Motivated by Bott periodicity, we will explore the space of based maps \mathbb{P}^1 \to \mathrm{Flags}(\mathbb{C}^n) . Using cohomological tools we will realize this moduli space as stable representations of a quiver, and then explicitly as an affine variety, and explain some ongoing work on the topological implications of this result. A special case of this result has been published as a postcard. This is joint work in progress with Jim Bryan and Ravi Vakil.