We use high-resolution cosmological zoom-in simulations from the Feedback in Realistic Environment (FIRE) project to study the galaxy mass-metallicity relations (MZR) from z = 0-6. These simulations include explicit models of the multi-phase ISM, star formation, and stellar feedback. The simulations cover halo masses M halo = 10 9 -10 13 M and stellar masses M * = 10 4 -10 11 M at z = 0 and have been shown to produce many observed galaxy properties from z = 0-6. For the first time, our simulations agree reasonably well with the observed mass-metallicity relations at z = 0-3 for a broad range of galaxy masses. We predict the evolution of the MZR from z = 0-6, as log( 04, for gas-phase and stellar metallicity, respectively. Our simulations suggest that the evolution of MZR is associated with the evolution of stellar/gas mass fractions at different redshifts, indicating the existence of a universal metallicity relation between stellar mass, gas mass, and metallicities. In our simulations, galaxies above M * = 10 6 M are able to retain a large fraction of their metals inside the halo, because metal-rich winds fail to escape completely and are recycled into the galaxy. This resolves a long-standing discrepancy between "sub-grid" wind models (and semi-analytic models) and observations, where common sub-grid models cannot simultaneously reproduce the MZR and the stellar mass functions.

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We investigate the spectral geometry and spectral action functionals associated to 1D Supersymmetry Algebras, using the classification of these superalgebras in terms of Adinkra graphs and the construction of associated dessin d'enfant and origami curves. The resulting spectral action functionals are computed in terms of the Selberg (super) trace formula.

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