|Date: Wednesday, March 16, 2016
Location: 2866 East Hall (4:10 PM to 5:00 PM)
Title: Ziwet Lecture 2: Riemann-Hilbert problems
Abstract: The great utility of special functions, such as Bessel functions, Legendre functions, hypergeometric functions etc., rests in large part on the fact that the asymptotic behavior of these functions as some associated parameter becomes large can be described with great accuracy. This is possible because these functions all have integral representations from which the asymptotics can be deduced in turn using, for example, the classical steepest-descent/stationary phase method. The Riemann-Hilbert problem provides a nonlinear, non-commutative generalization of integral representations, which makes possible the detailed analysis, particularly the asymptotic
analysis, of a wide variety of nonlinear problems such as KdV, NLS etc., and also problems in areas such as orthogonal polynomials and random matrix theory: Here a nonlinear/ non-commutative version of the steepest- descent method plays a key role. The speaker will discuss developments in Riemann-Hilbert theory that have taken place in recent years.
Speaker: Percy Deift
Institution: Courant Institute, NYU