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Andy Jiang
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Andy Jiang
  • 2.3k
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  • 19

What is the current status of derived differential geometry?

I hope you will excuse this naive and general question. I've read from many places (e.g. Dominic Joyce's website, John Pardon's thesis, etc.) that the/a "right" foundations for many constructions in sympletic geometry, such as Fukaya category, and Gromov-Witten theory should be done starting from some formalism of derived differential geometry. I am aware that Dominic Joyce is still writing a series of books on this, but my question is more about let's say big picture understanding of this approach. Is there a consensus, assuming a general theory of derived manifolds, how these constructions should be done? If so, can someone explain, sacrificing the rigor needed, a high level outline of these constructions? Sorry if this is inside of say Joyce's writings.