Percy Deift
Published 2019-03-20Version 1
These lectures introduce the method of nonlinear steepest descent for Riemann-Hilbert problems. This method finds use in studying asymptotics associated to a variety of special functions such as the Painlev\'{e} equations and orthogonal polynomials, in solving the inverse scattering problem for certain integrable systems, and in proving universality for certain classes of random matrix ensembles. These lectures highlight a few such applications.
Orthogonal polynomials with discontinuous weights
Random matrix ensembles associated to compact symmetric spaces
On the families of orthogonal polynomials associated to the Razavy potential
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