These are the proceedings of the joint seminar by M.I.T. and Harvard on the current developments in mathematics for the year 2002. The organizing committee for the seminar consisted of distinguished mathematicians from the mathematics departments of both institutions: B. Mazur, W. Schmid, and S.T. Yau from Harvard, and D. Jerison, T. Mrowka, and R. Stanley from M.I.T. This year, the seminar was dedicated to Prof. Wilfried Schmid and Prof. George Lusztig. The 2002 speakers included Albert Bressan, Mark Haiman, Richard Hain, Stephen Kudla, Yair Minsky, John Morgan, Leslie Saper, Kari Vilonen, and David Vogan.