Mathematical Sciences Research Equipment

这是科学计算研究基金会的一笔拨款 该司数学科学方案的设备 数学科学。 这是为了购买特殊的 专用于支持研究的设备 数学科学 一般来说，这种设备是必需的。 几个研究项目，很难证明 就为了一个项目 国家科学院的支持 基金会加上折扣和捐款， 制造商，并与大量的成本分摊， 提交提案的机构。 这是一个 大学，工业和政府合作， 支持数学科学的基础研究。 本项目的设备将用于以下方面 研究项目：（1）与eta不变量相关的计算 （2）Ricci流，时空平滑， 爱因斯坦方程的解的边界表示 方程;（3）群论算法和格 数域和相关的有限几何;（4）维数 不可约模的表示论 李代数和代数群;（5）计算 李复化的同调与上同调 关于的真实的约化李群的代数 抛物子代数的幂零根;（6）幂单根 类的约化代数群和幂零轨道 它们的李代数;（7）对偶几何及其 广义线性模型的应用

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.