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Explore a lecture on the noncommutative minimal model program and its implications for the stability manifold of triangulated categories. Delve into Daniel Halpern-Leistner's proposed framework, which connects the quantum differential equation of projective varieties to paths in the stability manifold. Examine how these paths converge in a partial compactification known as the space of "augmented stability conditions." Learn about multi-scale decompositions, a generalization of semiorthogonal decompositions, and the moduli space of multi-scale lines. Investigate the main conjecture regarding the space of augmented stability conditions as a manifold with corners and its potential consequences for moduli spaces of semistable objects in smooth and proper dg-categories.
