The principal investigator will continue his study of problems in complex differential geometry and functions of several complex variables. In particular he will attempt to prove cohomology vanishing theorems under weak positivity assumptions. He will use curvature methods, positive currents, estimates for the d" operator, and some ideas from the work of Mok and Demailly. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.
