Mathematical Sciences: Microlocal Approaches to Spectral Problems II

乌里韦教授将继续研究全球分析中的问题。特别是他将研究椭圆算子的谱渐近性及其与辛几何的关系。一个主要问题是将薛定谔算符的渐近性质与该算符所表示的系统的经典力学联系起来。第二个问题是在量子化Kahler流形的情况下发展傅里叶积分算子的理论。这项研究的动机来自于数学物理和逆谱问题。逆谱理论试图通过研究算子如何将输入分离成离散部分来理解算子。特别是薛定谔算符在许多物理系统的建模中起着核心作用，更好地理解该算符的谱特性将具有广泛的应用。

Professor Uribe will continue his research on problems in global analysis. In particular he will study the spectral asymptotics of elliptic operators and their relationships with symplectic geometry. One main problem is to relate the asymptotic properties of the Schrodinger operator to the classical mechanics of the system represented by the operator. A second problem is to develop the theory of the Fourier integral operator in the setting of quantized Kahler manifolds. The motivation for this research comes from mathematical physics and inverse spectral problems. Inverse spectral theory tries to understand an operator by studying how the operator separates input into discrete parts. The Schrodinger operator in particular plays a central role in the modeling of many physical systems and a better understanding of the spectral properties of this operator would have broad application.