This volume contains the proceedings of a conference on Integrable Systems,
Random Matrix Theory, and Applications held in New York in May 2006. In ad-
dition to its scientific goals the conference served to celebrate the sixtieth birthday
of Percy A. Deift and to honor his many profound contributions to mathematics.
The theory of integrable systems had its modern rebirth in the 1960's when the
complete integrability of the Korteweg - de Vries equation was discovered and un-
derstood. Since that time, the theory has made many deep connections with diverse
areas of mathematics and the theory of random matrices is one of them. A mile-
stone in uncovering the beautiful relations between random matrices and integrable
the work of Baik, Deift and Johansson on the distribution of the length
of the longest increasing subsequence of random permutations. Using the nonlinear
steepest descent method for lliemann-Hilbert problems that was developed by Deift
and Zhou in the context of integrable systems they found a surprising connection
between random permutations and random matrices. This discovery triggered an
enormous amount of research activities that continues to this day and that involves
additional fields such as representation theory, orthogonal polynomials, spectral
theory, operator theory, probability and statistics. It was the scientific purpose of
this conference to bring researchers from these areas together in order to discuss
recent developments as well as future directions of research.
The five-day conference attracted 100 participants from 15 countries. The pro-
gram of the conference, audio and pdf files of most of the talks and a video of the Dis-
cussion Session can be found under http://math.arizona.edujrvmcl/ISRMA.html.
Finally, it is our happy task to thank those who made it all possible. We thank
the American Institute of Mathematics and the Courant Institute of Mathematical
Sciences for their support, both financial and infrastructural, which both got the
ball rolling, and carried the conference through to its conclusion, and we thank the
National Science Foundation for their support through grant NSF-DMS 0553069.
It is also a pleasure to thank the staff of the Courant Institute for the excellent
organization of the conference. Last (but certainly not least!) we express our
gratitude to the participants of the conference who made it an memorable event, to
the contributors to this volume and to Christine Thivierge and the AMS technical
staff for their professional and most welcome help with editing these proceedings.
Jinho Baik, University of Michigan
Thomas Kriecherbauer, Ruhr-Universitat Bochum
Luen-Chau Li, Pennsylvania State University
Kenneth D. T-R McLaughlin, University of Arizona
Carlos Tomei, PUC- llio de Janeiro