Dedicated to my mother Sheela, my father Pradeep, my brother Utkarsh, and to all my teachers and mentors, without whose guidance and support this endeavor would have been impossible. 1 Technically, this should be the Morrison monoid, because although we have an identity, are associative with one another, we do not have inverses to the best of my knowledge. vii humor. Working on heavy assignments at 3 AM has a tendency to bring out the best-arguably also the worst-forms of humor -and Justin,

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... k and I were party to this effect together. Karthik Subramanian's gift of excellent Ethiopian Yirgacheffe coffee beans have been crucial to the final stages of this work. The coffee machine co-operative at NMPP, Garching was also of particular help. Several open-source software packages, particularly Emacs, ack, and TikZ have saved a lot of frustration. Bouldin Creek Café's great food, and flexibility with off-menu orders of the "Hippie Shake", have kept me going during this process. I cannot ignore my high school and undergraduate teachers, and the people at the Bangalore planetarium, who contributed to the foundation in physics that made me feel prepared entering grad school.