CBMS Conference: Fitting Smooth Functions to Data

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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.