Title: Novel Applications of Kernel Methods in Data Science and Approximation Theory

Abstract: Kernel methods have seen use in a wide range of academic disciplines such as approximation theory, numerical analysis, spatial statistics, statistical learning, and beyond. In this talk, we highlight some recent research on the applications of kernel methods over a diverse set of scientific domains including: i) the recovery of vector fields from trajectory data, ii) image classification, and iii) fractional order spline interpolation. Moreover, throughout the course of the presentation we will demonstrate how kernel-based techniques can be exploited in a variety of ways. For instance, by carefully selecting our kernel we can guarantee that any learned vector-field analytically satisfies a divergence-free constraint and by making use of statistical techniques such as the maximum mean discrepancy we can compare the distributions of learned features in an image classification problem. Additionally, we will move beyond the familiar world of symmetric kernels to establish novel fractional order spline approximations in reproducing kernel Banach spaces.  At the end of the talk, we will take a moment to explore various avenues for students and researchers can get involved in these new and exciting topics.