High Energy Physics seminar - Vishnu Jejjala (University of the Witwatersrand, Johannesburg, South Africa) "Aspects of Calabi-Yau Geometries"

We explore the distribution of topological numbers in Calabi-Yau manifolds using the Kreuzer-Skarke dataset of hypersurfaces in toric varieties as a testing ground. While the Hodge numbers are well-known to exhibit mirror symmetry, patterns in frequencies exhibit striking new patterns. In analyzing the Kreuzer-Skarke database, we present a new algorithm to isolate Swiss cheese solutions, many of which have multiple large cycles. Such Swiss cheese geometries facilitate moduli stabilization in string compactifications and provide flat directions for cosmological inflation. We discuss ongoing and future work with these datasets.