In this talk, we will study the relation between the wall-crossing phenomenon in algebraic geometry and Stokes phenomenon for the ordinary differential equation on CP^1 with irregular singularities. The characteristic functions of semi-stable object form the Ringel-Hall algebra with associative product. And we will show that the wall-crossing formula can be expressed as the Stokes data of the irregular connection which varies isomonodromically.

 

Reference

Bridgeland and Toledano Laredo, Inventiones Mathematicae 187 (2012), 61-98