Geometric Analysis of Complex Laplacians

复杂拉普拉斯算子的几何分析

• 批准号: 0805852
• 负责人: Siqi Fu
• 金额: $ 9.13万
• 依托单位: Rutgers University Camden
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805852&HistoricalAwards=false
• 关键词: Geometric; Analysis; Complex; Laplacians

Abstract-DMS-0805852This project systematically studies spectral theory of complex Laplacians and its applications to complex and algebraic geometries. The main focus of the project is the interplays between the spectrum of the complex Laplacians and the geometric and algebraic structures of the underlined spaces.Complex analysis and differential equations arise naturally in engineering and physical sciences. Spectral analysis of differential operators plays an important role in quantum mechanics. This project will also have impacts on the development of human resources. It will support development of a new topic course as well as summer research of a student. It will also help facilitate interdisciplinary research activities with other scientists.

Abstract-DMS-0805852该项目系统地研究了复拉普拉斯谱理论及其在复代数几何中的应用。该项目的主要焦点是复拉普拉斯算子的谱与下划线空间的几何和代数结构之间的相互作用。复分析和微分方程在工程和物理科学中自然出现。微分算子的谱分析在量子力学中起着重要作用。该项目还将对人力资源开发产生影响。它将支持新主题课程的开发以及学生的暑期研究。它还将有助于促进与其他科学家的跨学科研究活动。