13 problems

An algebraic knot is a knot arising from an algebraic plane curve singularity; these knots are, in particular, iterated cables of torus knots. The smooth knot concordance group is…

Let $P:\mathbb{C}^2\to\mathbb{C}$ have an isolated critical point at the origin, and let $K=P^{-1}(0)\cap S^3_\epsilon$ be the resulting algebraic knot. The Milnor fiber of the ass…

Shastri's conjecture. The algebraic trefoil knot embedding is non-rectifiable over $\mathbb{C}$.

Let $\mathcal{J}_\ell$ be the moduli space of flags of modules associated with an algebraic knot, and let its geometric superpolynomial be defined using the Borel–Moore homology of…

Let $Z=\{f(x,y)=0\}\subset\mathbb{C}^2$ be a curve with a unibranch singularity at $0$, and let $K=K_Z$ denote its link, which is a knot. Let $\delta$ be the Milnor number of…

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.

Let an uncolored algebraic knot be evaluated through the DAHA superpolynomial coefficients, and call a pair of zeros irregular when it is not on the Riemann-Hypothesis circle and r…

Let $\varpi_i=\infty\{\omega'_i\}$ be the threshold from the strong Riemann-hypothesis conjecture for the $i$th coefficient of an uncolored algebraic knot. Threshold conjecture. Fo…

Let $\mathcal{A}$ be the subgroup of the smooth concordance group generated by algebraic knots, and let $\mathcal{L}$ be the subgroup generated by $L$-space knots. A subgroup is fr…

Let $\mathcal{H}_{\{\vec{\mathsf r},\vec{\mathsf s}\}}$ be the uncolored DAHA superpolynomial associated with an algebraic knot, and write it as a polynomial in its variables. DAHA…

ORS geometric conjecture. The reduced HOMFLY homology of the knot link$(C,x)$ has Poincare polynomial

Let $\mathcal{C}$ be the abelian group of concordance classes of oriented knots, and call a knot algebraic if it is an algebraic knot. Let $\mathcal{A}\subset\mathcal{C}$ be the su…