A classical result in SCV is the fact that a nonconstant holomorphic map sending a piece of the unit sphere in $\mathbb C^N$ into itself is necessarily locally biholomorphic (and, in fact, extends as an automorphism of the unit ball). Generalizations and variations of this result for mappings between real hypersurfaces have been obtained by a number of mathematicians over the last 30 years. In this talk, we shall discuss some recent joint work with L. Rothschild along these lines for mappings between CR manifolds of higher codimension.

The primitive equations describe hydrodynamical flows in thin layers of fluid (such as the atmosphere and the oceans). Due to the shallowness of the fluid layer the
the vertical motion is much smaller than the horizontal one and hence the former is modeled, in the primitive equations, by the hydrostatic balance. The primitive equations are considered to be a very good model
for large scale ocean circulations and for global atmospheric flows. As a result they are used in most global climate models. In this talk we will introduce a mathematical framework for studying various models of atmospheric and oceanic dynamics. In particular, the planetary geostrophic equations and the primitive equations. Furthermore, I will show the global well posedness of these equations.