Dear past life Jacob,

Find a specific geometric problem that this stuff solves, which you think is interesting, and then you will find yourself magically learning it. For you, this problem was extending Donaldson-Thomas theory to Calabi-Yau 4-folds. Even in the Calabi-Yau 3-fold case, shifted symplectic structures show Behrend's notion of symmetric obstruction theory comes from a secret $-1$-shifted symplectic structure (this amazed you).

First read Behrend's paper (https://arxiv.org/abs/math/0507523) introducing symmetric obstruction theories, then possibly Joyce's paper on derived critical loci and DT3 invariants, and the Joyce-Borisov/Cao-Leung papers (https://arxiv.org/pdf/1504.00690.pdf /https://arxiv.org/pdf/1407.7659.pdf) on DT4 invariants. At that point you will not be able to sleep until you read PTVV.

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