11 problems

Stable flatness conjecture. The algebra $\widehat{U}(\mathfrak g)$ is stably flat over $U(\mathfrak g)$ for every nilpotent Lie algebra $\mathfrak g$.

Collins–Fontenot conjecture. The following conditions are equivalent: $X$ is paracompact; $C_0(X)$ has a strictly totally bounded canonical approximate identity; and $C_0(X)$ has a…

Let $V$ be the weight sequence on $\mathbb{N}^2$ given by the preceding construction, and let $k_\infty(\mathbb{N}^2,V)$ be the corresponding Köthe co-echelon algebra. Property (v)…

Let $\mathsf{C}$ be an admissible subcategory of $\mathsf{CLCS}$, let $A\in\mathsf{alg}(\mathsf{C})$, and let $X\in A\text{-}\!\mathop{\mathsf{mod}}(\mathsf{C})$. The module $X$ is…

Let $\mathcal{E}'(\mathbb{R})$ be the commutative unital convolution algebra of compactly supported distributions on $\mathbb{R}$. Its Bass stable rank…

Let $A$ be an algebra and let $M$ be an invertible $A$-bimodule, with inverse $M^{-1}$. Write $4\widehat{A}4$, $4\widehat{M}4$, and $4\widehat{M^{-1}}4$ for their Arens–Michael env…

A topological lattice is a lattice $(L,\overline{\wedge},\overline{\vee})$ whose meet and join operations are continuous, and a space is compact and connected in the usual topologi…

Boundedness-to-algebra conjecture. A complete topological partial -algebra $\mathfrak{A}$ whose elements are all bounded is necessarily an algebra.

Let $A$ be a Fréchet algebra, and let a character on $A$ mean a nonzero multiplicative linear functional on $A$. Michael's conjecture. Every character on $A$ is continuous. The con…

Finite-codimensional subalgebra question. Must every subalgebra of finite codimension in $A$ be open?

Pointwise parametrization conjecture. Every element of $\Phi^{r}_{A(G)}$ is of the form $\alpha_{\gamma}$ for some $\gamma\in\Delta^{r}$, and $\Delta^{r}$ with the topology of poin…