Mathematical Sciences: Matrix Functions on Riemann Surfaces

克兰西教授将研究闭黎曼曲面的矩阵函数理论。具体地说，他将研究零极点数据的内插和有界的值内插(内万林纳-皮克内插)中的问题。这些问题在现实世界的问题中很重要，研究将试图提供明确的解决方案。克兰西教授的研究是关于复值可微函数理论和希尔伯特空间算子理论之间的接口。希尔伯特空间算子本质上是复数的无限矩阵。这些运算符在应用科学的各个领域都有应用，在纯数学中也是如此。这种类型的研究是对此类物体的某些重要家族进行分类的一种尝试。

Professor Clancey will study the matrix function theory of closed Riemann surfaces. Specifically, he will investigate problems in interpolation of zero-pole data and interpolation of values with bounds (Nevanlinna-Pick interpolation). These problems are important in real world questions and the research will attempt to provide explicit solutions. Professor Clancey's research is on the interface between the theory of complex valued differentiable functions and the theory of Hilbert space operators. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important families of such objects.