Mathematical Sciences: Geometry and Analysis in Manifolds

数学科学：流形几何与分析

• 批准号: 8907710
• 负责人: Victor Guillemin
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8907710&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Analysis; Manifolds

One senior investigator will analyze spectral and symplectic invariants of Hamiltonian actions by Lie groups. In related work, a second senior investigator will study a new pseudo-differential calculus of operators and inverse scattering. Working with these two geometers, a post doctoral investigator will study the Connes-Getzler formalism and Connes' Chern character for non- commutative algebras. Work will proceed on a variety of geometric and analytic problems which arise from the study of inverse scattering. This theory is used to interpret reflected signals. In seismology, inverse scattering is used to reconstruct the shape of oil or water reservoirs. Other applications include sonar, radar, and X- ray crystallography.

一位资深研究员将通过李群分析哈密顿作用的谱不变量和辛不变量。在相关工作中，第二名高级研究员将研究一种新的算子伪微积分和逆散射。一位博士后研究人员将与这两个几何学家合作，研究非交换代数的Connes-Getzler形式论和Connes‘Chern特征标。我们将继续研究各种几何和解析问题，这些问题是从研究逆散射中产生的。这个理论被用来解释反射信号。在地震学中，逆散射被用来重建油层或水层的形状。其他应用包括声纳、雷达和X射线结晶学。