Mathematical Sciences: Geometric Group Theory

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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.