U.S.-Germany Cooperative Research into the Geometry of Convex Sets

美德合作研究凸集几何

• 批准号: 9123373
• 负责人: Paul Goodey
• 金额: $ 1.03万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123373&HistoricalAwards=false
• 关键词: U.S.; Germany; Cooperative; Research; into

This award supports Professor Paul Goodey of the University of Oklahoma to collaborate with Professor Wolfgang Weil of the Mathematics Institute of the University of Karlsruhe, Germany. Their collaboration focusses on problems which frequently have a three- dimensional motivation and involve the reconstruction of sets from knowledge of their cross sections or projections into other sets. Professor Goodey brings to the collaboration particular expertise in convexity and stereology while Professor Weil has made substantial contributions in stochastic geometry. The specific research problems to be discussed involve interactions between convex geometry and the Radon transform, and questions regarding translative integral geometry and stochastic geometry. These problems can lead to various applications in mathematics as well as engineering, biology and medicine. U.S. mathematics will benefit from exposure to significant research directions in Europe in this area, which has been dominated by Europeans. The research proposed here includes important and difficult state-of-the-art problems and links two outstanding mathematicians who are contributing fundamental advances through their approach.

该奖项支持俄克拉荷马大学的保罗·古迪教授与德国卡尔斯鲁厄大学数学研究所的沃尔夫冈·韦尔教授合作。他们的合作集中在通常具有三维动机的问题上，并涉及将集合的横截面或投影知识重构为其他集合。古迪教授为合作带来了在凸性和体视学方面的特殊专业知识，而韦尔教授在随机几何方面做出了重大贡献。要讨论的具体研究问题涉及凸几何和Radon变换之间的相互作用，以及关于平移积分几何和随机几何的问题。这些问题可以导致在数学以及工程、生物和医学中的各种应用。美国数学将受益于欧洲在这一领域的重要研究方向，该领域一直由欧洲人主导。这里提出的研究包括重要和困难的最新技术问题，并将两位杰出的数学家联系在一起，他们通过他们的方法做出了根本性的进步。