7 problems

A ring polymer is a closed polymer chain, and a ring polymer is nontrivially knotted when its embedding in space has nontrivial knot type. Frisch–Wasserman–Delbrück conjecture. Non…

A polygon is a closed self-avoiding polymer chain, and its prime factors are the prime knot summands in its knot decomposition. Prime factors are tight and isolated from each other…

Let $\beta_c^Q$ denote the quenched critical value for adsorption, and let the models be lattice trees and lattice animals in dimension $d$. Finite critical value conjecture. The q…

Let $\beta_c^Q(\mathcal{P}^X)$ denote the quenched critical value for the model $\mathcal{P}^X$, with $\mathcal{T}^{\circ \! |\! \circ}$ and $\mathcal{T}^+$ the penetrable and impe…

A linear polymer in dilute solution is sufficiently long and undergoes a ring-closure reaction, producing a ring polymer. Frisch–Delbrück conjecture. Such ring polymers should be k…

Consider the free boundary position $s(t)$ in the free boundary model for the diffusion of solvent molecules into EPDM rubber, with the numerical instance corresponding to Figure (…

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…