Abstracts for Conference "Galois representations and pencils of Calabi-Yau motives"

I will briefly describe a construction of mixed (Anderson) motives for the symplectic group $GSp_2$. These mixed motives are labelled by  automorphic cusp forms $f$ on $Sl_2$ and they are extensions of pure Tate motives. I will give a formula for the Betti-de-Rham extension classes. Some rather speculative arguments suggest that these motives "create" congruences between elliptic and Siegel modular forms. These congruences have been checked in experiments by Berstroem, Faber, van der Geer and Ghitza, Ryan and Sulon.