## Welcome

This course will explore applications of mathematical data science to analysis and statistical modeling of dynamical systems. We will focus on operator-theoretic approaches, which characterize dynamical systems through their induced action on linear spaces of observables. Remarkably, this action is through linear evolution operators—the *Koopman operators*, which act on observables by composition with the dynamical flow map, and the *transfer operators*, which are the dual operators acting on spaces of measures. Using this framework, we will study how techniques from linear operator theory can be employed in a variety of problems in nonlinear dynamics, such as forecasting and identification of coherent observables. In addition, we will study, both theoretically and numerically, associated data-driven approximation techniques, using samples taken on dynamical trajectories to approximate observables and evolution operators.

A tentative weekly plan for the course can be found here.