7 problems

Let the $l$-polygon problem denote the vortex filament evolution whose initial curve is a planar $l$-polygon, and let a one-corner problem denote the corresponding evolution from i…

Fourier-coefficient limit conjecture. Numerical experiments suggest that

Let $a$ and $\varepsilon$ be the parameters of the symmetric Painlevé IV solutions $\sigma_{\pm a,\varepsilon}(s)$, let $\mathsf C(s)$ denote the curvature scaling function, and le…

Let $\widehat{\mathbf T_s}(t)$ denote the transformed tangent derivative in the three-corner case, and let $\alpha\approx0.258039752572419$ and $\beta\approx0.239126094505514$. Log…

Let $\widehat{\mathbf T_s}(t)$ denote the relevant transformed tangent derivative for the three-corner case $M=3$, and let $\widehat{T_{1,s}}(t)$ be its first component. Three-corn…

Let $M$ and $q$ be positive integers, let $p$ be coprime with $q$, let $\rho$ be the corner angle, let $\mathbf T_{\mathrm{alg},j}$ be the algebraic tangent vectors of the correspo…

Let $M$ be the number of sides of the initial regular planar polygon, and let $t_{pq}=(2\pi/M^2)(p/q)$, where $p\in\mathbb Z$, $q\in\mathbb N$, and $\gcd(p,q)=1$. At this rational…