Valerio Toledano Laredo

Title: Stability conditions and Stokes factors

Abstract: D. Joyce recently defined invariants counting semistable
objects in an abelian category A with a given class in K(A). He
obtained wall-crossing formulae with respect to a change of stability
condition for these invariants, constructed holomorphic generating
functions for these and showed that they satisfy an intriguing non-
linear PDE.  I will explain how Joyce's wall-crossing formulae may be
understood as Stokes phenomena for a connection on the Riemann sphere
taking value in the Ringel-Hall Lie algebra of the category A. This
allows one in particular to interpret his generating functions as
defining an isomonodromic family of such connections parametrised by
the space of stability conditions of A.

This is joint work with T. Bridgeland (arXiv:0801.3974).