8 problems

Uniform convergence conjecture. Uniform convergence over compact subsets of $[0,\infty)$ in the general case $H<\frac{1}{2\rho+1}$ should eventually be proved by obtaining suitable…

For any $\delta>0$, let $\mathcal{C}_{\mathfrak{s};\mathrm{loc}}^{-\delta}(\mathbf{R}_{>0}\times\mathbf{T}^{2})$ and $\mathcal{C}^{-\delta}(\mathbf{T}^{2})$ denote the correspondin…

Improved diagrammatic-bound conjecture. This bound is true whenever $d>3(2\wedge\alpha)$.

Let $\mathbb{F}$ be a field, and let $M$ be an $\mathbb{F}$-orientable $k$-stacked and $(k+1)$-neighbourly $\mathbb{F}$-homology manifold without boundary of dimension $2k+1$. Conj…

Let $M$ be a triangulated manifold, and suppose that $M$ is $\mathbb{F}$-tight, meaning tight over a field $\mathbb{F}$. Say that a triangulation is strongly minimal if it has the…

Let $X$ be a simplicial complex. Call $X$ $\mathbb{F}$-tight when it has the tightness property over a field $\mathbb{F}$, and call it strongly minimal when it achieves the compone…

Let $M^6_{16}$ be the constructed $16$-vertex combinatorial triangulation of $S^4\times S^2$, viewed as a $2$-Hamiltonian subcomplex of the $8$-dimensional cross polytope $\beta^8$…

Let $M$ be a $2$-neighborly combinatorial triangulation of $S^4\times S^2$ with $14$ vertices that lies in $\mathcal{K}^2(6)$. The preceding bounds force such a triangulation to be…