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.
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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.
1.1 History and Spacetime 1.2 Properties (horizon, ergo-sphere, singularity) 1.3 Geodesics
Speaker: | Nicolas Yunes (Montana State University, USA) |
Material: | Video notes |
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 |
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 |
Speaker: | Piotr Chrusciel (University of Vienna, Austria) |
Material: | Video |
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 non-negative scalar curvature. From a physical point of view, notions of quasi-local 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 |
2.1 Formation Scenarios and Gravitational Wave Modeling 2.2 The Semi-Relativistic Approximation 2.3 Kludge Waveforms 2.4 The Self-Force
Speaker: | Nicolas Yunes (Montana State University, USA) |
Material: | Video notes |
Speaker: | Piotr Chrusciel (University of Vienna, Austria) |
Material: | Video |
Location: | Adriatico GuestHouse - Terrace |
All participants are cordially invited to attend the welcome reception.
Speaker: | Richard Schoen (UC Irvine, USA) |
Material: | Video |
First block: participants with family name initials from A to K.
Speaker: | Robert Wald (Chicago University, USA) |
Material: | Video |
3.1 The Landau-Lifshitz Formulation of General Relativity 3.2 The Relaxed Einstein Equations 3.3 The DIRE Approach 3.4 Post-Newtonian Waveforms
Speaker: | Nicolas Yunes (Montana State University, USA) |
Material: | Video notes |
Speaker: | Piotr Chrusciel (University of Vienna, Austria) |
Material: | Video |
4.1 Scalar Field Example 4.2 Schwarzschild Perturbation Theory
Speaker: | Nicolas Yunes (Montana State University, USA) |
Material: | Video notes |
Speaker: | Richard Schoen (UC Irvine, USA) |
Material: | Video |
Speaker: | Robert Wald (Chicago University, USA) |
Material: | Video |
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 half-meal coupons or by cash - Euros 10. Looking forward to seeing you with your friends and families! Hosted Activities Office
Location: | Leonardo Building Terrace |
Speaker: | Robert Wald (Chicago University, USA) |
Material: | Video |
Speaker: | Andras Vasy (Stanford University, USA) |
Material: | Video |
Speaker: | Richard Schoen (UC Irvine, USA) |
Material: | Video |
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 |
Speaker: | Leonardo Senatore (Stanford University, USA) |
Material: | Video |
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) |
The aim is to give a pedagogical introduction to AdS-CFT 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 Anti-deSitter (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 |
Speaker: | Harvey Reall (DAMTP, University of Cambridge, UK) |
Static black hole uniqueness theorems, including newer developments about higher dimensions, non-vacuum settings, and photon sphere uniqueness.
Speaker: | Carla Cederbaum (University of Tubingen, Germany) |
Material: | Video |
Speaker: | Toby Wiseman (Imperial College London, UK) |
Material: | Video |
Speaker: | Mihalis Dafermos (Princeton University, USA and University of Cambridge, UK) |
Material: | Video |
Speaker: | Toby Wiseman (Imperial College London, UK) |
Material: | Video |
Second block: participants with family name initials from L to Z.
Speaker: | Carla Cederbaum (University of Tubingen, Germany) |
Material: | Video |
Speaker: | Harvey Reall (DAMTP, University of Cambridge, UK) |
Speaker: | Mihalis Dafermos (Princeton University, USA and University of Cambridge, UK) |
Material: | Video |
Speaker: | Harvey Reall (DAMTP, University of Cambridge, UK) |
Speaker: | Carla Cederbaum (University of Tubingen, Germany) |
Material: | Video |
Speaker: | Toby Wiseman (Imperial College London, UK) |
Material: | Video |
Speaker: | Carla Cederbaum (University of Tubingen, Germany) |
Material: | Video |
Speaker: | Mihalis Dafermos (Princeton University, USA and University of Cambridge, UK) |
Material: | Video |