Algebraic Sato-Tate group for motives

In my talk I will explain the notion of equidistibution, in particular the Sato-Tate conjecture concerning the equidistribution of Frobenius elements in l-adic representations. In particular  I will show how to apply the motivic Galois group to construct Algebraic Sato-Tate  group to study equidistribution of Frobenius elements for l-adic representations associated with motives. In principal this work is based on computations in algebraic  groups. This is joint work with Kiran Kedlaya.