Abstract: Symmetries and topology are central to our understanding of physical systems. Topology, for instance, explains the precise quantization of the Hall effect and the protection of surface states in topological insulators against scattering from disorder or bumps. However discrete symmetries and topology have not, until recently, contributed much to our understanding of the fluid dynamics of oceans and atmospheres. In this talk I show that, as a consequence of the rotation of the Earth that breaks time reversal symmetry, equatorial Kelvin and Yanai waves emerge as topologically protected edge modes. The non-trivial topology of the bulk Poincaré
waves is revealed through their winding number in frequency - wavevector space. Bulk-interface correspondence then guarantees the existence of the two equatorial waves. I discuss our recent direct detection of the winding number in observations of Earth’s stratosphere. Thus the oceans and atmosphere of Earth naturally share basic physics with topological insulators. As equatorially trapped Kelvin waves in the Pacific ocean are an important component of El Niño Southern Oscillation, the largest climate oscillation on time scales of a few years, topology plays a surprising role in Earth’s climate system. We also predict that waves of topological origin will arise in magnetized plasmas. The waves may appear in laboratory plasma experiments, and they may also arise in the solar system and beyond.