39 problems

Strong factorization conjecture. There exists a diagram

Weak factorization conjecture. Every such birational map admits this factorization, with the stated preservation of the open set and normal-crossings boundary.

Let $X$ and $Y$ be smooth complete varieties over a field of characteristic zero, and let $f:X\dashrightarrow Y$ be a birational map. A factorization of $f$ consists of a successio…

Let $\mathcal R_{\mathbb Q}=\bigcup_N\mathcal R_{1/N}$ be the rational Robba ring over $\mathbb C_p$, completed under the Gauss norm. Rational Robba-ring admissibility conjecture.…

Let $G$ be a graph of even order, and let $k$ be an integer. A graph is 1-factorable if its edges can be partitioned into 1-factors, equivalently if its chromatic index equals its…

Let $\mathcal{L}$ be a rational Landau diagram, and let $V_G$ be the associated variety with irreducible components $V_{G,\sigma}$. Let $\Delta_{\mathcal{L}}$ denote its LS discrim…

Let $n$ be a positive integer, and let $\mathbb{Z}^{\widetilde{O}(n^{n^{1/3}})}$ denote the integers in the indicated size range. The residue-class formulation. There exists a set…

Let $n$ be a positive integer, and let divisibility of a product mean that each integer in $\{1,\ldots,n\}$ divides that product. The most general divisor-set conjecture. For every…

Let $n$ be a positive integer. The $n$-divisor property means that every integer from $1$ through $n$ divides at least one member of a specified product. The generalized arithmetic…

Irreducible common-zero conjecture. If $h_1$ and $h_2$ have at least one common zero in $\mathbb C$, then

Ritt-type factorization conjecture. For every non-zero $E$-function $f$, there exist a unit $u\in\mathcal E^\times$, simple normalized $E$-functions $s_1,\ldots,s_p$ with pairwise…

Jossen's factorization conjecture. Every non-zero $E$-function $f$ can be written as a finite product of powers of $E$-functions with simple zeros, with distinct factors having no…

Block-partition factorization conjecture. There is an ordering $(\mathbf{T}_1,\ldots,\mathbf{T}_{(d-1)(k-1)-1},\mathbf{S})$ with…

Three-ary factorization conjecture. To leading order in these three parameters,

Brualdi–Busch conjecture. Some realization of $d70$ has $k$ edge-disjoint $1$-factors if and only if $\mathcal{D}_{k}(\pi)$ is graphic.

Two-component factorization conjecture. The ratio

Factorizability conjecture. If

Let $g\in VMO(S^1,SU(2))$. Let $A(g)$ and $A_1(g)$ be the operators associated with $g$, and let a triangular factorization mean the factorization specified in (II.3). A root subgr…

Let $k_2$ be the loop associated with a sequence $\zeta=(\zeta_n)$ satisfying $\zeta\in l^2$, and suppose the phases of the $\zeta_k$ are uniform and independent random variables.…

Let $r\geq 1$, and let $\bar F_{r,2}(x_1,x_2)$ be the determinant polynomial defined in the paper for $D=2$. Factorization conjecture. One has … The formula was supported by comput…

Let $X$ be the smooth scheme considered above, let $G$ be the reductive group with maximal torus $T$, and let $\ell$ be the chosen prime. Consider the diagram … The horizontal and…

The factorization conjecture. The canonical map factors through this fully faithful map, and the first arrow in the factorization

The equivalence conjecture. The map above is an isomorphism of Picard groupoids. This predicts that factorizable line bundles on the Ran affine Grassmannian are completely paramete…

Schinzel's non-cyclotomic factorization conjecture. There are finite sets $\Omega^0\subset\mathbb{Z}^{n\times n}$ of nonsingular matrices and $\Gamma\subset\mathbb{Z}^n$ of nonzero…

Multivariate pullback factorization conjecture. There is a finite set of matrices $\Omega\subset\mathbb{Z}^{n\times n}$ such that, for each $A\in\mathbb{Z}^{n\times k}$, there are…