Percy A. Deift
Silver Professor of Mathematics
Warren Weaver Hall, Office 1028
Ph.D., Mathematical Physics, Princeton University, USA, 1977.
M.S., Physics, Rhodes University, South Africa, 1971.
M.S., Chemical Engineering, University of Natal (Durban), South Africa, 1970.
B.S., Chemical Engineering, University of Natal (Durban), South Africa, 1967.
Integrable systems, random matrix theory, Riemann-Hilbert problems, and spectral theory
My basic interest is in integrable systems. This includes not only dynamical integrable systems, such as geodesic flow on an ellipsoid, the Toda lattice, the Korteweg de Vries equation, and the Nonlinear Schroedinger Equation, but also topics such as orthogonal polynomials and random matrix theory. Within these topics I am particularly interested in asymptotic questions, such as the long-time behavior of solutions of the Korteweg de Vries equation, or the behavior of random matrix ensembles when the size of the matrices becomes large (universality questions). An important tool in my work is the Riemann-Hilbert Problem, and the associated nonlinear steepest-descent method.
P. Deift, A. Its, and I. Krasovsky,
"Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities",
Annals of Mathematics
174, no. 2, 1243-1299 (2011)
P. Deift and J. Park,
"Long-time asymptotics for solutions of the NLS equation with a delta potential and even initial data",
International Mathematics Research Notices
24, 5505-5624 (2011)
P. Deift, C. S. Gunturk, and F. Krahmer,
"An optimal family of exponentially accurate one-bit sigma-delta quantization schemes",
Communications on Pure and Applied Mathematics
64, no.7, 883-919 (2011)