Description 
The purpose of the School is to expose graduate students and young researchers to a variety of topics, techniques and lines of research of common interest to geometers and physicists. The activity is intended for theoretical physicists and mathematicians with knowledge of Differential geometry and General Relativity.
Topics:
School Lectures: C. CEDERBAUM, University of Tubingen, Germany P. CHRUSCIEL, University of Vienna, Austria M. DAFERMOS, Princeton University, USA and University of Cambridge, UK H. REALL, DAMTP, University of Cambridge, UK R. SCHOEN, University of California Irvine, USA R. WALD, University of Chicago, USA T. WISEMAN, Imperial College London, UK N. YUNES, Montana State University, USA Grants:
A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee.

ICTP School on Geometry and Gravity  (smr 3311)
Go to day


08:30  17:15

08:30
Administrative and Financial formalities
1h0' (
Leonardo Building Lobby
)
REGISTRATION: Upon arrival, Visitors not staying in the ICTP Guest Houses, are kindly requested to complete registration formalities at the Leonardo Building (Lobby) from 8.30 till 9.30 TRAVEL UNIT (Only for those Visitors receiving daily living allowance/travel reimbursement) Only after having completed registration formalities, please go to the Travel Unit, EF, Main Entrance, Room T17, ground floor, open two days: Monday and Friday, 08.30  12.00 and 13.30  14.30 Please bring with you: badge/identity card or passport/any travel tickets and boarding passes, if reimbursement due.

09:30
Black Holes, Binary Systems, and Gravitational Waves  1. Kerr Black Hole
1h15'
1.1 History and Spacetime 1.2 Properties (horizon, ergosphere, singularity) 1.3 Geodesics
Speaker: Nicolas Yunes (Montana State University, USA) Material: Video notes  10:45 Coffee break 45'

11:30
Introduction to mass and energy in general relativity  Lecture 1
1h15'
Various approaches to the definition of total mass and energy in general relativity for asymptotically flat and asymptotically hyperbolic Riemannian manifolds, and sketch various elementary proofs of positivity will be described.
Speaker: Piotr Chrusciel (University of Vienna, Austria) Material: Link Video  12:45 Lunch break 1h30'

14:15
Black Hole Thermodynamics  Lecture 1
1h15'
These lectures will give a comprehensive introduction to black hole thermodynamics. The basic properties of black holes will be reviewed. The first law of black hole mechanics will be derived, and the notion of black hole entropy will be thereby introduced. The notion of canonical energy will be introduced and used to show that dynamical stability of a black hole is equivalent to its thermodynamic stability. A brief discussion will be given of quantum aspects of black hole thermodynamics.
Speaker: Robert Wald (Chicago University, USA) Material: Slides Video  15:30 Break 30'

16:00
Introduction to mass and energy in general relativity  Lecture 2
1h15'
Speaker: Piotr Chrusciel (University of Vienna, Austria) Material: Video

08:30
Administrative and Financial formalities
1h0' (
Leonardo Building Lobby
)

08:30  17:15


09:30  17:15

09:30
Some geometric properties of spacetime  Lecture 1
1h15'
The Einstein equations imply certain curvature inequalities on spacelike hypersurfaces in spacetime. These inequalities are responsible for successful notions of gravitational mass and energy, and they impose certain local constraints on the geometry. In the simplest case this leads to the study of Riemannian manifolds with nonnegative scalar curvature. From a physical point of view, notions of quasilocal mass and their positivity, are a reflection of such local constraints. From a geometric point of view comparison with a model space is a basic notion. In recent years both of these directions have been very active, and some of the results that have been obtained will be introduced and compared. In many of these results involving scalar curvature, the theory of stable minimal hypersurfaces plays a key role. In the general case this is replaced by the theory of stable MOTS (marginally outer trapped surfaces). This more general theory and some of its applications will be discussed.
Speaker: Richard Schoen (UC Irvine, USA) Material: Video  10:45 Coffee break 45'

11:30
Black Holes, Binary Systems, and Gravitational Waves  2. Extreme massratio inspirals
1h15'
2.1 Formation Scenarios and Gravitational Wave Modeling 2.2 The SemiRelativistic Approximation 2.3 Kludge Waveforms 2.4 The SelfForce
Speaker: Nicolas Yunes (Montana State University, USA) Material: Video notes  12:45 Lunch break 1h30'

14:15
Introduction to mass and energy in general relativity  Lecture 3
1h15'
Speaker: Piotr Chrusciel (University of Vienna, Austria) Material: Video  15:30 Break 30'

16:00
Discussion session
1h15'

09:30
Some geometric properties of spacetime  Lecture 1
1h15'

19:30  21:30
Location: Adriatico GuestHouse  Terrace 
19:30
Welcome reception
2h0'
All participants are cordially invited to attend the welcome reception.

