A Geometric Approach to Low-Rank Matrix and Tensor Completion
Low-rank completion asks: given only a fraction of the entries of a matrix or tensor, when and how can the missing entries be recovered? The question sits at the heart of recommender systems, image inpainting, and sensor data recovery, and its answer depends delicately on which entries are observed and what rank is assumed.
My doctoral dissertation, completed at the University of Georgia, develops a geometric approach to these completion problems — studying the structure of the set of low-rank matrices and tensors to understand when completion is possible and to design methods for computing it.