Simplifying Complicated Simplicial Complexes: Discrete Morse Theory and its Applications
Rachel Elana Zax, Michael J. Hopkins · 2013
Many thanks to my thesis advisor, Professor Michael Hopkins, for providing invaluable guidance, advice, and candy throughout the course of this project. I am also very grateful to Zachary Abel for his help throughout the year, and to those who read and commented on my drafts: Professor Peter Kronheimer, Ernie Fontes, Ariel Rabkin, and Yair Rosenberg. Thanks to my family for their support, both within the realm of mathematics and outside of it; in particular, thank you to my mother Marcia for passing along the genes for passing the AP Calculus exam, to my father David for looking at my thesis, to my brother Ben for reading my thesis, and to my brother Aryeh for reading at least a few pages of my thesis and providing a comment – more than anyone might expect from a 15-year-old. I am deeply indebted to my instructors in mathematics: my high school teachers; Professors Anil Nerode and Allen Hatcher at Cornell; and my instructors in college: Professors Noam Elkies (also my advisor for the past three years), Lydia Bieri, Gerald Sacks, Barry Mazur, Jacob Lurie, Antti Knowles, and (again) Michael Hopkins. I am likewise grateful to my instructors in theoretical computer science, who instilled in me not only an appreciation for computer science but a deeper understanding of mathematics as well: Professors Salil Vadhan, Michael Mitzenmacher, and Michael Rabin. Finally, my thanks go out to Randall Munroe of xkcd, who has, throughout my college career, provided an incentive for me to work on math until late in the evenings by posting a new comic strip online at midnight three nights a week. 1 1