A local-global theorem for $p$-adic supercongruences

In this talk, we provide a unified approach to constructing and proving $p$-adic supercongruences concerning truncated hypergeometric series. As applications, we establish several $p$-adic analogues of hypergeometric identities; in particular, we confirm a conjecture of Deines et al. This is a joint work with Hao Pan and Roberto Tauraso