This quantity is a suite of articles on orbifolds, algebraic curves with better spin constructions, and comparable invariants of Gromov-Witten kind. Orbifold Gromov-Witten conception generalizes quantum cohomology for orbifolds, while spin cohomological box thought relies at the moduli areas of upper spin curves and is said through Witten's conjecture to the Gelfand-Dickey integrable hierarchies. a typical characteristic of those very various having a look theories is the primary function performed by way of orbicurves in either one of them. Insights in a single concept can frequently yield insights into the opposite. This publication brings jointly for the 1st time papers concerning either side of this interplay. The articles within the assortment disguise assorted issues, reminiscent of geometry and topology of orbifolds, cohomological box theories, orbifold Gromov-Witten thought, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of upper spin curves and spin cohomological box conception.
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