My original goal was to read the PTVV paper *Shifted Symplectic Structures* <https://arxiv.org/pdf/1111.3209v4.pdf>. I was quickly humbled!


Being told the theory ought to generalize symplectic structures on algebraic varieties and schemes I was unable to find a clear reference for these structures. I could get a hold of a paper or talk here and there giving some definition, but nothing futher.



Reference for symplectic structures on schemes?
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. 


