7 problems

Let $\ell_1$ and $\ell_2$ be binary $\mathbb{Z}$-lattices with equal discriminants … Assume that the pair $(\ell_1,\ell_2)$ is buried in a genus of rank $3$. Burying conjecture. Th…

Quadratic successive-maxima conjecture. As $D$ increases from its minimum, the successive maxima of $C_{\varepsilon}(D)$ occur only for prime conductors $f_K=\ell$ with…

Successive-maxima conjecture. (i) As $f$ increases from its minimum, the successive maxima of $C_{\varepsilon}({\mathcal F}_{G,f}^s)$, $C'_{\varepsilon}({\mathcal F}'{}_{G,f}^s)$,…

Maximum-genus-range conjecture. The maximum genus range of assembly graphs with $2n$ vertices is

Genus-range characterization. Any DOW whose corresponding graph has genus range $\{0,1\}$ is obtained from the word

Uniform sphere-retraction conjecture. For every integer $d$ there is an integer $m>0$ such that, for every polyhedron $X$ of dimension $d$, there are maps

Bounded genus conjecture. For every positive integer $n$ there is an integer $c_n$ such that