Mathematical Sciences: Deformations of Complex Structures

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Irwin Kra will continue his research on Kleinian groups and their deformations, the automorphic forms and Eichler cohomology associated with Kleinian groups, and the accessory parameters associated with Fuchsian and Kleinian uniformizations of Riemann surfaces. Bernard Maskit will also work on Kleinian groups. In particular he will study constructions of special classes of Kleinian groups, parameter spaces of deformations of Fuchsian and Kleinian groups, and fundametal domains for the Teichmuller modular group. Many of the problems to be considered by Kra involve the geometric significance of the spaces of cusp forms. This is related to the problem of choosing finite spanning sets of relative Poincare series. The calculations of fundamental domains for Teichmuller modular groups, to be carried out by Maskit, are related to problems in both geometry and dynamics.