GLOBAL STUDIES OF EINSTEIN SPACETMES

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This project deals with two major areas of mathematical relativitywhich border on the fields of 3-manifold topology on the one hand andnumerical/experimental relativity on the other. The first researchtopic treats the question of how the spatial topology of the universeaffects its long-time evolution. The second topic involves thedevelopment of an efficient and accurate numerical scheme for thecomputation of gravitational waves produced by colliding black holes. The importance of the first topic is that it seeks to unify the studyof the evolutionary properties of the universe with variousgeometrization results and conjectures from pure mathematics, therebybroadening the scope of results in either field of study. Theimportance of the second topic is that it seeks to support theexperimental search for gravitational waves by improving thetheoretical understanding of possible sources of such waves.