6 problems

Let $K_1$ be an elliptic component and $K_2$ a hyperbolic component of a link $L=K_1\cup K_2$, and let $M$ be the embedded manifold whose holomorphic hull is denoted by…

Let $k$ be a fixed number, and consider links chosen randomly from links represented by grids whose size tends to infinity. Vanishing fixed-linking-number conjecture. The probabili…

Let $\mathscr{L}$ be an oriented link with two components. Its quadratic linking degree is…

Let $L_{mn}$ be the linking number of a random two-component link whose components have $n$ and $m$ segments, respectively, with vertices sampled independently from the same three-…

Let $b3$ be a piecewise linear unknot with vertices $p_i,dots,p_n$. Let $varepsilon>0$ be small enough that $N_varepsilon(b3)$ is a tubular neighborhood. For each choice of points…

Let $SL$ denote the self-linking number of an oriented uniform random walk or polygon in confined space, and let $E$ denote expectation. Mean absolute self-linking conjecture. As t…