4 problems

Let $\cal{P}$ be a parabola, let $\cal{C}$ be a focus-centered circle, and let $\cal{R}$ be a Poncelet family of $N$-gons inscribed in $\cal{P}$ and circumscribed about $\cal{C}$.…

Let $X=\mathbb{R}^n$ with $n\in\mathbb{N}$ and $n\geq 2$, and let $G=-I$. Consider the fixed-point equation for the polarity type operator referred to as equation (FixedPointConvex…

Self-polar maximizer conjecture. The maximizer of

Centrally symmetric realization conjecture. There is a $3$-polytope $P$ combinatorially equivalent to $Q$ such that