4 problems

Let $C$ be an irreducible plane curve singularity, let $L$ be the corresponding algebraic knot, and let $\beta$ be the corresponding braid on $n$ strands. Let $X(\beta\Delta;w_0)$…

Arbitrarily large four-genus conjecture. There are algebraically slice GA-knots with arbitrary large topological four-genus.

A knot is algebraic if it arises as the link of an isolated singularity of a complex curve. Let $\mathcal{C}$ denote the smooth knot concordance group. Rudolph's conjecture. The se…

Let $C$ be a curve in $\mathbb{C}^2$ given by $f(x,y)=0$ and passing through the origin. Intersecting $C$ with the boundary of a sufficiently small ball around the origin gives an…