Title: The Evolution of Galaxy Metallicities and Baryon Cycling Over the Past 12 Billion Years

Abstract: Understanding how galaxies assemble their baryonic content is one of the major open questions in galaxy formation and evolution. A general theory has emerged in which secular galaxy growth is governed by the interplay of key processes including gas accretion, star formation, energetic feedback from supernovae and/or accreting black holes, and gas outflows.  This interconnected process is known as the "cycle of baryons." The gas-phase metallicity of the interstellar medium is a sensitive probe of the cycle of baryons, and its scaling with galaxy properties such as stellar mass and star-formation rate encodes information about how gas flows behave as a function of these properties.  Recent spectroscopic surveys have enabled the determination of gas-phase metallicities for statistically large samples of galaxies at cosmic noon (z=1-3) for the first time. I will present the latest observational constraints on the evolution of the mass-metallicity relation and the fundamental metallicity relation (mass-SFR-metallicity) from z=0 to z~3.3, spanning the past 12 Gyr of cosmic history. I will discuss the implications for gas outflow rates and mass loading factors of galactic winds, including the scaling of mass loading with stellar mass and its evolution with redshift. I will also examine future observational prospects to improve the connection between gas flows and the metal and gas content of galaxies, and to extend gas-phase abundance studies into the epoch of reionization with JWST.