Elliptic Curves, Reality, and String Duality

String theories (there are several variants) require a space on which to compactify. This space is typically a Calabi-Yau manifold, but "toy models" which exhibit many essential features can even be low dimensional tori. We will explore how the classification of elliptic curves with involution sheds light on dualities between variant string theories, studying both through the topological lens of a real variant of K-theory.