Mathematical Sciences: Geometric Group Theory

该奖项支持几何群论的研究。 中心主题是考虑一个由一个人产生的群体， 一个几何对象通过它的凯莱图。 校长 研究者将研究（双）-自动组和（双）-可梳 群;等径不等式和等周不等式;自由 群自同构 群是一个代数对象， 定义在其中。 群可以有无限多个元素 或者有限数量的元素。 在无限群的情况下， 它们通常通过与它们相关联的有限对象来研究， 某种类型。 就本奖项而言，中心主题是 要将生成的组视为几何对象，请执行以下操作 通过它的凯莱图 这项工作与几个 数学领域，以及计算机科学。

This award supports research in geometric group theory. The central theme is to consider a finitely generated group as a geometric object through its Cayley graph. The principal investigator will study (bi)-automatic groups and (bi)-combable groups; isodiametric and isoperimetric inequalities; and free group automorphisms. 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 theme 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.