Mass, the Einstein Constraint Equations, and the Penrose Inequality Conjecture: September 18-22, 2023


Organizing Committee:
• Carla Cederbaum (University of Tübingen)
• Greg Galloway (University of Miami)
• Lan-Hsuan Huang (University of Connecticut Storrs)
• Jim Isenberg (University of Oregon)
• Marcus Khuri (Stony Brook University)
• David Maxwell (University of Alaska Fairbanks)

Scientific Committee:
• Anna Sakovich (Uppsala University)
• Richard Schoen (UC Irvine)
• Mu-Tao Wang (Columbia University)

A major direction of research in Mathematical General Relativity during the last 40 years has been to refine our understanding of the classical positive mass theorem proved by Schoen-Yau and by Witten. In recent years, new proof strategies for this result have been explored and implemented. Moreover, generalizations of the positive mass theorem to dimensions higher than three as well as to other asymptotic models have been studied. Also explored have been the rigidity and the stability of this theorem. Closely related to this work is the recent progress on understanding the continuity and other properties of the ADM mass functional. Similarly, we have seen important progress on the understanding of the Penrose inequality conjecture (which relates the mass of a black hole space-time to the area of the black hole’s horizon). An important tool for this progress is our increasing understanding of the properties of marginally outer trapped surfaces.

Another direction of intense research activity has been to explore and establish theorems for quasi-local notions of mass or energy. These are intimately related to the extension conjectures of Bartnik for which we have also seen significant progress. One goal of this workshop will be to explore connections between these various new branches of research.

At the same time, the construction and parametrization of relativistic initial data sets (which satisfy the Einstein constraint equations) via the conformal method and related tools has seen breakthroughs in various directions. This, as well as other possible approaches for constructing far from constant mean curvature solutions of the Einstein constraint equations, will be explored at this workshop.