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Explore a comprehensive lecture on the construction of globally defined shifted potential functionals over moduli stacks of stable sheaves on Calabi-Yau 4-folds. Delve into the development of globally defined shifted symplectic structures on DG Quot schemes of sheaves over DG manifolds, and examine the theory of dg Quot schemes as a homotopy site. Investigate the generalization of this construction over DG Quot stacks and learn about the existence of globally defined Lagrangian distributions on derived schemes with (-2)-shifted symplectic structures. Discover how these concepts apply to stable loci of derived Quot stacks of coherent sheaves on Calabi-Yau four-folds, resulting in perfectly obstructed smooth stacks with globally defined (-1)-shifted potentials. Gain insights from joint works with Borisov, Katzarkov, and Yau, based on research papers available on arXiv.
