## Moment Varieties of Polytopes

The moments of the uniform distribution on a convex polytope are rational functions in its vertex coordinates. We study the projective varieties parametrized by these moments.

## On the Bloch-Kato conjecture for automorphic polarized motives

The goal of these lectures is to present a proof towards some results predicted by the Bloch-Kato conjecture giving a link between the order of vanishing of the L-function of a motive and the rank of the corresponding Bloch-Kato-Selmer group.

## On the Bloch-Kato conjecture for automorphic polarized motives

The goal of these lectures is to present a proof towards some results predicted by the Bloch-Kato conjecture giving a link between the order of vanishing of the L-function of a motive and the rank of the corresponding Bloch-Kato-Selmer group.

## On the Bloch-Kato conjecture for automorphic polarized motives

The goal of these lectures is to present a proof towards some results predicted by the Bloch-Kato conjecture giving a link between the order of vanishing of the L-function of a motive and the rank of the corresponding Bloch-Kato-Selmer group.