Non-slice linear combinations of iterated torus knots

Algebraic knots are knots which arise as links of isolated singularities of complex curves. Lee Rudolph conjectured that the set of algebraic knots is linearly independent in the smooth knot concordance group. Rudolph’s conjecture is very closely related to one of the most important conjectures in knot theory - the Slice-Ribbon conjecture. The purpose of this this talk is to discuss some new evidence towards the veracity of Rudolph’s conjecture.