Optimal Recovery under Approximability Models, with Applications

Tuesday, September 17, 2019 - 1:25pm - 2:25pm
Lind 305
Simon Foucart (Texas A & M University)
For functions acquired through point evaluations, is there an optimal way to estimate a quantity of interest or even to approximate the functions in full? We give an affirmative answer to this question under the novel assumption that the functions belong to a model set defined by approximation capabilities. In fact, we produce implementable linear algorithms that are optimal in the worst-case setting. We present applications of the abstract theory in atmospheric science and in system identification.

Dr. Simon Foucart earned a Masters of Engineering from the Ecole Centrale Paris and a Masters of Mathematics from the University of Cambridge in 2001. In 2006, he received his Ph.D. in Mathematics at the University of Cambridge, specializing in Approximation Theory. After two postdoctoral positions at Vanderbilt University and Université Paris 6, he joined Drexel University in 2010 before moving to the University of Georgia in 2013. Since 2015, he has been with Texas A&M University, where is now professor. His recent work focuses on the field of Compressive Sensing, whose theory is exposed in the book ‘A Mathematical Introduction to Compressive Sensing’ he coauthored with Holger Rauhut. Dr. Foucart’s research was recognized by the Journal of Complexity, from which he received the 2010 Best Paper Award. Dr. Foucart’s current interests also include the mathematical aspects of Metagenomics, Optimization, Deep Learning and Data Science at Large