Hypergeometric Series in Arithmetic Geometry

Classical hypergeometric series are a generalisation of geometric series, wherein the ratios of consecutive terms are now rational functions, rather than constants. (They also appear very naturally from Gauss' hypergeometric differential equation.) Greene introduced an analogous notion of hypergeometric series on finite fields, which has given rise to a lot of recent work in the area. We will introduce all these concepts and also p-adic analogues of hypergeometric series and mention some of our results in this area. This talk will not assume a lot of background and we will introduce most of the notions as we move along.

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