• Afredo Wetzel
  • October 26, 1 PM
  • 2866 East Hall

Roughly speaking, Riemann-Hilbert problems consist on finding an unknown matrix that satisfies certain desired properties on the complex plane. In this presentation, I will introduce what  Riemann-Hilbert problems are and discuss briefly how they arise naturally when seeking solutions of certain non-linear partial  differential equations. I will continue by showing how singular integrals appear in a fundamental way in the study of Riemann-Hilbert  problems and finish by discussing how asymptotic properties of the solution can be found. For the talk, I will only assume some background in complex variables, linear algebra, and principal value integrals. Even so, an intuitive understanding of these disciplines will suffice.