GEOMETRIC ANALYSIS OF 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.