Five investigators will study problems in contemporary differential geometry which have close relations to nonlinear and linear partial differential equations. Among the areas of special emphasis are the geometry of submanifolds, symplectic and Poisson geometry, Gauge theory in principal bundles, Lie transformation groups, and complex manifolds. Differential geometry is an outgrowth of multi-variable calculus. Physics has been a rich source of unsolved problems which may be phrased naturally in differential geometric terms. Among these are questions arising from the geometry of space and time first understood by Einstein. Gauge theory is an attempt to go beyond these earlier studies toward a theory which explains both the physics of the small and of the large. This group of differential geometers will study a variety of problems related to modern gauge theory.
