The Combinatorial Nullstellensatz and some applications to additive combinatorics

The "polynomial method" - a family of tools of algebraic-combinatorial nature - has been successfully applied in the last few decades in tackling difficult problems in number theory, mostly (but not exclusively) additive combinatorics. In the talk, I present the most well-known member of this family, namely, the Combinatorial Nullstellensatz, and show a few applications, including the proof of the finite field Kakeya conjecture (a result of Dvir).