Mathematical Sciences: Groups, Geometry and Algorithms

夏皮罗计划研究几何群论中由负弯曲、自动、半双曲和可组合群的研究引起的问题。他计划使用他和其他人最近开发的概念来研究3流形组和其他几何特征的组的分类。他想看看双曲n空间等距的协紧群的某些标准结果是否可以推广到负弯曲群，并想看看负弯曲群的研究如何可以作为研究非正曲率空间上的协紧群的指南。

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.