### Hypergeometric motives of low degrees

Heilbronn Number Theory Seminar

7th February 2018, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

In this talk we will discuss the construction of hypergeometric motives as Chow motives in explicitly given algebraic varieties. The class of hypergeometric motives corresponds to Picard-Fuchs equations of hypergeometric type and forms a rich family of pure motives with nice L-functions. Following recent work of Beukers-Cohen-Mellit we will show how to realise certain hypergeometric motives of weights 0 and 2 as submotives in elliptic and hyperelliptic surfaces. An application of this work is computation of minimal polynomials of hypergeometric series with finite monodromy groups and proof of identities between certain hypergeometric finite sums, which mimics well-known identities for classical hypergeometric series.

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