Calabi-Yau Manifolds with Large Volume Vacua

We describe an efficient, construction independent, algorithmic test to determine whether Calabi–Yau threefolds admit a structure compatible with the Large Volume moduli stabilization scenario of type IIB superstring theory. Using the algorithm, we scan complete intersection and toric hypersurface Calabi-Yau threefolds with $2\le h^{1,1}\le 4$ and deduce that 418 among 4434 manifolds have a Large Volume Limit with a single large four-cycle. We describe major extensions to this survey, which are currently underway.