Mathematical Sciences: Groups, Geometry and Algorithms

夏皮罗计划研究几何群论中的问题，这些问题源于对负曲线、自动、半双曲和可梳群的研究。他计划使用他和其他人最近提出的概念来研究3-流形群和其他特征是几何的群的分类。他想知道双曲n-空间的等距余紧群的某些标准结果是否可以推广到负曲群，并且想知道负曲群的研究如何可以作为研究作用于非正曲率空间上的余紧的群的指南。

Shapiro plans to investigate questions in geometric group theory arising from the study of negatively curved, automatic, semi-hyperbolic and combable groups. He plans to use concepts developed recently by him and others to examine 3-manifold groups and an assortment of other groups which are geometric in character. He would like to see if certain standard results for co-compact groups of isometries of hyperbolic n-space can be extended to negatively curved groups, and would like to see in what ways the study of negatively curved groups can be used as a guide to the study of groups which act co-compactly on spaces of non-positive curvature.