Sep 09, 2013
Monday

09:15 AM  09:30 AM


Welcome

 Location
 MSRI: Simons Auditorium
 Video


 Abstract
 
 Supplements



09:30 AM  10:30 AM


Spacetime Geometry: A Setting for General Relativity
Daniel Pollack (University of Washington)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


The Einstein Field Equations: A PDE Perspective
Daniel Pollack (University of Washington)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


The conformal method of constructing Cauchy data for the Einstein equations
David Maxwell (University of Alaska)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 Initial data for the Cauchy problem in general relativity cannot be freely specified, but must solve an underdetermined system of PDEs known as the Einstein constraint equations. This twopart series of lectures discusses the conformal method and its cousins, which are the most prevalent techniques used for constructing solutions of the constraint equations. The talks will include a development of the conformal method, as well as a discussion of more recent results in the field and remaining open problems.
 Supplements

Notes
334 KB application/pdf

Notes
238 KB application/pdf


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



04:00 PM  05:00 PM


MSRI Evans Talk: On the topology of black holes and beyond.
Greg Galloway (University of Miami)

 Location
 Evans Hall
 Video


 Abstract
 There is a widely held belief in physics that a true astrophysical black hole, formed from the gravitational collapse of some stellar object, can be described by a certain exact solution to the Einstein equations discovered by Kerr in the 60's. This belief is based largely on a series of powerful results which shows that the Kerr solution is the unique solution to the vacuum (sourcefree) Einstein equations with certain prescribed properties. A basic step in the proof is Hawking's theorem on the topology of black holes which asserts that, under physically natural conditions, the surface of a black hole (crosssection of the event horizon) must be topologically a 2sphere.
Various developments in string theory have generated a great deal of interest in gravity in higher dimensions and, in particular, in higher dimensional black holes. The remarkable discovery of Emparan and Reall of a 4+1 dimensional vacuum black hole solution to the Einstein equations with nonspherical horizon topology raised the question as to what horizon topologies are allowable in higher dimensions.
In this talk we review Hawking's theorem on the topology of black holes in 3+1 dimensions and present a generalization of it to higher dimensions. The latter is a geometric result which places restrictions on the topology of black holes in higher dimensions. We shall also discuss recent work on the topology of space exterior to a black hole. This is closely connected to the Principle of Topological Censorship, which roughly asserts that the topology of the region outside of all black holes (and white holes) should be simple. All of the results to be discussed rely on the recently developed theory of marginally outer trapped surfaces, which are natural spacetime analogues of minimal surfaces in Riemannian geometry.
This talk is based primarily on joint work with Rick Schoen and with Michael Eichmair and Dan Pollack
 Supplements




Sep 10, 2013
Tuesday

09:30 AM  10:30 AM


Introduction to decay of fields outside black holes.
Pieter Blue (University of Edinburgh)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements

Notes
258 KB application/pdf


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


The conformal method of constructing Cauchy data for the Einstein equations
David Maxwell (University of Alaska)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 nitial data for the Cauchy problem in general relativity cannot be freely specified, but must solve an underdetermined system of PDEs known as the Einstein constraint equations. This twopart series of lectures discusses the conformal method and its cousins, which are the most prevalent techniques used for constructing solutions of the constraint equations. The talks will include a development of the conformal method, as well as a discussion of more recent results in the field and remaining open problems.
 Supplements

Notes
238 KB application/pdf


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


The cosmic censorship conjectures
Mihalis Dafermos (Princeton University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements

Notes
179 KB application/pdf


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Constructing localized solutions of the Einstein constraint equations
Richard Schoen (University of California, Irvine)

 Location
 MSRI: Simons Auditorium
 Video


 Abstract
 There are obstructions, such as the postive mass theorem, which require that general solutions of the Einstein equations must have nonvanishing asymptotic terms at infinity, and so cannot be localized. The extent to which they can be localized in light of these obstructions leads to constructions of interesting solutions with very special asymptotic behavior. We will describe such results and how they are obtained in this talk
 Supplements

Notes
177 KB application/pdf


04:30 PM  06:20 PM


Reception

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements




Sep 11, 2013
Wednesday

09:30 AM  10:30 AM


Further topics in decay of fields outside black holes.
Pieter Blue (University of Edinburgh)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements

Notes
189 KB application/pdf


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


The cosmic censorship conjectures
Mihalis Dafermos (Princeton University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements

