d invariants obstruction to sliceness of a class of algebraically slice knots

A long-standing question in knot theory asks whether the set of algebraic knots is linearly independent in the knot concordance group; in other words, whether every nontrivial linear combination of algebraic knots fails to be slice. Since a slice knot is necessarily algebraically slice, a natural refinement of this question is whether an algebraically slice linear combination of algebraic knots must also be smoothly slice. In this talk, I will introduce an obstruction from Heegaard Floer d-invariants and discuss the techniques for computation.