Atlanta, GA | Posted: March 10, 2003
Professor Percy Deift of the Courant Institute has been the winner of several prizes including the 1998 Polya Prize. His research interests include spectral theory, inverse spectral theory, integrable systems and numerical linear algebra. Dr. Deift earned his M.Sc. in chemical engineering from the University of Natal and his M.Sc. in physics from Rhodes University. He completed his Ph.D. in mathematical physics from Princeton University. He has served as a visiting professor both at Caltech and the Institute for Advanced Study in Princeton. The NSF has funded his work since the late 1970s and honored him with the Special Creativity Award in 1997, 1998 and 1999.
All physical systems in equilibrium obey the laws of thermodynamics. In other words, whatever the precise nature of the interaction between the atoms and molecules at the microscopic level, at the macroscopic level, physical systems exhibit universal behavior in the sense that they are all governed by the same laws and formulae of thermodynamics. The speaker will recount some of the history of these ideas starting with Wigner's model for the scattering of neutrons and how they have led mathematicians to investigate universal behavior for a variety of mathematical systems. This is true not only for systems which have a physical origin, but also systems which arise in a purely mathematical context such as the Riemann hypothesis, and a version of the card game solitaire called patience sorting.
An extraordinary variety of quantities of physical and/or mathematical interest can be expressed in terms of a Toeplitz or Hankel determinant. Such representations arise in the moment problem, in quantum and classical physics, as well as various branches of chemistry. Most often the issue at hand is the asymptotic behavior of the quantity of interest as some parameter in the problem becomes large. In this talk the speaker will describe some recent developments in the asymptotic evaluation of Toeplitz and Hankel determinants using Riemann-Hilbert techniques. Universal aspects of the asymptotic behavior will also be discussed.