On the Behavior of Solutions of Einstein's Equations and Other Geometric Nonlinear Partial Differential Equation Systems

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As the observational evidence supporting Einstein's theory of general relativity as the pre-eminent model for the gravitational field in astrophysics and cosmology grows stronger, it becomes increasingly important to use the latest mathematical tools to carefully explore the implications of the theory. This award supports a focus on new procedures for constructing spacetimes representing the the interaction of many bodies, and also on new techniques which allow us to probe the nature of the cosmological singularities predicted by Einstein's theory.This award also supports work which studies various aspects of Ricci flow, the analytical tool which has proven to be spectacularly successful in proving the Poincare Conjecture and the Geometrization Conjecture in three dimensions. There is much work to do in understanding the details of the dynamics of Ricci flow, and how it might be used to further analyze the relationship between geometry and topology, and this proposal supports such work, including a number of studies of Ricci flow stability.A graduate student will participate in the supported research as part of a PhD dissertation.