Georgia Institute of Technology College of Sciences

The rank r matrix completion problem studies whether a matrix where some of the entries have been filled in with generic complex numbers can be completed to a matrix of rank at most r. This problem is governed by the bipartite rigidity matroid, which is a matroid studied in combinatorial rigidity theory. We show that the study of the bipartite rigidity matroid is related to the study of tensor codes, a topic in information theory, and use this relation to understand new cases of both problems. Joint work with Joshua Brakensiek, Manik Dhar, Jiyang Gao, and Sivakanth Gopi.