Combinatorial nullstellensatz and its applications

Abstract

In 1999, Noga Alon proved a theorem, which he called the Combinatorial Nullstellensatz, that gives an upper bound to the number of zeros of a multivariate polynomial. The theorem has since seen heavy use in combinatorics, and more specifically in graph theory. In this thesis we will give an overview of the theorem, and of how it has since been applied by various researchers. Finally, we will provide an attempt at a proof utilizing a generalized version of the Combinatorial Nullstellensatz of the GM-MDS Conjecture.