4 problems

For each dimension $d$, let $\epsilon_d$ denote the universal exponent parameter for $d$-dimensional simplicial complexes. Universal exponent asymptotic conjecture. The universal e…

Let $d\geq 3$, let $\mathbb S^d$ be the $d$-dimensional sphere, and let $\operatorname{ex}_{\hom}(n,\mathbb S^d)$ denote its topological Turán number. Newman–Pavelka sphere exponen…

Let $X$ be a 2-dimensional simplicial complex in which every 1-simplex is contained in at least two 2-simplices. The topological Turán number is denoted by…

Let $X$ be any 2-dimensional simplicial complex. The topological Turán number is denoted by $\operatorname{ex}_{\hom}(n,X)$. Universal upper-bound conjecture. There is a constant…