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Summer Graduate School

Mathematics of General Relativity and Fluids (FORTH, Greece) July 21, 2024 - August 02, 2024
Parent Program: --
Location: FORTH, Greece
Organizers LEAD Mihalis Dafermos (Princeton University), Grigorios Fournodavlos (University of Crete), Juhi Jang (University of Southern California), Igor Rodnianski (Princeton University)
Lecturer(s)

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Speaker(s)

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Description
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ALCF Visualization and Data Analytics Team; Adam Burrows and the Princeton Supernova Theory Group, Princeton University

This summer school will give an accessible introduction to the mathematical study of general relativity, a field which in the past has had barriers to entry due to its interdisciplinary nature, and whose study has been concentrated at specific institutions, to a wider audience of students studying at institutions throughout the U.S., Europe and Greece. Another goal of the summer school will be to demonstrate the common underlying mathematical themes in many problems which traditionally have been studied by separate research communities.

This school will introduce graduate students to some of the main problems of current interest in the mathematical study of general relativity and fluid mechanics, centered mainly around the Einstein equations and the compressible Euler equations, and related systems, and centered around themes such as singularity formation, black holes, stabilities and instabilities, and shock formation.

School Structure

The daily schedule consists centrally of two or three lectures per day, interspersed with open problem sessions, discussions, tutorials and other scientific activities.

Prerequisites

A standard first year graduate analysis courses in real and functional analysis. Some previous exposure to PDE’s and very basic concepts of differential geometry will be useful, but most of this material will be introduced by hand in the lectures. All necessary basic material from analysis and differential geometry which will be referred to in the course is reviewed in accessible form in the textbook: H. Ringstrom “The Cauchy problem in general relativity”, EMS Press, 2009 (see in particular Part I for a review of basic first-year analysis and Section 10.1 for a review of manifolds).

Resources

Useful additional references for the material lectured in the school itself include, besides Ringstrom’s textbook, the following:

  • S. Aretakis “Dynamics of Extremal Black holes”, Springer Briefs in Mathematical Physics, 2020, (Part I, Sections 1–2)
  • M. Dafermos and I. Rodnianski “Lectures on black holes and linear waves”, Proceedings of the Clay Summer School, 2013 (Sections 1–3)
  • M. Hadzic and J. Jang “Lectures on Dynamics of self-gravitating fluids”, in preparation.

Application Procedure

SLMath is only able to support a limited number of students to attend this school.  Therefore, it is likely that only one student per institution will be funded by SLMath.

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

Venue

The summer school will be held at the Foundation for Research and Technology (ITE), Iraklio, Crete. The participants will be housed near the facilities.


Schedule, Notes/Handouts & Videos
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Jul 22, 2024
Monday
09:00 AM - 09:15 AM
  Welcome to SLMath
09:30 AM - 10:30 AM
  Lecture: Chapter 1 of ETH lecture notes
Mihalis Dafermos (Princeton University)
10:30 AM - 10:40 AM
  Break
10:40 AM - 12:00 PM
  Coffee Break
10:40 AM - 11:40 AM
  Tutorial
Ryan Unger (Princeton University)
12:00 PM - 01:00 PM
  Lecture: Black holes I
Mihalis Dafermos (Princeton University)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Ryan Unger (Princeton University)
Jul 23, 2024
Tuesday
09:30 AM - 10:30 AM
  Lecture: Compressible Euler flows
Juhi Jang (University of Southern California)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Lecture: Black holes II
Mihalis Dafermos (Princeton University)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Tutorial
Ryan Unger (Princeton University)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Ryan Unger (Princeton University)
Jul 24, 2024
Wednesday
09:30 AM - 10:30 AM
  Tutorial
Serban Cicortas (Princeton University)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Tutorial
Serban Cicortas (Princeton University)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Lecture: Hyerbolic conservation laws I
Matthew Shrecker (University College London)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Matthew Shrecker (University College London)
Jul 25, 2024
Thursday
09:30 AM - 10:30 AM
  Tutorial: Hyerbolic conservation laws II
Matthew Shrecker (University College London)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Lecture: Vacuum Free boundary problems
Juhi Jang (University of Southern California)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Lecture: Vaccum Free boundary problems II
Juhi Jang (University of Southern California)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Matthew Shrecker (University College London)
Jul 26, 2024
Friday
09:30 AM - 10:30 AM
  Tutorial: Newtonian gravitational Collapse I
Matthew Shrecker (University College London)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Lecture: Fluids I
Igor Rodnianski (Princeton University)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Lecture: Fluids II
Igor Rodnianski (Princeton University)
01:00 PM - 02:30 PM
  Lunch Break
Jul 29, 2024
Monday
09:30 AM - 10:30 AM
  Tutorial
Serban Cicortas (Princeton University), Warren Li (Princeton University)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Tutorial
Serban Cicortas (Princeton University), Warren Li (Princeton University)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Tutorial: Newtonian gravitational Collapse II
Matthew Shrecker (University College London)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Serban Cicortas (Princeton University)
Jul 30, 2024
Tuesday
09:30 AM - 10:30 AM
  Lecture
Demetrios Christodoulou (ETH Zürich)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Tutorial
Rita Teixeira da Costa (Princeton University)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Lecture: T-boundedness and Morawetz
Mihalis Dafermos (Princeton University)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Warren Li (Princeton University)
Jul 31, 2024
Wednesday
09:30 AM - 10:30 AM
  Tutorial
Georgios Moschidis (University of California, Berkeley)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Tutorial
Georgios Moschidis (University of California, Berkeley)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Lecture: Naked Singularities in vacuum I
Igor Rodnianski (Princeton University)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Rita Teixeira da Costa (Princeton University)
Aug 01, 2024
Thursday
09:30 AM - 10:30 AM
  Lecture
Demetrios Christodoulou (ETH Zürich)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Tutorial
Rita Teixeira da Costa (Princeton University)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Lecture: Naked singularities in vacuum II
Igor Rodnianski (Princeton University)
01:00 PM - 02:30 PM
  Lunch Break
02:30 PM - 04:30 PM
  Problem Session
Georgios Moschidis (University of California, Berkeley)
Aug 02, 2024
Friday
09:30 AM - 10:30 AM
  Lecture
Demetrios Christodoulou (ETH Zürich)
10:30 AM - 10:40 AM
  Break
10:40 AM - 11:40 AM
  Lecture: Naked singularities Einstein-Euler
Juhi Jang (University of Southern California)
11:40 AM - 12:00 PM
  Coffee Break
12:00 PM - 01:00 PM
  Lecture: Redshift effect, Aretakis instability, Event horizon jumping
Mihalis Dafermos (Princeton University)
01:00 PM - 02:30 PM
  Lunch Break