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03/14/03 Colloquium
DR. MICHAEL REID
UNIVERSITY OF ARIZONAA
UNIVERSITY OF ARIZONAA
Combinatorial Group Theory and Discrete Tiling Problems
Abstract: In 1990, Conway and Lagarias published a method of analyzing discrete tiling problems by using finitely presented groups. Their method has been successfully used to understand a handful of tiling problems, both in their original article, and by subsequent authors.Many computational questions about general finitely presented groups are not solvable by any algorithm, and those that are, are often difficult.
My work shows that the finitely presented groups that typically arise can often be understood, at least to some degree. I have found numerous new cases of tiling problems in which I can apply the Conway-Lagarias method successfully, and they should exist in abundance, in light of my technique.
I also consider tiling restrictions that cannot be detected by the Conway-Lagarias technique, as well as some further directions for future research, and some open problems and conjectures.
This talk will be accessible to a fairly general mathematical audience.
