Commutative Algebra and Algebraic Geometry: Genus-One Landau-Ginzburg/Calabi-Yau Correspondence

Seminar | March 7 | 5-6 p.m. | 939 Evans Hall

 Dustin Ross, San Francisco State University

 Department of Mathematics

First suggested by physicists in the late 1980'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, which is determined from genus-zero data alone. 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.