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Origins Seminar presented on February 21, 2022. Title: Molten exoplanets as a window into the earliest Earth Abstract: Due to the absence of a reliable rock record from the Hadean eon, our understanding of the planetary environment that gave rise to life on the earliest Earth is clouded. Upcoming exoplanet surveys, however, will significantly expand our view of the distribution and variability of rocky planets and their chemical inventories, giving opportunity to test scenarios of early planetary evolution. I will describe recent efforts to establish a comprehensive theoretical framework to simulate the coupled evolution of solidifying planetary mantles and their outgassing atmospheres on young rocky worlds for a wide range of instellation, mass, and composition. The presence or absence of magma oceans on short-period exoplanets can alter the observationally inferred bulk water abundance by up to one order of magnitude, motivating reassessments of previous escape studies including volatile locking in the planetary interior. Alternating cooling trajectories during primary envelope loss on sub-Neptunes can quench metal core formation and thus induce a qualitative change in mantle redox state, which alters the expected compositions of secondary atmospheres on super-Earths. Both of these effects are within the currently observationally accessible limits for individual exoplanetary systems and will be statistically testable with next-generation transit surveys. Increasing reconnaissance of high-temperature super-Earths will enable us to infer the early climatic and geodynamic evolution of temperate rocky worlds, and thus provide crucial information on the environmental context of the origins of life on Earth. Find more information about the Origins Seminar series here: http://eos-nexus.org/origins-seminar/