Studies on Einstein Metrics and Related Topics

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

Abstract Award: DMS-0072591 Principal Investigator: Michael T. Anderson Anderson and LeBrun both plan to study the global Riemannian geometry of low-dimensional manifolds, with an eye towards the ramifications of these results for smooth topology, algebraic geometry, and theoretical physics. Anderson will continue work on Thurston's geometrization conjecture, and study relations of this conjecture with global existence and singularity formation for vacuum space-times in general relativity. LeBrun will study relations between properties of the total scalar curvature functional and smooth topology, as well as related problems concerning quadratic curvature functionals. In addition, Anderson and LeBrun both plan to investigate topics in the geometry of asymptotically hyperbolic manifolds, and relations with current issues in string theory and the AdS/CFT correspondence. Anderson's investigations are directly related to questions regarding the physics of black holes and the shape and long-term evolution of the universe. LeBrun's work studies fundamental questions arising from Hawking's quantum gravity program, and relates the Seiberg-Witten equations of high-energy physics to the study of gravitational phenomena.