19:30
Welcome reception
2h0'

09:30  17:15


09:30  17:15

09:30
Some geometric properties of spacetime  Lecture 2
1h15'
Speaker: Richard Schoen (UC Irvine, USA) Material: Video 
10:45
Poster session and coffee break
45'
First block: participants with family name initials from A to K.

11:30
Black Hole Thermodynamics  Lecture 2
1h15'
Speaker: Robert Wald (Chicago University, USA) Material: Video  12:45 Lunch break 1h30'

14:15
Black Holes, Binary Systems, and Gravitational Waves  3. ComparableMass Binaries
1h15'
3.1 The LandauLifshitz Formulation of General Relativity 3.2 The Relaxed Einstein Equations 3.3 The DIRE Approach 3.4 PostNewtonian Waveforms
Speaker: Nicolas Yunes (Montana State University, USA) Material: Video notes  15:30 Break 30'

16:00
Introduction to mass and energy in general relativity  Lecture 4
1h15'
Speaker: Piotr Chrusciel (University of Vienna, Austria) Material: Video

09:30
Some geometric properties of spacetime  Lecture 2
1h15'

09:30  17:15


09:30  17:15

09:30
Black Holes, Binary Systems, and Gravitational Waves  4. Black Hole Perturbation Theory
1h15'
4.1 Scalar Field Example 4.2 Schwarzschild Perturbation Theory
Speaker: Nicolas Yunes (Montana State University, USA) Material: Video notes  10:45 Coffee break 45'

11:30
Some geometric properties of spacetime  Lecture 3
1h15'
Speaker: Richard Schoen (UC Irvine, USA) Material: Video  12:45 Lunch break 1h30'

14:15
Black Hole Thermodynamics  Lecture 3
1h15'
Speaker: Robert Wald (Chicago University, USA) Material: Video  15:30 Group Photo 5'
 15:35 Break 25'

16:00
Discussion Session
1h15'

09:30
Black Holes, Binary Systems, and Gravitational Waves  4. Black Hole Perturbation Theory
1h15'

19:30  23:00
ICTP SOCIAL EVENT  "From Africa to Asia"
There's no better place to celebrate summer than an "African Asian" party at the ICTP featuring live percussionists and performers plus great dance music from all continents with DJ Patrick! Join the party at the Leonardo Building Terrace on Thursday 18 July 2019 from 19:30 to 23:00 hrs! A special buffet dinner will be served at the Leonardo Cafeteria starting at 19:30 and payable with two halfmeal coupons or by cash  Euros 10. Looking forward to seeing you with your friends and families! Hosted Activities Office
Location: Leonardo Building Terrace

09:30  17:15


09:30  15:30

09:30
Black Hole Thermodynamics  Lecture 4
1h15'
Speaker: Robert Wald (Chicago University, USA) Material: Video  10:45 Coffee break 45'

11:30
Black hole stability: global and microlocal analysis aspects
1h15'
Speaker: Andras Vasy (Stanford University, USA) Material: Video  12:45 Lunch break 1h30'

14:15
Some geometric properties of spacetime  Lecture 4
1h15'
Speaker: Richard Schoen (UC Irvine, USA) Material: Video

09:30
Black Hole Thermodynamics  Lecture 4
1h15'

09:30  15:30


09:30  17:15

09:30
The cosmic censorship conjectures in general relativity  Lecture 1
1h15'
It will be given an introduction to the cosmic censorship conjectures (both weak and strong) in classical general relativity and related issues concerning the structure of spacetime singularities. The collapse of self gravitating matter under spherical symmetry will provide an elementary setting for understanding many of the issues involved. The course will review basic material (initial value problem, Penrose diagrams) as necessary.
Speaker: Mihalis Dafermos (Princeton University, USA and University of Cambridge, UK) Material: Video  10:45 Coffee break 45'

11:30
Asymptotic Behaviour of Cosmologies with Lambda >0
1h15'
Speaker: Leonardo Senatore (Stanford University, USA) Material: Video  12:45 Lunch break 1h30'

