
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
Constraint
equations and MassMomentum inequalities
May 11  15, 2015
Organizing
Committee 
Focus
Week Organizers 
Location 
Spyros
Alexakis, University of Toronto
Mihalis Dafermos, Princeton University
Luis Lehner, Perimeter Institute for Theoretical
Physics and University of Guelph
Harald Pfeiffer, Canadian Institute for Theoretical
Astrophysics (CITA)
Eric Poisson, University of Guelph

Sergio
Dain, Universidad Nacional de Córdoba
Michael Holst,University of California, San Diego
MuTao
Wang,
Columbia University

Room
210 at The Fields Institute 







Overview
Constraint equations, Massmomentum inequalities. Some of the most wellknown
aspects of the mathematical study of Einstein's equations are the proofs
of positivity of the ADM mass for isolated systems. This has raised the
challenge of generalizing and strengthening the control one has on the mass
to the setting of black holes. An example would be the stipulated Penrose
inequality which asserts that the size of black holes should provide a lower
bound on the mass. Originally proposed by Penrose as a form of evidence
in favor of his proposed weak cosmic censorship conjecture and what he termed
the "establishment view" on the evolution and nal state of dynamical
black holes, this inequality and its generalizations (including angular
momentum) has attracted much attention, with a resolution in the timesymmetric
case about thirteen years ago. We feel that recent progress on the dynamical
black holes might be useful in these questions. Such proposed inequalities
have been studied in conjunction with the constraint equations for spacelike
initial data sets. This topic is often also studied numerically, due to
its usefulness of numerical simulations to the understanding of the dynamical
evolution of the Einstein equations. Nonuniqueness in certain formulations
of the Einstein constraint equations was rst discovered numerically. Moreover,
numerical evolutions of black holes regularly monitor the black holes for
violations of the bound of black hole spin on a Kerr black hole, as a possible
indication of violation of cosmic censorship.
Schedule
Monday,
May 11 
11:0012:00

Sergio Dain, Geometric
inequalities for black holes and bodies 
2:003:00

Michael Holst, Overview
of the analysis frameworks for nonCMC solutions to the conformal method
equations (Part I)
slides 
3:003:30

Coffee Break 
3:304:30

Marcus Khuri, A
MassAngular MomentumCharge Inequality for Multiple Black Holes, SizeAngular
MomentumCharge Inequalities, and Existence of Black Holes 
Tuesday, May 12 
9:3010:00

Michael Holst, Overview
of the analysis frameworks for nonCMC solutions to the conformal method
equations (Part II)
slides 
10:0010:30

Hari Krishna Kunduri 
10:3011:00

Coffee Break 
11:0012:00

MuTao Wang, Conserved
quantities in general relativity, Part I 
2:003:00

Sergio Dain, Geometric
inequalities for black holes and bodies, Part II 
3:003:30

Coffee Break 
3:304:30

Ye Sle Cha 
Wednesday,
May 13 
9:3010:30

David Maxwell 
10:3011:00

Coffee Break 
11:0012:00

Gantumur Tsogtgerel, On
the Lichnerowicz equation and the prescribed scalarmean curvature problem
in the compactwithboundary setting 
2:002:30

MuTao Wang, Conserved
quantities in general relativity, Part II 
2:303:00

PeiKen Hung, GibbonsPenrose
inequality 
3:003:30

Coffee Break 
3:304:30

PoNing Chen 
Thursday,
May 14 
9:3010:30

Lydia Bieri, Spacetime
Geometry and Radiation 
10:3011:00

Coffee Break 
11:0012:00

Daniel Lee,
Stability of the positive mass theorem 
2:003:00

Walter Simon, Initial
data for rotating cosmologies Initial data for rotating cosmologies

3:30

James Dilts, The conformal method on asymptotically
Euclidean manifolds 
Friday,
May 15 
9:3010:30

Carla Cederbaum, Uniqueness
of static photon spheres 
10:3011:00

Coffee Break 
11:0012:00

Greg Galloway, Rigidity
of marginally outer trapped 2spheres 
Participants
as of May 6, 2015
* Indicates
not yet confirmed
Full Name

University/Affiliation

Aghil Alaee 
Memorial University of Newfoundland 
Lydia Bieri 
University of Michigan 
Carla Cederbaum 
University of Tübingen 
Ye Sle Cha 
Freie Universität Berlin 
PoNing Chen 
Columbia University 
Sergio Dain 
Ciudad Universitaria de Córdoba 
María Eugenia Gabach Clément 
Ciudad Universitaria 
Greg Galloway 
University of Miami 
Gary Gibbons 
University of Cambridge 
Michael Holst 
University of California, San Diego 
Marcus Khuri 
Stony Brook University 
Hari Krishna Kunduri 
Memorial University of Newfoundland 
Dan Lee 
Queen's College CUNY 
David Maxwell 
University of Alaska Fairbanks 
Volker Schlue 
University of Toronto 
Walter Simon 
University of Vienna 
Gantumur Tsogtgerel 
McGill University 
MuTao Wang 
Columbia University 
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