I will talk about the LG/CY correspondence for some simple examples, mainly elliptic orbifold curves.

In the first part of my talk I will present the joint work arXiv:1603.02660 with Yefeng Shen about the proof of LG/CY correspondence for elliptic orbifold curves using A-model techniques and modular forms. I will focus on its explanation in terms of change of local trivializations of some vector bundles. Different trivializations of the same section describe generating series in different enumerative theories, and the transition function is related by modular transformation. This can be regarded as a toy model of Givental's formalism, but using only elementary tools from the theory of modular forms.
Speaker(s): Jie Zhou (Perimeter Institute)