# Summer Graduate School

Parent Program: |
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Location: |
FORTH, Greece |

## Show List of Lecturers

- Demetrios Christodoulou (ETH Zürich)

## Show List of Speakers

- Mihalis Dafermos (Princeton University)
- Juhi Jang (University of Southern California)
- Igor Rodnianski (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.

**Keywords and Mathematics Subject Classification (MSC)**

**Tags/Keywords**

general relativity

Einstein equations

black holes

spacetime singularities

Euler equations

compressible flows

self-gravitating fluids

gravitational collapse

**Primary Mathematics Subject Classification**

35L67 - Shocks and singularities for hyperbolic equations [See also 58Kxx, 74J40, 76L05]

35Q75 - PDEs in connection with relativity and gravitational theory

76Lxx - Shock waves and blast waves in fluid mechanics [See also 35L67]

76E20 - Stability and instability of geophysical and astrophysical flows

83C05 - Einstein's equations (general structure, canonical formalism, Cauchy problems)

**Secondary Mathematics Subject Classification**No Secondary AMS MSC