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

Welcome to Mathematics of General Relativity and Fluids, Summer Graduate School 2024 : July 22 - August 2

This two week summer graduate school is a collaboration between SLMath and the IACM-FORTH Institute in Crete. The purpose of the school is to 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.

The 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.

Suggested 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).

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). pdf
  • M. Hadzic and J. Jang “Lectures on Dynamics of self-gravitating fluids”, in preparation.

Support for this summer school is provided by the Simons Laufer Mathematical Sciences Institute, Berkeley, CA and the European Research Council (ERC starting grant 2022, under the European Union's Horizon Europe program for research and innovation, project 101078061 SINGinGR).



Organizers

Mihalis Dafermos

Professor of Mathematics

Princeton University and University of Cambridge

dafermos@math.princeton.edu

Grigorios Fournodavlos

Assistant Professor of Mathematics

University of Crete

gfournodavlos@uoc.gr

Juhi Jang

Professor of Mathematics

University of Southern California

juhijang@usc.edu

Igor Rodnianski

Professor of Mathematics

Princeton University

irod@math.princeton.edu

Main lecturers

Mihalis Dafermos

Professor of Mathematics

Princeton University and University of Cambridge

Juhi Jang

Professor of Mathematics

University of Southern California

Igor Rodnianski

Professor of Mathematics

Princeton University

Guest lecturer

Demetrios Christodoulou

Professor of Mathematics

ETH Zürich

Research and problem discussions

Rita Teixeira da Costa

Assistant Professor of Mathematics

University of Cambridge

Georgios Moschidis

Assistant Professor of Mathematics

EPFL

Matthew Schrecker

EPSRC Research Fellow

University College London

Ryan Unger

Postdoctoral Researcher of Mathematics

Stanford University

Applications for admittance to the School - Eligibility

  • All students who have not been nominated through SLMath need to apply through IACM-FORTH, see How to apply

  • Students from Greek Institutions are especially encouraged to apply. While the school is aimed for graduate students, a few especially advanced undergraduate students from Greek Universities (only) will be considered as well.

  • Hotel accommodations and/or lunch at the Cultural Center will be provided to qualified applicants. Please indicate your interest.