Geometric Analysis of Complex Laplacians

本项目系统地研究了复拉普拉斯的谱理论及其在复几何和代数几何中的应用。该项目的主要焦点是复拉普拉斯函数的频谱与带下划线的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而然地出现。微分算符的谱分析在量子力学中占有重要的地位。该项目还将对人力资源开发产生影响。它将支持开发一门新的主题课程，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。

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.