Mathematical Sciences: Deformations of Complex Structures

欧文克拉将继续他对克莱因群的研究， 它们的变形、自守形式和Eichler上同调 与Kleinian群相关联，以及辅助参数 与黎曼的Fuchsian和Kleinian单值化有关 表面。Bernard Maskit还将研究Kleinian群。在 特别是他将研究特殊类的结构， Kleinian群，Fuchsian变形的参数空间， Kleinian群与Teichmuller的基元整环 模群 Kra要考虑的许多问题都涉及到 尖点形式空间的几何意义。这是 关于选择有限生成集的问题， 相对庞加莱级数基本域的计算 对于Teichmuller模群，将由Maskit进行，是 与几何学和动力学的问题有关。

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.