**Abstract**: In this talk we will introduce a mathematical framework to embed non-linear dynamical systems into a reproducing kernel Hilbert space using trajectories as a fundamental unit of data. This is done via a novel kernel, dubbed an “occupation kernel.” We’ll talk about applications to system identification problems and in particular motion tomography problems, which seek to recreate a vector field from trajectory data. Moreover, we’ll discuss further applications to dynamic mode decomposition.

**Speaker’s Bio**: Benjamin Russo received his Ph.D in Mathematics from the University of Florida in operator theory and functional analysis. Subsequently, he held a visiting position at the University of Connecticut and currently holds an assistant professor position at Farmingdale State College SUNY. His current research efforts are directed towards a blend of both applied and pure functional analysis, focusing on the development of novel and robust approaches to learning theory in dynamical systems and categorical approaches to quantum information theory.

Last Updated: February 8, 2021 - 7:51 am