7 problems

Bigelow–Gonçalves–Kamada–Nakamura conjecture. The image $C(P_m^+)$ is the set of matrices $M=(M_{ij})\in {\rm Mat}_m^0$ satisfying: (I) $M$ is symmetric; (II) every $M_{ij}$ is a n…

Let $K$ be a positive braid knot, meaning a knot represented as the closure of a braid whose crossings are all positive. Let $b(K)$ denote its bridge index and $\beta(K)$ its braid…

Let $\hat\beta_1$ and $\hat\beta_2$ be positive braid knots. A positive path from $\hat\beta_2$ to $\hat\beta_1$ is a sequence of positive braid knots beginning at $\hat\beta_2$ an…

Let $T(2,a)$ and $T(4,b)$ denote torus knots, and write $K\leq_g J$ when $K$ is Gordian adjacent to $J$, meaning that $K$ can be obtained from $J$ by changing exactly $u(J)-u(K)$ c…

Let $A=(a_{ij})$ be a positively realizable symmetric matrix, and call a position $(i,j)$ fully supported if, for every $k$ between $i$ and $j$, at least one of $a_{ik}$ and…

Let $L$ be a positive braid link, and let $z$ be a zero of its Alexander polynomial. Positive braid Alexander-root conjecture. The real part of every such zero satisfies … with str…

Let the surface minor order be the order on surfaces defined by taking surface minors, and consider the canonical Seifert surfaces associated with positive braids, with no restrict…