Bartosz Naskręcki

Title: Hypergeometric motives of low degrees

Abstract: 
In this talk we will discuss the construction of hypergeometric motives 
as Chow motives in explicitely 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.