first suggested by witten in the early 1990's, the landau-ginzburg/calabi-yau correspondence studies a relationship between spaces of maps from curves to the quintic 3-fold (the calabi-yau side) and spaces of curves with 5th roots of their canonical bundle (the landau-ginzburg side). the correspondence was put on a firm mathematical footing in 2008 when chiodo and ruan proved a precise statement for the case of genus-zero curves, along with an explicit conjecture for the higher-genus correspondence. in this talk, i will begin by describing the motivation and the mathematical formulation of the lg/cy correspondence, and i will report on recent work with shuai guo that verifies the higher-genus correspondence in the case of genus-one curves.