The Landau-Ginzburg/Calabi-Yau correspondence refers to a conjectural equivalence between Gromov-Witten invariants (virtual counts of curves in hypersurfaces) and Fan-Jarvis-Ruan-Witten invariants (virtual counts of curves equipped with a root of their canonical bundle). Originally suggested by Witten, the Landau-Ginzburg/Calabi-Yau correspondence was made mathematically precise and proved for genus-zero invariants by Chiodo and Ruan in 2008. Moreover, Chiodo and Ruan suggested an explicit higher-genus correspondence written purely in terms of genus-zero data.

In this talk, I will describe the genus-one verification of Chiodo and Ruan's higher-genus conjecture for the quintic threefold. The first hour will focus on discussing the background of the problem and previous results, including our recent result that provides an explicit formula for genus-one FJRW invariants. The second hour will be devoted to discussing the higher-genus formulation of the Landau-Ginzburg/Calabi-Yau correspondence in terms of quantized symplectic operators, and the proof of the restriction to the genus-one invariants. This is a report on joint work with Shuai Guo. Speaker(s): Dustin Ross (San Francisco State)