Graduate Group ChairpersonAcknowledgements

Most graduate students search for one good advisor; I am fortunate to have two wonderful advisors, Dennis DeTurck and Herman Gluck. Maybe I needed twice the guidance of an average student. They both have been extremely generous with their time, insights, and patience. Herman taught me that math simply cannot be done without tea and cookies. He also taught me that, no matter how hectic academic life may be, there is always time to play tennis or at least talk wistfully about it. Dennis is probably the most efficient person I know; he is excellent at multi-tasking. Dennis taught me a lot about math when I was teaching with him and taught me a lot about teaching when I was working on math with him. My years at Penn would not nearly have been as pleasant or productive without the great office staff here. Janet Burns has gone out of her way to assist me whenever I needed it; she encouraged me and kept me out of trouble for six years, even as I procrastinated my way past deadline after deadline. Janet, I appreciate everything you have done for me! Paula Airey, Monica Pallanti, and Robin Toney have been terrifically helpful; Paula and Monica can cheer up even the dreariest day. I want to acknowledge the continued support of my parents, who have always believed in me and helped me succeed. There are many others at Penn whose wisdom and camaraderie are much appreciated. Among the faculty, I especially want to mention Chris Croke, John Etnyre, and Steve Shatz. So many graduate students have been encouraging, including a great list of officemates: Darren Glass, Nadia Masri, Nakia Rimmer, Sukhendu Mehrotra, and Fred Butler. My girlfriend Sarah has inspired me, comforted me, kept me sane, and forced me to enjoy life during a hectic time. Thanks for all your understanding Sarah! The Biot-Savart operator and electrodynamics on bounded subdomains of the three-spher