Towards a generalization of the Doran-Harder-Thompson (DHT) conjecture

Doran-Harder-Thompson proposed a topological mirror construction of a Calabi-Yau manifold that degenerates into a union of two quasi-Fano manifolds. This construction involves gluing mirror Landau-Ginzburg models, each representing a Calabi-Yau fibration over a disc, for each quasi-Fano component so that it yields a Calabi-Yau fibration over a projective line. In this talk, I will describe how to extend this construction to a more general type of degeneration. A key component is a multi-potential analogue of the LG model, which will be reviewed. If time permits, I will also discuss the relationship between this gluing construction and the mirror Clemens-Schmid sequence, recently introduced by Doran-Thompson.