BAUM-CONNES CONJECTURE, FLAG VARIETIES AND REPRESENTATIONS OF SEMISIMPLE LIE GROUPS

Without the advise and encouragement of many people, this work would never have come into existence. The most immediate thanks go out to Jonathan Block, my advisor, who introduced me this subject including the original problem. He shared his insights and knowledge freely, and gave me a clear picture of an ideal career as a mathematician. I must also thank him for his warm hospitality, especially the thanksgiving dinners. I am also thankful to Vasily Dolgushev, Nigel Higson and Alexandra Kirillov, for their help and useful conversations. I must thank the office staff at Penn: Janet, Monica, Robin, Paula. They make my my Ph.D. life very enjoyable. The task of producing significant mathematical research was daunting for me, and brought me to the edge of burn-out on a number of occasions. I am infinitely grateful to have had classmates who were also solid friends. In this regard I am most in debt to Alberto García-Raboso, Taisong Jing, Hua Qiang and Aaron Smith. But singling out a few doesn't do justice to the warmth and cameraderie of the graduate department at Penn. Last but not least, I thank my family for their everlasting encouragement and support in every aspect of my life. i