Event description
Abstract: The significance of Calabi-Yau manifolds transcends both Complex
Geometry and String Theory. One possible approach to constructing
Calabi-Yau manifolds involves intersecting hypersurfaces within the
product of projective spaces, defined by polynomials of a specific
degree. We show a method to construct all possible complete
intersections Calabi-Yau five-folds within a product of four or less
complex projective spaces, with up to four constraints. This results
in a comprehensive set of 27,068 distinct spaces. For approximately
half of these constructions, excluding the product spaces, we can
compute the cohomological data, yielding 2,375 distinct Hodge
diamonds. We present distributions of the invariants and engage in a
comparative analysis with their lower-dimensional counterparts.
Supervised machine learning techniques are applied to the
cohomological data. The Hodge number $h^{1,1}$ can be learnt with high
efficiency; however, accuracy diminishes for other Hodge numbers due
to the extensive ranges of potential values.
The talk is a joint collaboration with Rashid Alawadhi, Andrea
Leonardo, and Tancredi Schettini Gherardini.