Mathematical Sciences: Geometric Group Theory

该奖项支持几何群论的研究。中心主题是通过其Cayley图将有限生成的群视为几何对象。主要研究人员将研究(Bi)-自动机群和(Bi)-可梳群；等径和等周不等式；以及自由群自同构。群是定义了乘法的代数对象。群可以有无限个元素，也可以有有限个元素。在无限群的情况下，通常通过将某些类型的有限对象与它们联系在一起来研究它们。在这个奖项的案例中，中心主题一直是通过其Cayley图将有限生成的群视为几何对象。这项工作涉及到数学的几个领域，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.