

My research lies at the interface of approximation theory, harmonic analysis and numerical analysis. I study kernels, radial basis functions, splines, and wavelets: i.e., basic tools for scattered data approximation, machine learning, and meshless solution of PDEs. I am interested in the approximation power of these tools, and in applying them to interesting problems. My work is supported by National Science Foundation grant DMS2010051, New Directions in MeshFree Approximation with Localizable Kernels. 



Recent Preprints 



Recent Talks 

Local Approximation with Kernels, AT15, San Antonio, May 2016 Kernel Approximation, Elliptic PDE and Boundary Effects, ICMA, Schloss Rauischholzhausen, March 2016 Beyond Quasiunifomity: Kernel Approximation with a Local Mesh Ratio, CSE 15, Salt Lake City, March 2015 Recent progress on boundary effects in kernel approximation, FOCM 2014, Montevideo, December 2014 On boundaries in approximation by polyharmonic kernels, Curves and Surfaces 8, Paris, June 2014 

Teaching 

In Spring 2020 I am teaching Math 633 (Functional Analysis). If you are a student in one of my classes, course materials can be found on Laulima. Previous Courses: Fall 2019: Math 402 (Introduction to Partial Differential Equations) Spring 2019: Math 100 (Survey of Mathematics), Math 242 (Calculus 2) Fall 2018: Math 649 (Topics in Analysis: Abstract Harmonic Analysis) Spring 2018: Math 633 (Functional Analysis) Fall 2017: on leave Spring 2017: Math 305 (Probabilistic Models) Fall 2016: Math 241 (Calculus 1), Math 631 (Measure and Integration) Spring 2016: Math 242 (Calculus 2) Fall 2015: Math 321 (Intro to Advanced Mathematics), Math 649 (Harmonic Analysis) Spring 2015: Math 633 (Functional Analysis) Fall 2014: Math 252A (Accelerated Calculus 2), Math 431 (Principles of Analysis 1) 
