On the Behavior of Solutions of Einstein's Equations and the Behavior of Ricci Flows (Physics)

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The research of Prof. Isenberg involves primarily two areas of study: (1) The dynamics of gravitational fields and their behavior near singularities in spacetimes satisfying Einstein's equations; and (2) The convergence and nonconvergence of Ricci flows of Reimannian metrics on three- dimensional manifolds. While the interest in the first area comes from physics and that in the second area is mathematical, in both areas the analysis focuses on geometrically-based systems of partial differential equations. Moreover, in both, the most pressing (and difficult) issues involve the long-time behavior of the solutions, and the behavior of the fields as they become singular. Therefore it is not surprising that the progress achieved in the two areas has been often based on the use of somewhat similar tools. Also not surprising is the considerable cross-fertilization which has occurred between the physically-motivated ideas and mathematically-based concepts which are used in studying both problems.