Combinatorial Nullstellensatz

A recently formulated technique in algebraic combinatorics will be considered. After introducing the framework and proving the main theorem, some applications of Combinatorial Nullstellensatz to number theory and combinatorics will be shown, such as Chevalley-Warning and Cauchy-Davenport theorems, Erdős-Heilbronn conjecture, and a problem of a hyperplane covering of the vertices of a hypercube.