Graduate Student Seminar, 4:30pm September 30, 2002, Hayes-Healy 229


Phil Harrington


An Introduction to the d-bar Neumann Problem


In several complex variables, we can characterize holomorphic functions as the solutions to the Cauchy-Riemann equations (appropriately generalized from one variable). In order to understand the properties of holomorphic functions, it is helpful to be able to "solve" the Cauchy-Riemann equations, which amounts to solving a first-order partial differential equation. The first successful solution to this problem was Kohn's solution in the 1960's. Kohn solved the problem by first solving an equivalent problem: the d-bar Neumann problem, which was of independent interest in the theory of partial differential equations. I will attempt to provide a gentle introduction to the d-bar Neumann problem in order to show how it can be used to "solve" the Cauchy-Riemann equations.

To volunteer to give a talk, or for any other questions regarding this schedule, contact Wesley Calvert