U.S.-Western Europe Cooperative Research in Spectral Theory (Applied Mathematics)

该奖项支持爱荷华大学的Thomas P.Branson教授和Palle Jorgensen教授以及俄勒冈大学的Peter Gilkey与德国和丹麦的三个强大的研究小组在应用数学方面进行合作。他们的合作伙伴是格斯图尔·奥拉夫松、哥廷根大学、莱因哈德·维尔纳、奥斯纳布吕克大学、本特·奥斯特德、欧登塞大学和亨里克·施利希特克鲁尔，丹麦皇家兽医和农业大学。他们的合作是围绕“光谱理论”一般领域内的六个主题展开的。这些问题的部分动机是数学物理和保角几何中的问题，并将用现代分析和偏微分算子的方法来解决。这一领域是欧洲最活跃的领域之一，拥有许多强大的团队和悠久的研究传统，为美国的参与提供了多样化的机会。在这个合作项目中，美国的参与者在“硬分析”和几何方面提供了技术力量，而欧洲的参与者在不变群方法方面带来了巨大的优势。光谱理论是涉及光谱的所有科学工作的数学基础，范围从光和电磁理论到化学。在数学中，光谱理论是几何和分析中几个领域工作的主要工具。

This award supports Professor Thomas P. Branson and Palle Jorgensen of the University of Iowa and Peter Gilkey of the University of Oregon to collaborate in applied mathematics with three strong research groups in Germany and Denmark. Their partners are Gestur Olafsson, University of Gottingen, Reinhard Werner, University of Osnabruck, Bent Oersted, Odense University and Henrik Schlichtkrull, Danish Royal Veterinary and Agricultural University. Their collaboration is framed around six topics within the general area of "spectral theory." These problems are motivated in part by questions in mathematical physics and also in conformal geometry, and will be approached with methods from modern analysis and partial differential operators. This field is one of great activity in Europe, with many strong groups and a long tradition of research that offers diverse opportunities for U.S. participation. In this cooperative project, the U.S. participants offer technical power in the "hard analytic" and geometric aspects, while the European groups bring great strengths in invariance group methods. Spectral theory is the mathematical underpinning of all scientific work involving a spectrum, ranging from the theories of light and electromagnetism to chemistry. In mathematics, spectral theory is a major tool in work in several areas in geometry and analysis.