Recorded 05 February 2026. Gary Froyland of the University of New South Wales presents "Operator-theoretic methods for earth systems: atmosphere, ocean, and ML" at IPAM's Mathematics and Machine Learning for Earth System Simulation Workshop. Abstract: The transfer operator is the natural evolution operator for functions of the underlying state variables in a dynamical system. Its spectrum and eigenfunctions carry important dynamic information, and the operator can be adjusted to perform a variety of tasks. I will discuss three related topics. First, I will describe a time-inflation of the transfer operator (the inflated generator) and show how its eigenfunctions reveal the emergence and dissipation of atmospheric blocks. Second, I will introduce the notions of linear response and optimal linear response, whereby the perturbations that a system is most sensitive to are identified. This will be illustrated with sea-surface temperature perturbations that are optimised to maximally influence the strength and the frequency of the ENSO cycle. Finally, I will touch on a novel approach for machine learning function bases in which to compactly and accurately represent transfer operators. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/mathematics-and-machine-learning-for-earth-system-simulation/?tab=overview