I will begin with a gentle introduction to derived algebraic geometry and derived moduli spaces. Then, I will explain joint work with Hyeonjun Park ( arXiv:2604.04008), in which we construct shifted symplectic derived enhancements for rigidified moduli spaces of sheaves on Calabi-Yau varieties of dimension at least two. I will also discuss how this symplectic rigidification construction can be applied to reduced Donaldson-Thomas theory of Calabi-Yau 4-folds.
