There are many people, including officemates, classmates and their spouses, roommates, neighbors, and the mathletes, who have made Iowa City feel like home for the past six years. In particular, I would like to thank Christine, Julia, Catie, Mario, Nathaniel, Colin, Kevin, and Ze for their friendship. I feel lucky to have been surrounded by such wonderful people. Finally, I am grateful to my mom, Nancy, my dad, Mike, my sister, Emily, and my partner, Nate, for their unwavering support and an earnest interest in my work. Without your encouragement, I might have given up a long time ago.