The Ax-Grothendieck Theorem

The Ax-Grothendieck theorem states that every injective polynomial from C^n to C^n is bijective. I'll "prove" this theorem using model theory. Along the way, we'll take a brief tour of some important but surprisingly accessible theorems related to first-order logic. I won't assume any previous knowledge of the subject. (This is the same talk I gave two years ago, but I wanted to give it again because this is my favorite proof.)