Mathematical Sciences: Microlocal Approaches to Spectral Problems II

乌里韦教授将继续他的研究问题， 全球分析。特别是他将研究光谱 椭圆算子的渐近性及其与 辛几何一个主要问题是将渐近 薛定谔算子对经典力学的性质 由运营商代表的系统。第二个问题是 发展傅立叶积分算子理论， 量子化Kahler流形的设置。 这项研究的动机来自数学 物理和逆谱问题。逆谱理论 试图通过研究操作员如何 将输入分成离散部分。中的薛定谔算子 特别是在许多物理建模中起着核心作用， 系统和更好地了解光谱特性的 该算子将具有广泛的应用。

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.