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.