Caleb Fong, Rutgers University

Abstract

The n-dimensional Boolean hypercube Q_n can be easily covered with 2 hyperplanes. If you add the additional restriction that exactly one point must remain uncovered, it takes some work to show—as Alon and Furedi did in 1993—that you need at least n hyperplanes to cover the rest. We will see the quick Combinatorial Nullstellensatz proof of this result, along with some more recent work on k-fold hyperplane covers of the hypercube (minus a point) due to Alexander Clifton and Hao Huang in 2019. 

See: https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html