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Explore the fourth lecture in a series on stability manifolds and their applications in algebraic geometry, delivered by Daniel Halpern-Leistner from Cornell University at the M-Seminar, Kansas State University. Delve into the structure of the boundary of augmented stability conditions, examining the manifold-with-corners conjecture and its implications. Investigate how this conjecture, if proven for smooth and proper dg-categories, could lead to the existence of proper moduli spaces of semistable objects for any stability condition. Gain insights into the noncommutative minimal model program, multi-scale decompositions, and the space of augmented stability conditions. This 1-hour 17-minute talk builds upon previous lectures in the series, offering a deep dive into cutting-edge research at the intersection of homological algebra, algebraic geometry, and category theory.
