Dispatches from the Ends of the Stability Manifold - Lecture 2

Explore a lecture on the space of n-pointed multi-scale lines, delivered by Alekos Robotis from Cornell University as part of Daniel Halpern-Leistner's lecture series. Delve into the concept of multi-scale decomposition in triangulated categories, which generalizes semiorthogonal decomposition. Examine the newly introduced moduli space of multi-scale lines and its relation to moduli spaces of multi-scale differentials in dynamics. Investigate the proposed "noncommutative minimal model program" and its implications for defining canonical decompositions of derived categories. Learn about the partial compactification of the stability manifold through augmented stability conditions and the conjecture that this space is a manifold with corners. Understand the potential consequences of this conjecture, including the existence of proper moduli spaces of semistable objects for smooth and proper dg-categories.