This research will cover many aspects of contemporary geometry. The geometers at Berkeley form one of the world's major centers of excellence. All four investigators have consistently made outstanding contributions to geometry and the prospects for substantial progress in the present research program are very exciting. Hsiang will continue his work in global differential geometry of submanifolds, in geometry of simplexes in constant curvature spaces and symmetric spaces and in the geometry and the topology of Lie transformation groups. Weinstein will carry out research in symplectic geometry and its relations with other areas of geometric analysis and mathematical physics. In particular he will investigate the connections between symplectic geometry and operator algebra. This is one of the most exciting areas of modern geometry and Weinstein is universally acknowledged as being at the forefront of this research. Chern is the grand old man of modern differential geometry whose continued activity into his seventies is inspiring. He will work principally on two projects. The first concerns taut immersions and Lie sphere geometry. The second continues work done with Wolfson concerning harmonic maps of a surface into classical spaces. Wu will work on harmonic maps, the geometry of 4-manifolds and rational homotopy in Riemannian geometry. This will continue his excellent work on Kaehler manifolds relating function theory with curvature properties.
