Mathematical Sciences: Rewriting Systems and Geometric Group Theory

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9623088 Hermiller This grant supports the research of Professor S. Hermiller to work on problems in geometric group theory. She will study rewriting systems for Artin groups, triangles of groups and small cancellation products of groups in the hope of finding normal forms or automatic structures. She will also study extensions of the properties of almost convexity and rational growth that will be independent of presentation. She also hopes to extend the theory of finite derivation type to higher dimensions. This is research in the field of group theory. Group theory can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's.