# ESI-EMS-IAMP Summer school on Mathematical Relativity

# Erwin Schrödinger Institute, Vienna, July 28- August 1, 2014

Lectures will take place in the Lise Meitner Lecture Hall, Faculty of Physics, Strudlhofgasse 4, A 1090 Wien

Registration starts at 8.45 on Monday July 28 in front of the Lise Meitner Lecture Hall

The lectures start at 9.30 on Monday, and at 9.00 the remaining days

On Tuesday evening at 19.00, Classical and Quantum Gravity invites all participants for a glass of wine at the Weinhof Zimmermann, Mitterwurzergasse 20, 1190 Wien (you can get there from the Faculty of Physics with the tramway 37 or 38 and bus 35A; and from the Franz Jozef Hotel with the bus 39A).

Outline of schedule [click here for a detailed schedule in pdf format]:

Monday: | L1 | L1 | L2 | L2 | L3 | L4 |

Tuesday: | L2 | L3 | L3 | L4 | L5 | L6 |

Wednesday: | L3 | L4 | L5 | |||

Thursday: | L4 | L5 | L5 | L6 | L6 | L7 |

Friday: | L3 | L4 | L7 | L5 | L6 | L6 |

- L1: "Introduction to differential geometry" by Robert Beig; two hours [slides]
- L2: "Introduction to general relativity" by Marc Mars; three hours [slides]
- L3: "Lorentzian causality" by Gregory Galloway; five hours [slides] [Lecture notes]
- L4: "Constraint equations" by Justin Corvino (Lafayette); five hours [slides] [problem sheets]
- L5: "The Evolution problem in General Relativity" by Hans Ringstroem (KTH Stockholm): five hours [reading materials]
- L6: "Wave equations on black hole space-times" by Gustav Holzegel (Imperial, London); five hours
- L7: "The galactic center" by Stefan Gillessen (Max-Planck-Institut für extraterrestrische Physik, Garching); two hours

- for L1 and L3: B. O'Neill, "Semi-Riemannian Geometry with Applications to Relativity"; Christian Bär's Erweitertes Skript zur Vorlesung Differentialgeometrie aus dem SS 2006 (in german)
- for L1 and L2: early chapters of the Lecture Notes on General Relativity by S. Aretakis; Christian Bär's Skript zur Vorlesung über Lorentzgeometrie aus dem Sommersemester 2004 (in german); Vienna lecture notes by P.T.Chruściel
- for L3: Lecture Notes on Lorentzian Causality and slides by G. Galloway
- for L5: a general knowledge of Semi-Riemannian geometry, measure and integration theory, Fourier analysis and PDE is recommended. Example references include O'Neill's Semi-Riemannian Geometry, Rudin's Real and complex analysis, or Evan's book on PDE
- for L6: Lectures on black holes and linear waves by M. Dafermos and I. Rodnianski; Chapters 8-10 of the Lecture Notes on General Relativity by S. Aretakis. On a more general level, the PDE book by L.C. Evans Partial differential equations, American Mathematical Society, Providence, RI, 2010 will be useful.