9500758 Li Li will investigate several problems in complex analysis, including the Corona problem in several complex variables; the theory of function spaces, such as Hardy spaces, Bergman spaces, and Lipschitz spaces, on domains in complex Euclidean space; and operator theory on function spaces. He will also study the boundary value problem of complex non-linear differential equations. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.
