ABSTRACT Song-Ying Li Li is investigating several problems in harmonic analysis, complex analysis and non-linear partial differential equations. His project includes the Corona problem in several complex variables. Li will consider Hankel operators, commutators, composition operators and the complex Monge-Ampere operator. Li is focusing on the existence, uniqueness and regularity of solutions of complex Monge-Ampere equations on smoothly bounded weakly pseudoconvex domains. These results can be directly applied to the study of the boundary behavior of Kahler-Einstein metrics. The project of Li is aimed at developing both the theory and application of harmonic analysis, complex analysis and partial differential equations. The theoretical part of the project is concerned with several important problems in these fields. The main problems of this project are strongly related to control theory, mathematical physics, especially quantum mechanics and approximation theory. The theory of systems control can be directly applied to Electrical and Computer Engineering and approximation theory can be used to deal with problems in signal processing.
