PI: Deift DMS-9500867 Deift will continue his investigations into forced lattice vibrations, semi-classical limit for the focusing NLS equation, random matrix theory, integrable models, and rotating black holes. Riemann-Hilbert techniques will be used to evaluate the asymptotics of probability distributions that arise in random matrix theory, to investigate asymptotic questions that arise in the theory of integrable quantum field theories and statistical mechanical models, and to study the force of interaction between two rotating black holes in equilibrium as the separation of the holes goes to infinity. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.
