SCIENTIFIC PROGRAMS AND ACTIVITIES

April 26, 2017

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Constraint equations and Mass-Momentum 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

Mu-Tao Wang, Columbia University


Room 210 at The Fields Institute  

 

On-line Registration open to May 3
also on-site during Focus Weeks
$100 registration fees, students and PDF $50


*Please note that a nominal registration fee is required of all participants for this Focus Program. Your contributions allow us to provide the Program with refreshments and social events for each of the Focus Weeks.

Application for Participant support
Deadline to apply April 30, 2015
Accommodation in Toronto Information for speakers Reimbursement information for funded participants Map to Fields

Overview

Constraint equations, Mass-momentum inequalities. Some of the most well-known 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 time-symmetric 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 space-like 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. Non-uniqueness 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
11:00-12:00
Sergio Dain, Geometric inequalities for black holes and bodies
2:00-3:00
Michael Holst, Overview of the analysis frameworks for non-CMC solutions to the conformal method equations (Part I)
slides
3:00-3:30
Coffee Break
3:30-4:30
Marcus Khuri, A Mass-Angular Momentum-Charge Inequality for Multiple Black Holes, Size-Angular Momentum-Charge Inequalities, and Existence of Black Holes
Tuesday, May 12
9:30-10:00
Michael Holst, Overview of the analysis frameworks for non-CMC solutions to the conformal method equations (Part II)
slides
10:00-10:30
Hari Krishna Kunduri
10:30-11:00
Coffee Break
11:00-12:00
Mu-Tao Wang, Conserved quantities in general relativity, Part I
2:00-3:00
Sergio Dain, Geometric inequalities for black holes and bodies, Part II
3:00-3:30
Coffee Break
3:30-4:30
Ye Sle Cha
Wednesday, May 13
9:30-10:30
David Maxwell
10:30-11:00
Coffee Break
11:00-12:00
Gantumur Tsogtgerel, On the Lichnerowicz equation and the prescribed scalar-mean curvature problem in the compact-with-boundary setting
2:00-2:30
Mu-Tao Wang, Conserved quantities in general relativity, Part II
2:30-3:00
Pei-Ken Hung, Gibbons-Penrose inequality
3:00-3:30
Coffee Break
3:30-4:30
Po-Ning Chen
Thursday, May 14
9:30-10:30
Lydia Bieri, Spacetime Geometry and Radiation
10:30-11:00
Coffee Break
11:00-12:00
Daniel Lee, Stability of the positive mass theorem
2:00-3:00
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
9:30-10:30
Carla Cederbaum, Uniqueness of static photon spheres
10:30-11:00
Coffee Break
11:00-12:00
Greg Galloway, Rigidity of marginally outer trapped 2-spheres

 

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
Po-Ning 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
Mu-Tao Wang Columbia University

 

 

 

 

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