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Summer Graduate School

Mathematical General Relativity July 09, 2012 - July 20, 2012
Parent Program: Mathematical General Relativity
Location: Mathematical Sciences Research Institute, Berkeley CA
Organizers Justin Corvino* (Lafayette College) and Pengzi Miao (University of Miami)
Lecturer(s) No Lecturers Assigned Yet.
Speaker(s)

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Description

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


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Schedule
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Jul 09, 2012
Monday
09:15 AM - 09:30 AM
  Welcome to MSRI
09:30 AM - 10:45 AM
  Lecture (Justin Corvino)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Pengzi Miao)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Justin Corvino)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 10, 2012
Tuesday
09:30 AM - 10:45 AM
  Lecture (Pengzi Miao)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Justin Corvino)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Pengzi Miao)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 11, 2012
Wednesday
09:15 AM - 10:15 AM
  Lecture (Pengzi Miao)
10:15 AM - 10:30 AM
  Tea
10:15 AM - 10:30 AM
  Break
10:30 AM - 11:30 AM
  Break
10:30 AM - 11:30 AM
  Lecture (Justin Corvino)
11:30 AM - 02:00 PM
  BBQ Lunch at nearby park
11:30 AM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Justin Corvino/Pengzi Miao)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 12, 2012
Thursday
09:30 AM - 10:45 AM
  Lecture (Justin Corvino)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Pengzi Miao)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Justin Corvino)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 13, 2012
Friday
09:30 AM - 10:45 AM
  Lecture (Pengzi Miao)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Justin Corvino)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Pengzi Miao)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 16, 2012
Monday
09:30 AM - 10:45 AM
  Lecture (Fernando Schwartz)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Lan-Hsuan Huang)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Justin Corvino)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 17, 2012
Tuesday
09:30 AM - 10:45 AM
  Lecture (Fernando Schwartz)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Lan-Hsuan Huang)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Pengzi Miao)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 18, 2012
Wednesday
09:30 AM - 10:45 AM
  Lecture (Fernando Schwartz)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Lan-Hsuan Huang)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Justin Corvino)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
Jul 19, 2012
Thursday
09:30 AM - 10:45 AM
  Lecture (Fernando Schwartz)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Lan-Hsuan Huang)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (Pengzi Miao)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  TA Session
07:05 PM - 10:00 PM
  Oakland A's Baseball Game
Jul 20, 2012
Friday
09:30 AM - 10:45 AM
  Lecture (Fernando Schwartz)
10:45 AM - 11:15 AM
  Tea
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture (Lan-Hsuan Huang)
11:15 AM - 12:30 PM
  Break
12:30 PM - 02:00 PM
  Lunch
12:30 PM - 02:00 PM
  Break
02:00 PM - 03:15 PM
  Lecture (TBA)
02:00 PM - 03:15 PM
  Break
03:15 PM - 03:45 PM
  Tea
03:15 PM - 03:45 PM
  Break
03:45 PM - 05:00 PM
  Wrap Up (Justin Corvino/Pengzi Miao)