Mathematical Sciences Research Equipment

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This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences. It is for the purchase of special purpose equipment dedicated to the support of research in the mathematical sciences. In general, this equipment is required by several research projects, and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers, and with substantial cost-sharing from the institution submitting the proposal. This is an instance of university, industrial, and government cooperation in the support of basic research in the mathematical sciences. The equipment in this project will be used in the following research projects: (1) Calculations relating the eta invariant to bordism and K-theory; (2) Ricci flow, spacetime smoothing, and ambitwistorial representation of solutions of Einstein's equations; (3) Group-theoretic algorithms and lattices over number fields and associated finite geometries; (4) Dimensions of irreducible modules in the representation theory of simple Lie algebras and algebraic groups; (5) Computation of the homology and cohomology of the complexification of the Lie algebra of a real reductive Lie group with respect to the nilpotent radical of a parabolic subalgebra; (6) Unipotent classes of reductive algebraic groups and nilpotent orbits in their Lie algebras; and (7) Dual geometries and their applications to generalized linear models.