Rachel Kirsch

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Contents Introduction 1 1. Representations of the fundamental group 3 2. Abelian groups and rank one Higgs bundles 5 3. Stable vector bundles and Higgs bundles 6 4. Hyperbolic geometry: G = PSL(2, R) 8 5. Moduli of hyperbolic structures and representations 13 6. Rank two Higgs bundles 19 7. Split R-forms and Hitchin's Teichmüller component 21 8. Hermitian(More)
As the Hispanic population in the United States increases, English language education for Hispanic students becomes a vital issue. Numerous factors can affect an individual's acquisition of a second language. This study analyzed the effects of media exposure to, interaction in, and valorization of English on the English skills of heritage Spanish speaking(More)
In the 1997 paper of Lenin, Parthasarathy, Schoutens, and Van Assche [15], the authors study a birth-death process related to the Rogers-Ramanujan continued fraction r(q). We generalize their results to establish a correspondence between birth-death processes and a larger family of q-continued fractions. It turns out that many of these continued fractions,(More)
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