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This dissertation explores pseudo-Anosov elements of the mapping class group of an oriented surface from the point of view of fibered face theory. This theory runs dual to the classical way of thought where, rather than fixing a surface...
This dissertation applies knot theory, DNA topology, linear algebra, statistics, probability theory and statistical mechanics to address questions about knotted, double-stranded DNA. The three main investigations are the cellular effects...
We construct sequences of pseudo-Anosov examples which we use to bound the minimal dilatation on arbitrary surfaces. We show that these bounds give the asymptotic behavior of the minimal dilatations for certain sequences. Further we show...
This thesis has two parts. The first part concerns topological invariants of the n-gonal plane curves. Our first result is an application of Krammer representations to the Libgober invariant for plane curve complements. This gives a...
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