5 problems

For $d\ge 3$, let $T_d$ be the recursively defined polynomial in the elementary symmetric functions on the standard simplex $T^d$, and write $\|T_d\|_{C(T^d)}$ for its uniform norm…

Filliman's conjecture. The minimum $k$-dimensional projection volume is attained by $T_{\ast}$:

Let $S_d$ be the real $d$-simplex, let $F_4$ be the set of $N=\binom{d+4}{4}$ points constructed in the paper, and let $\ell_j$ be the associated fundamental Lagrange polynomials.…

Let $S_d$ be the real $d$-simplex, let $F_4$ be the set of $N_4=\binom{d+4}{4}$ points constructed in the paper, and let $\ell_i$ be its fundamental Lagrange polynomials. The degre…

Let $c(d,n,k)$ denote the extremal signed-sum quantity studied in the paper, and let $\omega_{d+1}$ be the corresponding extremal vector configuration. For a linear subspace…