Six proofs of mirror symmetry for elliptic curves

While originally a conjecture about Calabi-Yau manifolds in dimension 3, a key testing ground for techniques in mirror symmetry is dimension 1, in which case closed Calabi-Yau manifolds correspond to elliptic curves. I will describe six approaches to proving mirror symmetry for elliptic curves, starting with the original proof by Polischuck and Zaslow which establishes an explicit correspondence between objects, and ending with the use of Family Floer homology. In the process, we will discuss a variety of tools and methods that are generally useful in mirror symmetry.