Quantum Ergodicity and the Analysis of Semiclassical Pseudodifferential Operators A thesis presented by

I have had the fortune to meet some of my closest friends and wisest advisors during my time as an undergraduate at Harvard. I humbly thank my advisor, Clifford Taubes, without whose advice and patience this thesis would not have been possible. Aside from suggesting useful sources in the literature, discussing the role of PDEs in geometry, promptly responding to my questions, correcting my many misunderstandings in spectral and geometric analysis, and reviewing numerous drafts of my thesis, Professor Taubes has taught me a great many things, not the least of which is how to become a better mathematician. I thank my concentration advisor, Wilfried Schmid, for his keen insight and wise di-rection throughout my time as a mathematics concentrator. Professor Schmid has always made himself available for me at the most ungodly hours, and his advice for both my studies and life in general has never fallen short of amazing. I thank several great mathematicians from whom I’ve had the delightful opportunity to learn, including my research mentor Jeremy Gunawardena and professors Sukhada Fadnavis, Benedict Gross, Joe Harris, Peter Kronheimer, Siu Cheong Lau, Martin Nowak, and Horng