The study of enumerative invariants dates back at least as far as Euclid’s work circa 300 BC, who observed that through two distinct points in the plane there is a unique line. In 1849, Cayley-Salmon found that there are 27 lines on a nonsingular cubic surface. In 1879, Schubert found that there are 2875 lines on a generic non-singular quintic threefold; Katz correctly counted 609250 conics in a generic nonsingular quintic threefold in 1986. In 1991, physicists Candelas-de la Ossa-Green-Parkes gave a generating function for genus 0 Gromov-Witten invariants of a generic non-singular quintic threefold by studying the mirror space. This observation represented a change in our approach to enumerative problems by counting rational degree d curves inside of the quintic threefold “all at once;” other landmark achievements in modern enumerative geometry include Kontsevich-Manin’s recursive formula for the number of rational plane curves. From the perspective of homological mirror symmetry, enumerative invariants come from the Hochschild cohomology of the Fukaya category. I’m interested in a different question, which asks what enumerative data can be gleaned from the bounded derived category of coherent sheaves. I’ll share results on giving presentations of derived categories, and if time allows, will describe Kalashnikov’s method to recover Givental’s small J-function and the genus 0 Gromov-Witten potential for CP^1 by viewing it as a toric quiver variety associated to the Kronecker quiver; i.e., from a presentation of the bounded derived category of coherent sheaves.