Title: The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds

Abstract: We will discuss an open version of Ruan's Crepant Transformation Conjecture, which is an identification of disk invariants of toric Calabi-Yau 3-orbifolds related by crepant birational transformations. Our main tool is a mirror theorem of Fang-Liu-Tseng that relates these disk invariants to local coordinates on the B-model mirror curves. Treating crepant transformations as wall-crossings in the GKZ secondary fan, we will establish the identification of disk invariants through constructing a global family of mirror curves over charts of the secondary variety and understanding analytic continuations of local coordinates. Our work generalizes previous results of Ke-Zhou on a particular type of crepant resolutions and of Brini-Cavalieri-Ross on the example of A_n-singularities.