14:15
The initial value problem for gravitational theories  Lecture 1
1h15'
Effective field theories of gravity; the initial value problem for GR; the initial value problem for theories beyond GR
Speaker: Harvey Reall (DAMTP, University of Cambridge, UK)  15:30 Break 30'

16:00
Introduction to the AdSCFT conjecture from a GR perspective  Lecture 1
1h15'
The aim is to give a pedagogical introduction to AdSCFT emphasising the GR and geometrical aspects of it. Description of how the conjecture relates certain field theories (CFTs) to certain quantum gravitational theories in asymptotically AntideSitter (AdS) spacetimes. Discussion about why this is interesting, and why the conjecture should be taken seriously. Focus on the explicit map between the two theories when the gravitational side has classical geometric character. Description of how certain field theory observables are mapped to geometric objects, and how geometry can then constrain and determine their behaviour. Discussion on some interesting open geometric questions which fall in the remit of mathematical GR.
Speaker: Toby Wiseman (Imperial College London, UK) Material: Video

09:30
The cosmic censorship conjectures in general relativity  Lecture 1
1h15'

09:30  17:15


09:30  17:15

09:30
The initial value problem for gravitational theories  Lecture 2
1h15'
Speaker: Harvey Reall (DAMTP, University of Cambridge, UK)  10:45 Coffee break 45'

11:30
Static black hole uniqueness theorems  Lecture 1
1h15'
Static black hole uniqueness theorems, including newer developments about higher dimensions, nonvacuum settings, and photon sphere uniqueness.
Speaker: Carla Cederbaum (University of Tubingen, Germany) Material: Video  12:45 Lunch break 1h30'

14:15
Introduction to the AdSCFT conjecture from a GR perspective  Lecture 2
1h15'
Speaker: Toby Wiseman (Imperial College London, UK) Material: Video  15:30 Break 30'

16:00
The cosmic censorship conjectures in general relativity  Lecture 2
1h15'
Speaker: Mihalis Dafermos (Princeton University, USA and University of Cambridge, UK) Material: Video

09:30
The initial value problem for gravitational theories  Lecture 2
1h15'

09:30  17:15


09:30  17:15

09:30
Introduction to the AdSCFT conjecture from a GR perspective  Lecture 3
1h15'
Speaker: Toby Wiseman (Imperial College London, UK) Material: Video 
10:45
Poster session and coffee break
45'
Second block: participants with family name initials from L to Z.

11:30
Static black hole uniqueness theorems  Lecture 2
1h15'
Speaker: Carla Cederbaum (University of Tubingen, Germany) Material: Video  12:45 Lunch break 1h30'

14:15
The initial value problem for gravitational theories  Lecture 3
1h15'
Speaker: Harvey Reall (DAMTP, University of Cambridge, UK)  15:30 Break 30'

16:00
The cosmic censorship conjectures in general relativity  Lecture 3
1h15'
Speaker: Mihalis Dafermos (Princeton University, USA and University of Cambridge, UK) Material: Video

09:30
Introduction to the AdSCFT conjecture from a GR perspective  Lecture 3
1h15'

09:30  17:15


09:30  17:15

09:30
The initial value problem for gravitational theories  Lecture 4
1h15'
Speaker: Harvey Reall (DAMTP, University of Cambridge, UK)  10:45 Coffee break 45'

11:30
Static black hole uniqueness theorems  Lecture 3
1h15'
Speaker: Carla Cederbaum (University of Tubingen, Germany) Material: Video  12:45 Lunch break 1h30'

14:15
Introduction to the AdSCFT conjecture from a GR perspective  Lecture 4
1h15'
Speaker: Toby Wiseman (Imperial College London, UK) Material: Video  15:30 Group Photo 5'
 15:35 Break 25'

16:00
Discussion session
1h15'

09:30
The initial value problem for gravitational theories  Lecture 4
1h15'

09:30  17:15


09:30  12:45

09:30
Static black hole uniqueness theorems  Lecture 4
1h15'
Speaker: Carla Cederbaum (University of Tubingen, Germany) Material: Video  10:45 Coffee break 45'

11:30
The cosmic censorship conjectures in general relativity  Lecture 4
1h15'
Speaker: Mihalis Dafermos (Princeton University, USA and University of Cambridge, UK) Material: Video

09:30
Static black hole uniqueness theorems  Lecture 4
1h15'

09:30  12:45