PDF)
Intro-GR-Lecture (PDF)
Some Exact Solutions (PDF)
Causality Lecture 1 (PDF)
Causality Lecture 2 (PDF)
Causality Lecture 3 (PDF)
Basic Schw Probs (PDF)
Basic Scalar Probs (PDF)
Basic Geom Probs (PDF)
Basic pde Probs (PDF)
More on Schwarzschild Spacetime (PDF)
Riccati and Raychaudhuri Equations (PDF)
Singularity Theorems (PDF)
Prof. Lan-Hsuan Huang's Problems (PDF)
Prof. Lan-Hsuan Huang's Lecture Notes (PDF)
SV-CM Notes (PDF)
Parry-Scalar Field Dark Matter-Presentation (PDF)
Cauchy Problem and Cosmic Censorship (PDF)

For eligibility and how to apply, see the Summer Graduate Workshop homepage