Kaie Kubias - Aalto University, Department of Mathematics and Systems Analysis We study the problem whether a partial tensor is completable to a rank-one tensor and if yes, whether the completion is unique or finite. A partial tensor is completable to a rank-one tensor over complex numbers if its entries satisfy a set of polynomial equations and it is zero-consistent. We also characterize when a partial tensor that is completable to a rank-one tensor over complex numbers is completable to a rank-one tensor over real numbers. Finally, we will present results on unique and finite completability to rank-one tensors. The talk is based on joint work with Thomas Kahle, Mario Kummer and Zvi Rosen.