Research on Geometric Scattering

几何散射研究

• 批准号: 0500788
• 负责人: Antonio Sa Barreto
• 金额: $ 12.5万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-15 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500788&HistoricalAwards=false
• 关键词: Research; Geometric; Scattering

Research on Geometric Scattering.Antonio Sa BarretoPurdue University.AbstractThis award will support mathematical research centering on the constructionof scattering operators and the investigation of their properties on compactsmooth manifolds with a complete Riemannian metric. This includes topics indynamical scattering theory on asymptotically hyperbolic manifolds andmanifolds with cusps. This allows the scattering matrices to be viewedas an analogue of Dirichlet to Neumann map associated with an operator on amanifold. Another project is to prove certain trace formulae for thespectrum of the Laplacian on asymptotically hyperbolic manifolds and toinvestigate the distribution of resonances. Certain other propertiesinvolving the scattering operator on geometrically finite hyperbolicmanifolds will also be studied.Scattering theory has a long history and was a central topic in mathematicalphysics. The mathematical analysis of many aspects of the theory hasundergone significant advances in recent years and this project willinvestigate a variety of currently open mathematical questions.

该奖项将支持以散射算子的构造及其在具有完备黎曼度量的紧致光滑流形上的性质的研究为中心的数学研究。 其中包括渐进双曲流形和带尖点流形上的动态散射理论的主题。这使得散射矩阵被视为一个类似的狄利克雷诺依曼映射与一个运营商上的流形。另一个项目是证明渐近双曲流形上Laplacian谱的迹公式，并研究共振的分布。几何有限双曲流形上的散射算子的某些性质也将被研究。散射理论有着悠久的历史，是物理学的中心课题。近年来，该理论的许多方面的数学分析都取得了重大进展，本项目将研究各种目前尚未解决的数学问题.