SCIENTIFIC PROGRAMS AND ACTIVITIES

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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