Author Description

These are the proceedings of the joint seminar by M.I.T. and Harvard on the current Developments in mathematics for the year 1997. Established in 1995, this seminar has been continued on the third weekend of November every year. The organizing committee for the seminar consisted of distinguished mathematicians from the mathematics departments of both institutions: Raoul Bott, Arthur Jaffe, and Shing-Tung Yau from Harvard, and David Jerison, George Lustig and Isadore Singer from M.I.T.. We trust that these proceedings will be of interest to many mathematicians, and will inspire future developments and research pursuits in mathematics. Papers include: Alain Connes, College de France, "Trace Formula in Noncommutative Geometry and the Zeros of the Riemann Zeta Function" Lawrence C. Evans, U.C. Berkeley, "Partial Differential Equations and Monge-Kantorovich Mass Transfer" Peter Sarnak, Princeton, "Quantum Chaos, Symmetry and Zeta Functions" W. Soergel, "Character Formulas for Tilting Modules over Quantum Groups at Roots of One" U. Frisch, Observatoire de Nice, "Is There Finite-Time Blow-Up in 3-D Euler Flow?"