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null (Ed.)Abstract The hybrid model is the Landau–Ginzburg-type theory that is expected, via the Landau–Ginzburg/ Calabi–Yau correspondence, to match the Gromov–Witten theory of a complete intersection in weighted projective space. We prove a wall-crossing formula exhibiting the dependence of the genus-zero hybrid model on its stability parameter, generalizing the work of [21] for quantum singularity theory and paralleling the work of Ciocan-Fontanine–Kim [7] for quasimaps. This completes the proof of the genus-zero Landau– Ginzburg/Calabi–Yau correspondence for complete intersections of hypersurfaces of the same degree, as well as the proof of the all-genus hybrid wall-crossing [11].more » « less
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null (Ed.)Abstract We lay the foundation for a version of $$r$$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $$r$$-spin disks, their moduli space, and the Witten bundle; we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically relatively oriented relative to the moduli space. In the sequel to this paper, we use these constructions to define open $$r$$-spin intersection theory and relate it to the Gelfand–Dickey hierarchy, thus providing an analog of Witten’s $$r$$-spin conjecture in the open setting.more » « less
