Pseudodifferential Operators and Geometric Analysis

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The purpose of this project is to present sophisticated methods of analysis on curved spaces. Two of our main results are the following. First, we significantly improved the known facts on Berezin-Toeplitz operators acting on the image of a certain Fourier integral operators with a complex phase. Secondly, we studied the initial value problem for the Schrodinger map flow of a Riemannian manifold to an almost Kahler manifold. We clarified the meaning of the assumption of the Kahler property of the target space in all the preceding results, and succeeded in dropping this assumption by introducing pseudodifferential calculus on induced bundle associated with a map between Riemannian manifolds.