Hypergeometric families and Beilinson’s conjectures

I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions.  One can view this as a “higher” version of the Mordell-Weil group for families of elliptic curves, giving rise to sections of “higher” Jacobian bundles which produce solutions to certain inhomogeneous Picard-Fuchs equations.  This is part of a joint project with Vasily Golyshev which aims to numerically verify Beilinson’s conjectures in some new cases.