4 problems

Let $C$ be a piecewise $C^2$ curve with positive corner angles. Its tantrix is the image of its unit tangent map on the unit sphere, together with the great-circle arcs joining the…

Let $\operatorname{Wr}$ denote the writhe of a curve, and let the $C^1$ norm measure the distance between curves and their first derivatives. Continuity conjecture. The writhe…

Let $C$ be a smooth projective curve, let $L$ be a line bundle on $C$, and let $V\subseteq H^0(C,L)$ be a subspace such that $(L,V)$ is a generating pair, meaning that $V$ generate…

Let $X \subseteq \mathbb{P}^n$ be a smooth curve of genus $g$ and degree $d \geq 2g+2k+1$. Let $\Sigma_k$ denote its $k$th secant variety, and let $\mathcal{I}_{\Sigma_k}$ be the i…