Variation of GIT quotients and Wall-crossing in Gromov-Witten theory

Given an action of a reductive group $G$ on a smooth projective variety, Iwill give a wall
crossing formula that relates the Gromov Witten graph potentials of the GIT quotients
$X//G$ as we vary the polarisation, under suitable stable=semi-stable conditions.  
If time permits I will describe how to use this formula to show a version of the crepant
transformation conjecture of Li-Ruan, in the case when the trasformation comes from
variation of GIT. This is work with Chris Woodward.