U.S.-France Cooperative Research: Inverse Problems in Spectral Geometry

美法合作研究：谱几何反问题

• 批准号: 9415803
• 负责人: Carolyn Gordon
• 金额: $ 1.85万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-04-15 至 1998-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9415803&HistoricalAwards=false
• 关键词: U.S.; France; Cooperative; Research; Inverse

This three-year award will support U.S.-France cooperative research in mathematics and involves ten U.S. university-based investigators, including 5 recent doctorates, and an equal number of investigators in Grenoble, France. The American and French groups, consisting of participants from different institutions, will be led by Carolyn Gordon of Dartmouth College and Pierre Berard of the Institut Fourier, University of Grenoble. The focus of their research is inverse spectral problems in Riemannian geometry. They will study the extent to which eigenvalue spectrum of the Laplace operator on a Riemannian manifold determines the geometry of the manifold. This problem is frequently phrased as `Can one hear the shape of a drum.` General techniques for constructing manifolds with the same spectrum; questions of spectral rigidity; and relationships between the spectrum and the geometry of Riemannian manifolds will be addressed. The proposal brings together mathematicians with complementary abilities and mutual interests. The results of the project will have important applications in all fields of mathematics and for example, in signal processing and remote sensing.

这个为期三年的奖项将支持美国-法国数学合作研究，涉及10名美国大学的研究人员，包括5名最近的博士学位，以及法国格勒诺布尔的同等数量的研究人员。 由来自不同机构的参与者组成的美国和法国小组将由达特茅斯学院的卡罗琳·戈登和格勒诺布尔大学傅立叶研究所的皮埃尔·贝拉尔领导。 他们的研究重点是黎曼几何中的逆谱问题。 他们将研究黎曼流形上的拉普拉斯算子的本征值谱在多大程度上决定了流形的几何形状。 这个问题经常被表述为“人们能听到鼓的形状吗？” 一般技术建设流形具有相同的频谱;问题的频谱刚性;和关系之间的频谱和几何的黎曼流形将得到解决。 该提案将具有互补能力和共同兴趣的数学家聚集在一起。 该项目的成果将在所有数学领域，例如在信号处理和遥感方面有重要的应用。