Summer Graduate School

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.