Joseph Ayoub: Motivic Galois groups and periods

I'll explain the construction of a motivic Galois group \(G_{mot}(k,\sigma)\) associated to a field k endowed with a complex embedding \(\sigma\). I'll discuss some known results and some conjectures. In particular, I'll describe the conjectural relation to periods of algebraic varieties and the non-conjectural relation to solutions of Gauss–Manin connections.