4 problems

Let $M_k$ denote the maximal length of a closed geodesic with $k$ self-intersections on a hyperbolic surface, and let $\Gamma$ be a corkscrew geodesic on a thrice-punctured sphere.…

Asymptotic self-intersection conjecture. The limit is always equal to $1$, regardless of whether $X$ has a cusp or not:

Let $n\geq 2$ be an integer, and denote by $\sigma_{bn}$ and $\sigma_{cn}$ the buckling and contact pressures for the corresponding $n$-mode ring shape. For pressures satisfying…

Let $L_n\subseteq\mathbb{R}^n$ be a tropical line, and let $\pi:\mathbb{R}^n\to\mathbb{R}^2$ be a rational projection. A self-intersection point of $\pi(L_n)$ is a point where dist…