The main goal of this talk will be to motivate the study of algebraic geometry with a few elementary examples of varieties and toric varieties. In the first half, we will carefully explore the geometric ideas behind the notion of a variety, and relate geometric and algebraic data. Afterwards, we will proceed to construct toric varieties through their relations to convex geometry. Time permitting, we will further illustrate this dichotomy with a simple theorem.
The talk should be widely accessible -- basic geometric intuition and algebra recommended.