Matthew Kwan, Very sparse random discrete matrices

Extremely sparse random binary matrices tend to be singular, due to the likely presence of “local combinatorial dependencies” such as all-zero columns or pairs of identical columns. We discuss this phenomenon, and some results showing that these kinds of combinatorial dependencies are in some sense the “only” causes of singularity. This is joint work with Asaf Ferber, Margalit Glasgow, Ashwin Sah and Mehtaab Sawhney.