The Computational Theory of Riemann-Hilbert Problems - Lecture 1

Explore the computational theory of Riemann-Hilbert problems in this comprehensive lecture by Thomas Trogdon at the International Centre for Theoretical Sciences. Delve into key concepts including simple Riemann-Hilbert problems, function definitions, properties of Psi, Cauchy integrals, and analytical functions. Examine important facts and classifications related to the topic. Part of a broader program on integrable systems in mathematics, condensed matter, and statistical physics, this lecture provides a solid foundation for understanding the computational aspects of Riemann-Hilbert problems and their applications in various fields of mathematics and physics.

Integrable systems in Mathematics, Condensed Matter and Statistical Physics
The computational theory of Riemann-Hilbert problems Lecture 1
Outline
A simple Riemann-Hilbert problem
Goal
Function Define
Properties of Psi
Cauchy integrals
First question: When does this give an analytic function off of Gamma?
Fact
Another fact
Class 1
Fact