Ngô Quốc Anh

MSRI Workshops

Here you can find a list of workshops and summer schools concerning general relativity hosted by MSRI.

The mathematical study of the dynamics of the Einstein equations forms a central part of both partial differential equations and geometry, and is intimately related to our current physical understanding of gravitational collapse. The celebrated singularity theorems of Penrose, proven in the 1960s, showed that geodesic incompleteness is inevitable provided that initial data contain what is known as a closed trapped surface. Trapped surfaces are also related to the presence of black holes. A breakthrough into the understanding of trapped surface formation has recently been achieved by Christodoulou in his 600 page monograph: “The formation of black holes in General Relativity”, Publications of the EMS, January 2009, where it is shown that trapped surfaces form in evolution for the Einstein vacuum equations from completely dispersed initial confgurations, a phenomenon caused purely by the focussing of gravitational waves. The proof brings together ideas from geometric analysis and non-linear hyperbolic equations and at the same time introduces new techniques adapted to large data problems. The methods will undoubtedly have many future applications in both general relativity and other equations of mathematical physics. Inparticular, the work provides the first global “large data” result in general relativity (without symmetry assumptions) and opens the possibility for many new developments on dynamical problems relating to black holes.

Mathematical general relativity is the study of mathematical problems related to Einstein’s theory of gravitation. There are interesting connections between the physical theory and problems in differential geometry and partial differential equations.

The purpose of the workshop is to introduce graduate students to some fundamental aspects of mathematical general relativity, with particular emphasis on the geometry of the Einstein constraint equations and the Positive Mass Theorem.  These topics will comprise a component of the upcoming semester program at MSRI in Fall 2013.

There will be mini-courses, as well as several research lectures. Students are expected to have had courses in graduate real analysis and Riemannian geometry, while a course in graduate-level partial differential equations is recommended.

Ever since the epic work of Yvonne Choquet-Bruhat on the well-posedness of Einstein’s equations initiated the mathematical study of general relativity, women have played an important role in many areas of mathematical relativity. In this workshop, some of the leading women researchers in mathematical relativity present their work.

Mathematical relativity is a very widely ranging area of mathematical study, spanning differential geometry, elliptic and hyperbolic PDE, and dynamical systems. We introduce in this workshop some of the leading areas of current interest associated with problems in cosmology, the theory of black holes, and the geometry and physics of the Cauchy problem (initial data constraints and evolution) for the Einstein equations.

The introductory workshop serves as an overview to the overlying programmatic theme. It aims to familiarize graduate students, postdocs, and non-experts to major and new topics of the current program. Though the audience is expected to have a general mathematical background, knowledge of technical terminology and recent findings is not assumed.

This workshop discusses recent developments both in the study of the properties of initial data for Einstein’s equations, and in the study of solutions of the Einstein evolution problem. Cosmic censorship, the formation and stability of black holes, the role of mass and quasi-local mass, and the construction of solutions of the Einstein constraint equations are focus problems for the workshop. We highlight recent developments, and examine major areas in which future progress is likely.<

Last update: December 18, 2013.

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