This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.
Percy Deift at integer times by C. Tomei Birkhoff normal form for the periodic toda lattice by A. Henrici and T. Kappeler Asymptotics of a class of operator determinants with application to the cylindrical toda equations by H. Widom Connection formulas for the third Painleve transcendent in the complex plane by V. Y. Novokshenov Nonlinear Fourier transforms and integrability in multidimensions by A. S. Fokas Numerical study of a multiscale expansion of Korteweg-de Vries and Camassa-Holm equation by T. Grava and C. Klein Long-time asymptotics of the Camassa-Holm equation on the line by A. Boutet de Monvel and D. Shepelsky Semiclassical focusing nonlinear Schrodinger equation in the pure radiation case: Riemann-Hilbert problem approach by A. Tovbis, S. Venakides, and X. Zhou From stationary phase to steepest descent by S. Kamvissis Riemann-Hilbert problems with lots of discrete spectrum by P. D. Miller Locating the zeros of partial sums of $e^z$ with Riemann-Hilbert methods by T. Kriecherbauer, A. B. J. Kuijlaars, K. D. T-R McLaughlin, and P. D. Miller Two variable deformations of the Chebyshev measure by J. S. Geronimo and P. Iliev Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump by A. Its and I. Krasovsky Orthogonal polynomials, Jacobi matrices and random matrices by L. Pastur Universality in unitary random matrix ensembles when the soft edge meets the hard edge by T. Claeys and A. B. J. Kuijlaars A new approach to universality limits at the edge of the spectrum by D. S. Lubinsky On the gap probability generating function at the spectrum edge in the case of orthogonal symmetry by P. J. Forrester An interpolation between Airy and Pearcey processes by M. Adler and P. van Moerbeke The universal Airy$ 1$ and Airy$ 2$ processes in the toally asymmetric simple exclusion process by P. L. Ferrari On some special directed last-passage percolation models by K. Johansson Discrete spacetime and its applications by E. Bachmat The arctic circle revisited by F. Colomo and A. G. Pronko Moduli of continuity and average decay of Fourier transforms: Two-sided estimates by D. Gioev Eigenvalues of Schrodinger operators in gaps of the essential spectrum--An overview by R. Hempel Transition measures for the stochastic Burgers equation by J. C. Mattingly and T. M. Suidan Some open problems in random matrix theory and the theory of integrable systems by P. Deift.