4 problems

Let $P$ be a convex $n$-gon, and place $n$ distinct points on the moment curve in $\mathbb{R}^{4}$. The associated bar-and-joint rigidity matroid is represented by the rigidity mat…

Let $P$ be a convex $n$-gon, and let $k$-triangulations be its maximal sets of diagonals containing no $k+1$ mutually crossing diagonals. Place $n$ generic points on the moment cur…

For integers $n\geq 2$, parameters $0\leq \beta\leq n-1$, and $s\geq 1$, let $e(t)=e^{2\pi i t}$ and integrate over $[0,1]^{n-1}\times[0,N^{-\beta}]$. Mean value conjecture for the…

For integers $k,n$ with $k>3$, let $\mathcal{A}_{k,n}$ denote the Minkowski sum of $n$ copies of the moment-curve segment $\{(t,t^2,\ldots,t^k)\mid -1\leq t\leq 1\}$. Let…