Sept 29 at 17:30 in 507

Title:  The space of augmented stability conditions

Abstract:

Talk 1: I will briefly review some background material and then present Bridgeland stability conditions on triangulated categories. After that, I will discuss two key examples in depth, elliptic curves, and the projective line. Time permitting, I will give the intuition of why paths of stability conditions should correspond to semiorthogonal decompositions of a category.

Talk 2: I will discuss the formalism of quasi-convergent paths, and explain how this framework suggests that (some) boundary points of the space of stability conditions should correspond to polarised semiorthogonal decompositions.  After this, I will take a detour into algebraic geometry to present the construction of a moduli space of "multi-scale lines" and indicate how it is related to compactifying the space of stability conditions.

Talk 3: In this final talk, I will combine all of the ingredients from the previous talks to explain a new partial compactification of the space of Bridgeland stability conditions, which is joint work with Daniel Halpern-Leistner. The boundary points consist of objects called augmented stability conditions. I will conclude by explaining the partial compactification in the case of an elliptic curve and the projective line.