Professor Bourdon will investigate the iteration of holomorphic maps of the unit disk of the complex plane into itself. The project concerns finding a linear fractional model of the map in question. The investigation will take place in the framework of composition operators on a Hilbert space of analytic functions. A major component of the work will involve the use of a computer to generate conjectures and then prove them analytically. Part of the project will be done with the active participation of undergraduates. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. Bourdon's research is an attempt to understand certain important classes of such objects.
