| Abstract |
Period integrals are numbers which can be expressed as an integral (e.g. an integral of an algebraic differential over a homology cycle). Given a family of complex algebraic manifolds, one can study the geometry of the family via the so-called period map; it is a variation of ratios of period integrals. For Calabi--Yau (CY) manifolds, period integrals contain important information about their complex moduli spaces and thus finding (calculating) period integrals becomes one of the main approaches of understanding their moduli spaces. Moreover, as predicted by mirror symmetry, they also encode the enumerative geometry of another CY manifold. In this talk, I will explain the ideas as well as our program on singular CY varieties; in short, for our singular CY varieties, it turns out that the period integrals compute orbifold GW invariants of another singular CY variety. This is based on joint works with Shinobu Hosono, Bong Lian, Mauricio Romo, and Shing-Tung Yau. |
