Zikê zaroka tijeye lê zimanê wan nagere... iii ACKNOWLEDGEMENTS First and foremost, I would like to express my deep gratitude to my advisor John Etnyre. His constant support, guidance and availability throughout the three years of graduate school made this work possible. There is no question that I will always feel very lucky, like all others, for being his student. Thanks John, for everything.hammad Ghomi and Will Kazez, for your valuable comments and efforts. A special thanks goes to Will Kazez to make it all the way from Athens. I am thankful to the faculty and staff of School of Mathematics for providing me excellent conditions both academically and socially. I am, in particular, grateful to Luca Dieci for his financial and academic support as a graduate director from my very first day here at Tech, to Klara Grodzinsky and Cate Jacobson for extremely helpful guidance in my teaching experience here at Tech, to amazing crowd of ladies, Genola Igor Belegradek for putting a great deal in organizing conferences, seminars, working seminars and reading courses around our research interests. Vuong, Rebecca Winarsky and many others, for your lovely friendship and contribution to my knowledge. Thanks to Douglas LaFountain for useful discussions and for our collaboration in iv .