Mathematical Sciences: Geometric Group Theory

该奖项支持几何群论方面的工作。首席研究员将继续将群体作为几何对象来研究，并将这些想法扩展到处理涉及由组和子组组成的成对的几何问题。特别是，他将确定双曲群的有限表示子群的结构。他还将研究各种群的准等距类型。群是在其上定义了乘法的代数对象。组可以有无限个元素，也可以有有限个元素。在无限群的情况下，通常通过将某种类型的有限对象与无限群联系起来来研究它们。在这个奖项的案例中，他们的中心思想是通过Cayley图将有限生成的群视为几何对象。这项工作与数学的几个领域以及计算机科学有联系。

This award supports work in geometric group theory. The principal investigator will continue to study groups as geometric objects and to extend these ideas to handle geometric questions involving pairs consisting of a group and a subgroup. In particular, he will determine the structure of finitely presented subgroups of a hyperbolic group. He will also study the quasi-isometry types of various groups. A group is an algebraic object having a multiplication defined on it. Groups can have an infinite number of elements or a finite number of elements. In the case of infinite groups, they are often studied by associating with them finite objects of some type. In the case of this award, the central them has been to consider a finitely generated group as a geometric object through its Cayley graph. This work has connections to several areas of mathematics, as well as computer science.