Gromov-Witten theory and variation of Hodge structure under conifold transitions for Calabi-Yau threefolds


Yuan-Pin Lee

10:00:00 - 10:50:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

The moduli of Calabi-Yau threefolds are generally believed to be connected by geometric processes called transitions, which are roughly speaking degenerations followed by small resolutions. In this talk, I will explain a phenomenon of partial exchange of A model (Gromov-Witten theory) and B model (variation of Hodge structure) when a Calabi-Yau threefold undergoes a conifold transition.

In particular, it is well known that both A and B models (at genus zero) can be described by flat connections, Dubrovin connection for the A model and Gauss-Manin connection for the B-model. In the process of conifold transitions, the residues of the regular singular part of connections are exchanged via the topological data. This suggests a possibility of a flat connection on a combined “A+B theory”, which, if exists, should be invariant under transitions.

This talk is based on joint work with Hui-Wen Lin and Chin-Lung Wang