Moduli Spaces and Related Topics | Hodge properties of confluent hypergeometric connections

Abstract:

Sabbah and Yu computed the irregular Hodge numbers associated with hypergeometric connections. In this talk, we introduce a new approach for hypergeometric connections whose defining parameters are rational numbers. Our method relies on a geometric interpretation of hypergeometric connections, which enables us to describe the irregular Hodge filtrations explicitly and derive several arithmetic applications on hypergeometric sums. This research is conducted in collaboration with Daxin Xu.