Smooth and topological concordance of satellites of torus knots

Two knots in the 3-sphere are called concordant if they cobound an annulus in the cylinder. The resulting equivalence classes form a group called the concordance group. There are several variants, the smooth (i.e. C^infty), the topological (i.e C^0) and the algebraic (which classifies concordance in dimensions>4) concordance groups. I'll describe and outline the proofs of two results concerning satellites of knots obtained as links of algebraic singularities. First, that the Whitehead doubles of torus knots span a infinite rank subgroup of the smooth concordance group which lies in the kernel of the forgetful map to the topological concordance group. Second, that a subgroup of the topological concordance group spanned by links of algebraic singularities form an infinite rank subgroup which lies in the kernel of the map to the algebraic concordance group.