NSF/CBMS Regional Conference in the Mathematical Sciences: The Interplay Between Convex Geometry and Harmonic Analysis, July 29 - August 2, 2006

这次会议是关于凸几何和调和分析之间的界面。主讲人是哥伦比亚密苏里大学的a . Koldobsky，他将发表十场讲座，内容涉及谐波分析学家和几何学者共同感兴趣的一些主题。将特别关注傅立叶分析在凸几何（涉及凸体的截面和投影的问题，对偶问题），功能分析和概率中的应用。讲座将面向分析学家和几何学家，包括研究生和本科生。将特别提到大家关心的尚未解决的问题。每天（周六至周三上午和下午）将有两个小时的讲座，以及为学生提供的特别研讨会，问题和帮助课程。此外，还会有非正式讨论的时段，以及开放问题环节，以鼓励更高级的参与者之间的合作。凸几何类似于数论，因为问题陈述可以用最少的先决条件轻松理解，但可以使用广泛的工具来解决问题。这门学科非常古老，但由于最近引入了傅里叶变换方法，并且与有限维巴纳赫空间的几何、泛函分析、调和分析和概率论密切相关，因此现在对它很感兴趣。

This conference is on the interface between convex geometry and harmonic analysis. The principle lecturer is A. Koldobsky of the University of Missouri, Columbia, who will deliver ten lectures on a number of topics of common interest to both harmonic analysts and geometers.Particular attention will be given to applications of Fourier analysis to convex geometry (questions involving sections and projections of convex bodies, duality problems), functional analysis and probability.The talks will be generally accessible to analysts and geometers, including graduate and undergraduate students. Particular mention will be made of unsolved problems of general interest. There will be two hour-length talks each day (morning and afternoon, Saturday through Wednesday), as well as special seminars, problem and help sessions for students. In addition, there will be time slots for informal discussions, and open problem sessions to encourage collaboration between the more advanced participants.Convex geometry is similar to number theory in that problem statements may easily be understood with aminimum of prerequisites, yet a wide array of tools may be brought to bear on the questions. The subject is very old, but is of current interest because of the recent introduction of Fourier transform methods and close ties to the geometry of finite dimensional Banach spaces, functional analysis, harmonic analysis and probability theory.