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

该奖项支持教授保罗古迪的 俄克拉荷马州大学与教授合作 德国数学研究所的Wolfgang Weil 卡尔斯鲁厄大学，德国 他们的合作 关注的问题往往有三个- 三维动机，并涉及重建 从它们的横截面的知识或 投影到其他集合中。 古迪教授带来了 在凸度方面的合作， 虽然Weil教授已经做出了大量的 在随机几何学中的贡献。 要讨论的具体研究问题包括 凸几何与Radon的相互作用 变换，以及关于平移积分的问题 几何和随机几何。 这些问题可以 导致了数学中的各种应用， 工程、生物和医学。 美国数学 将受益于重要的研究 欧洲在这方面的方向，这是 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 问题和链接两个杰出的数学家谁 正在通过他们的 approach.

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.