Notes
142 KB application/pdf



Sep 12, 2013
Thursday

09:30 AM  10:30 AM


Quasilocal mass in general relativity
MuTao Wang (Columbia University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 One of the greatest accomplishments of the theory of general relativity in the past century is the proof of the positive mass/energy theorem for asymptotically flat spacetimes. However, the concept of mass/energy remains a challenging problem because of the lack of a quasilocal description. Most observable physical models are finitely extended spatial regions and measurement of mass/energy on such a region is essential in many fundamental issues. In my talks, I shall first survey several notions of quasilocal mass including the Hawking mass, the Bartnik mass, the BrownYork mass, and their applications. At the end, I shall describe a new proposal of quasilocal mass/energy and discuss its application in the invariant mass conjecture of general relativity.
 Supplements

Notes
168 KB application/pdf

Notes
168 KB application/pdf


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Null hypersurfaces in Lorentzian spacetimes
Lydia Bieri (University of Michigan)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 In the mathematical theory of general relativity, null hypersurfaces in Lorentzian spacetimes play a crucial role. In this talk, I introduce null geodesic vector fields, which are used to construct null hypersurfaces. Then the most important geometric features of such hypersurfaces are discussed, including the definitions of shear and torsion. We give an overview of the analysis of the latter. This will be used to explain gravitational radiation in the second talk. Results on structure and asymptotic behavior of null hypersurfaces yield insight into gravitational waves.
 Supplements

Notes
179 KB application/pdf


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Density Theorems for the Einstein Constraint Equations
LanHsuan Huang (University of Connecticut)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 We will start with a beautiful theorem of Corvino and Schoen which says that the asymptotically flat initial data sets with harmonic asymptotics are dense among general initial data sets. Then we will discuss several generalizations of the density theorem and their applications in the positive mass theorem and the constructions relating to the center of mass and angular momentum.
 Supplements

Notes
155 KB application/pdf


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


An introduction to the Penrose inequality conjecture
Marc Mars (University of Salamanca)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 The Penrose inequality is a conjecture relating the total mass of asymptotically flat spacetimes satisfying appropriate curvature conditions and the area of certain closed, spacelike and codimensiontwo surfaces describing black holes from a quasilocal perspective. This conjecture is motivated by physical properties of black holes and has been proven in a number of particular but very interesting cases, mainly concerning the socalled Riemannian Penrose inequality.
In this talk I will present the general inequality, explain in which sense it is supported by black hole physics and describe several known results in the Riemannian case, including recent results for graphs in Euclidean space where the proof becomes particularly simple. If time permits, an approach to the inequality in the general case will also be mentioned.
 Supplements

Notes
359 KB application/pdf



Sep 13, 2013
Friday

09:30 AM  10:30 AM


Quasilocal mass in general relativity
MuTao Wang (Columbia University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 One of the greatest accomplishments of the theory of general relativity in the past century is the proof of the positive mass/energy theorem for asymptotically flat spacetimes. However, the concept of mass/energy remains a challenging problem because of the lack of a quasilocal description. Most observable physical models are finitely extended spatial regions and measurement of mass/energy on such a region is essential in many fundamental issues. In my talks, I shall first survey several notions of quasilocal mass including the Hawking mass, the Bartnik mass, the BrownYork mass, and their applications. At the end, I shall describe a new proposal of quasilocal mass/energy and discuss its application in the invariant mass conjecture of general relativity.
 Supplements

Notes
170 KB application/pdf


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Gravitational radiation  a geometricanalytic approach
Lydia Bieri (University of Michigan)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 Gravitational waves are predicted by the general theory of relativity. Several experiments aim at detecting them in the near future. We can think of gravitational waves as fluctuations of the curvature of the spacetime manifold. They propagate at the speed of light along null hypersurfaces. In this talk, I show how by geometricanalytic methods we can lay open the structures of the relevant manifolds, and in particular of the asymptotics of the null hypersurfaces. Thereby, I explain the geometric picture of gravitational radiation and discuss also a specific nonlinear phenomenon. Finally, we relate the mathematical findings to experiments.
 Supplements

Notes
275 KB application/pdf


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Cosmology
Hans RingstrÃ¶m (Royal Institute of Technology (KTH))

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 The talk will contain an overview of mathematical problems arising in the study of the universe. Moreover, it will provide a description of various methods that have been used to address these problems, as well as results that have been obtained.
 Supplements

Notes
138 KB application/pdf


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



