Hypergeometric Supercongruences

In this talk, we will discuss supercongruences occurred to truncated hypergeometric series originated in the work and conjectures of Beukers and Coster. These congruences can be viewed as p-adic analogues of Hecke recursions satisfied by the coefficients of classical modular forms. Backgrounds and  approaches to supercongruences will be presented.
Then we will establish the supercongruences for the fourteen rigid Calabi--Yau threefolds, occurring as special fibers of explicit hypergeometric families. These supercongruences were conjectured by Rodriguez-Villegas. This is a joint work with Fang-Ting Tu, Noriko Yui and Wadim Zudilin.