Motivic Galois groups

Roughly speaking, the motivic Galois group of a field k is the group of
symmetries of the cohomology of algebraic varieties over k. Grothendieck gave a
conjectural definition relying on his Standard Conjectures but non-conjectural
constructions were then found by André (pure case) and Nori (mixed case)... I will
focus on a construction rooted in the framework of Voevodsky motives. In the first
part of the talk, I'll define the motivic Galois group and explain its relation
to several classical objects (Galois representations, mixed Hodge structures, periods).
In the second half, I will focus on the action of the motivic Galois group on
(some part of) the fundamental group of algebraic varieties. This will lead to
some motivic versions of famous theorems of Belyi and Pop.