Synchronization is crucial for the success of many data-intensive applications. This problem involves estimating global states from relative measurements between states. While many studies have explored synchronization in different contexts using pairwise measurements, relying solely on pairwise measurements often fails to capture the full complexity of the system. In this work, we focus on a specific instance of the synchronization problem within the context of structure from motion (SfM) in computer vision, where each state represents the orientation and location of a camera. We exploit the higher-order interactions encoded in trifocal tensors and introduce the block trifocal tensor. We carefully study the mathematical properties of the block trifocal tensors and use these theoretical insights to develop an effective synchronization framework based on tensor decomposition. Experimental comparisons with state-of-the-art global synchronization methods on real datasets demonstrate the potential of this algorithm for significantly improving location estimation accuracy. To our knowledge, this is the first global SfM synchronization algorithm that directly operates on higher-order measurements. This is joint work with Joe Kileel (UT Austin) and Gilad Lerman (UMN). The talk will be on zoom (https://utexas.zoom.us/j/92486890961?pwd?v3UuP4yFjLCnYQO2ppynkAh1aR3d.1 with meeting ID 924 8689 0961 and passcode applmath). Additionally, a viewing party will take place in PMA 9.166.