Mathematical Conversations

One of the central topics in Complex Analysis deals with the issue of identifying natural conditions that uniquely determine a holomorphic function. A prominent role in this regard is played by the one-sided and transmission Riemann-Hilbert problems. These problems were first proposed by B. Riemann in 1851 and the first significant progress has been registered by D. Hilbert who suggested an approach based on singular integral operators. In this conversation I will use the Riemann-Hilbert problems to show the fruitful interplay between Complex Analysis, Potential Theory, Geometric Measure Theory, and Index Theory.