Ruth Charney

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Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications. This survey article is meant to introduce readers to these groups and to give an overview of the relevant literature.(More)
A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a(More)
The paper addresses the problem of synthesizing programs using a restricted set of input-output data. The program to be synthesized consists of assigning to individual Boolean variables x , the result of evaluating functions involving other Boolean variables x. The program can be initially viewed as a black box having n inputs corresponding to the variables(More)
Declaration This thesis is a presentation of my own original research work. Wherever contributions of others are involved, every effort has been made to indicate this clearly with due reference to the literature. Abstract In this thesis, I investigate a generalization to imaginary quadratic fields of the refined version of Serre's conjecture. I ask whether(More)
Dedication To my love. iii Acknowledgments This document being, primarily, a mathematical effort, I must first thank those who influenced this work mathematically. Thanks to my advisor, Ira Gessel. Many of the main theorems regarding descents were his ideas, and I'm sure if he had wanted to take the time, he could have produced proofs of all the theorems I(More)
This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic space. For a 2-dimensional Artin group the(More)
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