Speaker: Zongrui Yang (Columbia University)

Title: LG/CY correspondence between tt* geometries

Abstract: tt* geometric structure was introduced by physicists and then studied firstly in mathematics by C. Hertling. Given a nondegenerate homogeneous polynomial with degree equal to its number of variables, it defines a Calabi-Yau hypersurface in the projective space, whose universal deformation space has a tt* structure induced from variation of Hodge structures. Also the polynomial itself can be considered as a hypersurface singularity, whose unfolding of singularities has a tt* structure from Landau-Ginzburg theory. We prove that there exists a tt* substructure on the Landau-Ginzburg side that is isomorphic to the tt* structure on the Calabi-Yau side. This is my undergraduate work, joint with Huijun Fan and Tian Lan.