6 problems

Combinatorial formulation conjecture. Then

Symmetric area inequality conjecture. One has

Area inequality conjecture. Then

Quadripartite periodic square peg conjecture. The quadruplet

Periodic square peg conjecture. The union $\sigma_1(\mathbb{R}/L\mathbb{Z})\cup\sigma_2(\mathbb{R}/L\mathbb{Z})$ inscribes a square.

Let $T$ be an immersed curve in the plane, and let $St$, $J^+$, and $J^-$ denote its associated invariants. An inscribed square of a curve is a square whose vertices lie on the cur…