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Title:
Derived differential geometry and moduli spaces in differential geometry
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Abstract:
Derived Differential Geometry (DDG) is the study of "derived manifolds" and "derived orbifolds", where "derived" is in the sense of the Derived Algebraic Geometry of Jacob Lurie and Toen-Vezzosi. They include ordinary manifolds and orbifolds, but also many spaces which are singular at the classical level. There are several approaches to DDG, due to Spivak, Borisov-Noel and myself, all more-or-less equivalent. The "Kuranishi spaces" studied in symplectic geometry by Fukaya-Oh-Ohta-Ono are a prototype notion of derived orbifold.
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