Research Program: Geometry and Relativity

The research program “Geometry and Relativity” will be held at the Erwin Schrödinger Institute from July 17 to September 8, 2017.

The goal of the program is to bring together doctoral students, young researchers, and established experts who work on the overlap of geometric analysis and mathematical relativity. The recent developments in the area, and the new techniques that are proving to be particularly successful will be discussed. Above all, the program seeks to support existing collaborations and to inspire new ones.

The following topics have been seeing a surge of activity following spectacular recent breakthroughs. They form the thematic center of the program:

Geometry of initial data sets

New notions of mass, quasi-local mass, and center of mass, as well as new proofs of the positive energy theorem yield deep insights to the geometry of initial data for the Einstein equations. The incompatibility of some of these notions raises difficult new questions that are being explored. Important themes here also include new initial data singularity theorems based on topological properties, and progress on the geometry of stationary black hole initial data.

Construction of initial data sets

New gluing techniques for the constraint equations and progress on the solution of the classical conformal method allow for the construction of asymptotically flat and asymptotically hyperbolic initial data sets with surprising properties. New results on initial data with positive cosmological constant show a rich structure, including non-uniqueness and bifurcation phenomena, which deserves to be further explored.

Scalar Curvature

The spectacular recent results on scalar curvature rigidity and the discovery of global effects of scalar curvature on the large scale isoperimetric structure of a Riemannian manifold have given new impetus to this classical field and have opened avenues for future research.

A conference will take place on July 24–July 28. The following speakers have already confirmed participation: Mattias Dahl (Stockholm), Helmut Friedrich (Golm), Greg Galloway (Miami), Gerhard Huisken (Tuebingen), Michael Kunzinger (Vienna), Marc Mars (Salamanca), Rafe Mazzeo (Stanford), Richard Schoen (Irvine), Yuguang Shi (Peking), Robert Wald (Chicago) and Mu-Tao Wang (Columbia)

A Summer School will be part of the ESI Program and will take place in the week before the conference, July 17–July 21. Its goal is to present the latest developments in the field to younger colleagues and to researchers participating in the program and wishing to expand their research perspective. The school will also serve as a stepping stone for younger colleagues who wish to attend the conference. See the web site of the Summer School for more details.

The program is organized by Robert Beig (Vienna), Piotr T. Chruściel (Vienna), Michael Eichmair (Vienna), Greg Galloway (Miami) and Richard Schoen (Irvine). Local organisation: Piotr T. Chruściel, Michael Eichmair, Tim-Torben Paetz.