Claire Glanois (MPI, Bonn)
Multiple zeta values (MZV), and Euler sums are particularly interesting examples of periods (in the sens of Kontsevich-Zagier), appearing notably at the crossroad of number theory, algebraic geometry and quantum mechanics. First, we will give an overview of their algebraic properties, and in particular their conjectural Hopf algebra structure. Then, we will look how multiple zeta values embed into Euler sums, through a Galois descent perspective. We will also explain how, via this descent, thanks to the coaction (conjectural on MZV, existing on their motivic versions), we could deduce a new generating family (conjecturally basis) for MZV.
