### The Extremal Nevanlinna-Pick problem for Riemann Surfaces

- Series
- Analysis Seminar
- Time
- Wednesday, October 28, 2009 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Mrinal Ragupathi – Vanderbilt University

Given points $z_1,\ldots,z_n$ on a finite open Riemann
surface $R$ and complex scalars $w_1,\ldots,w_n$, the Nevanlinna-Pick
problem is to determine conditions for the existence of a holomorphic
map $f:R\to \mathbb{D}$ such that $f(z_i) = w_i$.
In this talk I will provide some background on the problem, and then
discuss the extremal case. We will try to discuss how a method of
McCullough can be used to provide more qualitative information about
the solution. In particular, we will show that extremal cases are
precisely the ones for which the solution is unique.