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.

Daniel Halpern-Leistner - Dispatches from the ends of the stability manifold (Lec 3)