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University College, Dublin
Title: p-adic hypergeometric series and supercongruences
Abstract: We discuss recent work in which we generalise Greene's hypergeometric series over finite fields in the p-adic setting. We provide congruences between these p-adic hypergeometric series and truncated ordinary hypergeometric series. We also relate a special value of the p-adic hypergeometric series to the p-th Fourier coefficient of a modular form, thus resolving an outstanding supercongruence conjecture of Rodriguez-Villegas.