Professor Garnett's research project is in function theory. The topics to be investigated include the algebra of bounded analytic functions on the unit disk, the corona problem in the plane, analytic capacity, and quasiconformal mappings. The main focus of Professor Garnett's research is the theory of functions of one complex variable which are differentiable in the sense of elementary calculus. These functions are defined on a domain in the plane but not necessarily on its boundary. Some of the most interesting problems in analysis concern the behavior of these functions as the complex variable approaches the boundary. Professor Garnett's research will focus in part on such questions.
