ELLIPTIC INVOLUTIVE STRUCTURES AND GENERALIZED HIGGS ALGEBROIDS

First I would like to thank my advisor, Jonathan Block, for spending so much time meeting with me and suggesting interesting mathematics to think about. His wide knowledge of geometry and topology made it easy for me to find research topics that excited me. I also thank Shilin Yu and Wolfgang Ziller for being on my committee and for useful remarks concerning my thesis. This work has greatly benefited from conversations with Zhaoting Wei, Tony Pantev, Nigel Higson, and Calder Daenzer. I am also extremely grateful to George Sparling, who took me under his wing when I was an undergraduate at the Univer-sity of Pittsburgh and who introduced me to the world of higher mathematics. I thank the administrative staff of the department, Janet Burns, Monica Pallanti, Paula Scarborough, and Robin Toney, for all of the behind-the-scenes work they do to make the department run smoothly. Last and not least, I thank my family (both blood and Boricua) for their love and support. Natalia, thanks for putting up with me! It is not easy to deal with the life of a graduate student, let alone when you are one yourself. I especially thank my parents, Amy and David Korman, and my grandmother, Betty Glick. Their unconditional support and encouragement throughout my life has allowed me to pursue my interests with confidence and pride. This work is dedicated to them. i