This Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports fundamental research on three-dimensional manifolds and their associated geometric and topological properties. The $300,000 award, effective from August 15, 2024 to July 31, 2027, aims to advance quantitative understanding of how geometry and large-scale topology of 3-manifolds are related. The research focuses on several important open questions in the study of hyperbolic 3-manifolds and their fundamental groups, with emphasis on effective computation and large-scale structure. No sub-awards are planned under this grant. The research has potential to yield significant new insights into the global structure of the universe, which is modeled as a 3-manifold, and to develop software tools for the mathematical community.
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