CBMS Conference: Fitting Smooth Functions to Data

该奖项将支持将于2019年8月19日至23日在德克萨斯大学奥斯汀分校举行的NSF-CBMS区域会议，主题是可拓理论与计算机科学、统计和数据科学的应用。主要演讲人是小赫伯特·E·琼斯的查尔斯·L·费弗曼。普林斯顿大学数学教授。这十个讲座将集中在插值法、函数逼近和流形学习方面的问题，这些问题对许多应用领域都很重要。此外，还将有四场由受邀演讲者提供的补充主题的讲座。可拓理论的最新进展是由费弗曼在惠特尼可拓问题上的深入数学工作推动的。当问题被描述为有限集上的函数时，它的形式是关于用光滑函数对数据进行插补的实际问题。这些问题与更困难的流形学习问题有关，在流形学习中，一个人试图通过一个有限的点集通过一个具有合理几何形状的光滑表面。专题的跨学科性质将促进不同社区之间研究和合作的新途径。课程设计将面向具有统计学、计算机科学或数学背景的研究生。有关更多信息，请参见会议网站http://www.ma.utexas.edu/conferences/cbms/This奖，该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award will support an NSF - CBMS regional conference to be held during the week of August 19-23, 2019 at the University of Texas at Austin on topics in extension theory with applications to computer science, statistics, and data science. The principal speaker is Charles L. Fefferman, Herbert E. Jones, Jr. Professor of Mathematics at Princeton University. The ten lectures will focus on problems in interpolation, function approximation, and manifold learning, which are of central importance to many applied fields. In addition, there will be four lectures on complementary topics delivered by invited speakers.Recent progress in extension theory has been driven by deep mathematical work of Fefferman on Whitney's extension problem. When the problem is formulated for functions on finite sets, it takes the form of a practical question about the interpolation of data by smooth functions. These problems are related to the more difficult problem of manifold learning, in which one attempts to pass a smooth surface with reasonable geometry through a finite set of points. The interdisciplinary nature of the featured topics will promote new avenues of research and collaboration between a diverse set of communities. Lectures will be designed to be accessible to graduate students with a background in statistics, computer science, or mathematics. For more information, see the conference website http://www.ma.utexas.edu/conferences/cbms/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.