TAUTOLOGICAL BUNDLES ON THE HILBERT SCHEME OF POINTS AND THE NORMALITY OF SECANT VARIETIES

First, I want to thank my advisor, Rob Lazarsfeld who has served as my teacher, my mentor, and my main mathematical influence. He has helped me choose great research problems, patiently taught me topics that I didn’t know, and given me ideas when I was stuck. He has also tirelessly helped me prepare papers and talks, often reading the same introduction numerous times until I got it right. Moreover, his insight and invaluable advice have greatly influenced me and made me a better mathematician. I am also grateful to my “adopted ” advisor Karen Smith. She is always willing to get into the gory details of my research and work out examples together. She has helped me immensely by providing a different mathematical perspective. Moreover, I am extremely appreciative of her encouragement and support throughout the job application and thesis writing process. I would like to thank all of the professors and post-docs at Michigan and elsewhere who have been my teachers and mentors, including but not limited to Bill Fulton