In this talk I will introduce a proof of Coates-Corti-Iritani-Tseng-Ruan version of the Crepant Transformation Conjecture for toric stack bundles. We follow Givental’s approach to transform this problem into finding a linear symplectic isomorphism between the corresponding symplectic spaces so the I-functions coincide after analytic continuation. We compare it with the Fourier-Mukai transformation between the K-groups to show they actually match up.

This talk is based on arXiv:2410.22670 and arxiv:2407.21288.