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Explore a one-hour lecture from Cornell University's Daniel Halpern-Leisnter examining the construction and implications of moduli spaces of semistable objects in dg-categories. Delve into how algebraic geometers utilize Bridgeland stability conditions to construct moduli spaces of complexes of coherent sheaves and analyze their wall-crossing phenomena. Learn about a conjectured mass-Hom inequality for stability conditions on general smooth and proper dg-categories, developed with Alekos Robotis, which suggests the existence of compact moduli spaces of semistable objects. Discover how these findings impact symplectic topology and potentially transform homological mirror symmetry from a "conjectural conjecture" to a "conjecture."
