To Daria ACKNOWLEDGMENTS

This thesis would not have been possible without the help of my relatives, mentors and colleagues. First and foremost, I am thankful to my parents for igniting in me the passion for scientific discovery, for teaching me how to think and how to wonder. I was lucky to have a father who could explain trigonometry to a ten year old, and a mother who taught me to strive for perfection. I was also fortunate to have grandparents who served as role models of determination and hard work. I am truly indebted to John Stuber; without his kindness my life would have taken a very different path. I want to give special thanks to my wife for her understanding, patience and unending support during these difficult years. Having two academic advisors is a challenging but fascinating experience. I was fortunate to work closely with Bruce Croft, whose knowledge of the field is truly astounding, and who showed me the importance of seeing the wood behind the trees. I am also tremendously thankful to James Allan, who guided me since the early days of my undergraduate studies. I am particularly grateful to James for his willingness to give unbiased advice, even when it may have run contrary to his interests. I would like to thank Louise Knouse for turning the dry art of abstract mathematics into an accessible and fun discipline. I am also grateful to Donald Geman and Alexey Koloydenko for showing me the power and the awe-inspiring beauty of probability theory. I am thankful to Sherre Myers for proofreading this work