This project is mathematical research in complex analysis in dimension greater than one. The general theme is the exploration of phenomena that cannot occur in the one-dimensional case. An important notion, well understood in dimension one but very difficult in higher dimensions, is that of the polynomial hull of a set in complex space. Recent work by Professor Wermer and a collaborator of his has led to a new approach to the problem of finding the polynomial hull of a given set. This approach suggests questions and methods for a number of problems: polynomial approximation, the study of bounded analytic functions in one variable, singularities of analytic functions of several variables, and boundaries of complex manifolds. These problems will be explored using abstract methods from the theory of function algebras.
