Dispatches from the Ends of the Stability Manifold - Lecture 3

Explore the third lecture in a series on stability manifolds and noncommutative minimal model programs delivered by Daniel Halpern-Leistner from Cornell University at the M-Seminar, Kansas State University. Delve into the concept of augmented stability conditions, a partial compactification of the stability manifold. Learn about multi-scale decompositions, a generalization of semiorthogonal decompositions in triangulated categories, and discover the new moduli space of multi-scale lines. Examine the main conjecture regarding the space of augmented stability conditions as a manifold with corners and its potential implications for proper moduli spaces of semistable objects in smooth and proper dg-categories. Gain insights into the noncommutative minimal model program, where quantum differential equations of projective varieties determine paths toward infinity in the stability manifold, leading to canonical decompositions of derived categories.