MacCluer will continue her research on several problems which lie at the interface of operator theory and function theory, involving composition operators on analytic function spaces. Identification of the spectrum of a composition operator acting on a Hilbert space of analytic functions on the unit ball in C^n will be of particular concern. Ross will study the invariant subspaces of Bergman spaces on certain slit domains and investigate the relationship between the geometry of the slit and the behavior of the functions near the slit. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. In particular, when restricted to finite dimensional subspaces, an operator has the usual linear properties, and thus can be represented by a matrix. The central problem in operator theory is to classify operators satisfying additional conditions given in terms of associated operators (e.g. the adjoint) or in terms of the underlying space. Operator theory underlies much of mathematics, and many of the applications of mathematics to other sciences.
