EVENT DETAILS AND ABSTRACT

Title: Stability conditions and Stokes factors
Speaker: Professor Valerio Toledano Laredo
Speaker Info: Northeastern University
Brief Description:
Special Note:
Abstract:

This talk will be concerned with stability conditions on an abelian category A, a notion introduced by Bridgeland which generalises that of Mumford stability for vector bundles over a curve.

The space Stab(A) of all such conditions has the structure of a complex manifold and has attracted a lot of attention recently. D. Joyce defined invariants which count, in a suitable sense, semistable objects in A and showed how to organise these in a holomorphic generating function on Stab(A) which satisfies an intriguing non-linear PDE.

I will explain how the transformation rules of Joyce's invariants and his PDE can be understood as Stokes phenomena. The latter describe the monodromy of solutions of ODE's on the complex plane around irregular singularities, that is poles of order greater or equal to 2.

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