PhD course: Riemann-Hilbert methods in Asymptotic analysis

This course is intended as an introduction to Riemann-Hilbert techniques in Asymptotic analysis. In the past two decades, these techniques have lead to important breakthroughs in the understanding of, for example. orthogonal polynomials, Painlevé transcendents as well as long time behavior of solutions to non-linear PDEs such as the NLS and KdV equations. We start the course with a general introduction to Riemann-Hilbert problems, but quickly we take a very concrete approach and show how this method works for three special examples: The Strong Szego Limit Theorem for Toeplitz determinants, (asymptotic) properties of solution to the Painleve II equation and asymptotics of orthogonal polynomials. All three examples are motivated by applications to Random Matrix Theory, which we will also briefly discuss.

More information, including a full schedule, can be found at https://people.kth.se/~duits/RHPcourse/