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

该奖项支持俄克拉何马大学的Paul Goodey教授与德国卡尔斯鲁厄大学数学研究所的Wolfgang Weil教授合作。他们的合作集中在通常具有三维动机的问题上，并涉及从其横截面的知识或投影到其他集合的集合的重建。Goodey教授为合作带来了凸性和立体学方面的专业知识，而Weil教授在随机几何方面做出了重大贡献。具体的研究问题涉及凸几何和Radon变换之间的相互作用，以及平移积分几何和随机几何的问题。这些问题可以在数学、工程、生物学和医学中得到各种应用。美国数学将受益于欧洲在该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先进的问题，并联系两位杰出的数学家，他们通过他们的方法贡献了根本性的进步。

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.