16 problems

The conjecture. The category $\mathcal M(p)$ is equivalent to the category of modules over $\mathbf A^{(p)}\times\mathbb Z_{<p}^r$ for an appropriate $r$ depending on $p$.

Let $\mathbb{K}$ be a field, let $q\in\mathbb{K}^{\times}$ be a non-zero scalar, and let $F$ and $G$ be strict polynomial functors. Write $F^{(1)_q}$ and $G^{(1)_q}$ for their quan…

Polynomial comonad construction conjecture. Every polynomial comonad over $\mathcal{S}$ admits such a canonical construction, and every complete Segal space arises from this constr…

Let $d$ be a nonnegative integer, and let ${\mathsf{OEpi}}_{\leq d}$ be the category of finite-dimensional inner product spaces of dimension at most $d$ and orthogonal epimorphisms…

Let $r\in\mathbb{N}$, and let $\Phi^1[r+2,r]$ be the $\mathfrak{S}_{r+2}\times\mathfrak{S}_r$-module appearing in the relative polynomial-degree-$2$ Lie algebra homology calculatio…

Let $F$ and $G$ be strict polynomial functors, let $F^{(s)_q}$ and $G^{(s)_q}$ denote their $s$-th quantum Frobenius twists, and define … For each degree $k$, the iterated quantum…

Let $F$ and $G$ be strict polynomial functors, let $F^{(1)_q}$ and $G^{(1)_q}$ denote their quantum Frobenius twists, and let…

Let $E_r=\operatorname{Ext}_{\mathcal{P}^{}_q}^*(I^{(r)_q},I^{(r)_q})$ be the graded Ext-algebra, with multiplication given by the Yoneda product. The authors have not determined a…

Polynomial-functor conjecture. This integral transform can be described as a polynomial functor, with $p_\otimes$ and $o_\oplus$ corresponding respectively to the dependent product…

Non-holonomous polynomial construction conjecture. The construction

Let a topos with natural number object be a topos equipped with a natural number object, and let a monic polynomial with reductions be as considered in the paper. Initial-algebra f…

A monic polynomial with reductions is the polynomial-with-reductions structure considered in the paper whose underlying polynomial map is monic. Choice-necessity conjecture. In gen…

Let $F_n$ be a free group of rank $n$, and let $IA_n$ be the kernel of the canonical epimorphism ${\rm Aut}(F_n)\twoheadrightarrow GL_n(\mathbb{Z})$. For each $d\in\mathbb{N}$, let…

Let $F_n$ be a free group of rank $n$, and let $IA_n$ be the kernel of the canonical epimorphism ${\rm Aut}(F_n)\twoheadrightarrow GL_n(\mathbb{Z})$. For each $d\in\mathbb{N}$, let…

Weak polynomial degree conjecture. For every nonunital ring $I$ and every integer $n\in\mathbb{N}$, the functor $H_n(\Gamma_I)$ is weakly polynomial of degree at most $2n$.

Let $\Bbbk$ be an algebraically closed field of characteristic $p\neq 2$, and let … be the category of all spin polynomial functors over $\Bbbk$. The spin polynomial functor catego…