The overall purpose of the course is to discuss the Riemann Hilbert approach in the asymptotic analysis of special functions/orthogonal polynomials and differential equations.
After the course, the student is expected to explain and work with the following concepts:
- Monodromy for differential equations
- Riemann-Hilbert problems
- Isomonodromic deformations
- Painlevé equations
- Lax pairs
- Discrete Painlevé equations and orthogonal polynomials
- Deift/Zhou steepest descent for Riemann-Hilbert problems
- g-functions
- Global parametrix
- Local parametrices
After the course, the student should have sufficient skills to independently and efficiently read research papers on the topic.