22 problems

Flexible Atom Conjecture. Every finite integral relation algebra with a flexible atom is representable over a finite set.

Let $\beta$ denote the Burau representation of the braid group on $n$ strands, let $q$ be a $d$-th root of unity, and let $\sigma$ denote the relevant braid-group generator. Write…

Let $p$ be a prime, let $x$ and $z$ be elements considered modulo $p$, and let $b$, $c$, and $d$ be matrices. General matrix representation conjecture. The group of order $8(p-1)$…

Multiplicity-free holonomy conjecture. For every finite group $H$, there exists a Bieberbach group $\Gamma$ with $\mathbb{Q}$-multiplicity-free holonomy representation…

Let $f_n={\cal L}^n f$ for the linear operator ${\cal L}$ on $L^2(SO(3))$ associated with the orientation distribution, and consider its finite-dimensional blocks indexed by irredu…

Proper stable module category equivalence. There should be an equivalence of symmetric monoidal stable $\infty$-categories

Let $R$ be the valuation ring of a finite extension $K$ of $\mathbb Q_p$, let $G$ be a finite group, and let $A^D$ be a Hopf $R$-order in $K[G]$. Define the extension-of-scalars ma…

Non-split extension conjecture. The extension $\widehat{V}$ admits no non-split extensions.

Let $G$ be a group and let $P_*$ be an acyclic complex of projective modules over the group algebra of $G$. Acyclic-complex conjecture. The complex $P_*$ should be totally acyclic,…

HyperCube regularizer minimizer conjecture. The unitary group representation $A_g=B_g=C_g^\intercal=\varrho(g)$ describes the unique minimizer of $\mathcal{H}$ up to unitary basis…

Sparse-combination conjecture. The learned representation could be combining multiple sparse representations in a clever way such that the combined representation is even more spar…

Let $p$ be a prime, let $G$ be an elementary abelian $p$-group of rank $r$, and let $k$ be the coefficient field. For a finite-dimensional complex of free $kG$-modules, consider th…

Let $G$ be a group and let $\sigma:G\to\operatorname{GL}_k(\mathbb{C})$ be a homomorphism. Define $\widetilde{\sigma}:\mathbb{C}[G]\to\operatorname{Mat}_k(\mathbb{C}[G])$ by sendin…

Let $G$ be a Hermitian locally compact group, let $\widehat{G}$ denote its irreducible representations, and for $\pi\in\widehat{G}$ and a unit vector $\xi\in\mathcal{H}_\pi$ define…

Let $G$ be a Hermitian locally compact group. For a representation $pi$ of $G$ and a unit vector $xi$ in its representation space $\mathcal{H}_pi$, define … and, for $f\in L^1(G)$,…

Let $\Gamma$ be the group, let $\partial\Gamma$ be its boundary, and let $\pi:\Gamma\to\mathcal{U}(\mathcal{H})$ be an irreducible unitary representation weakly contained in the re…

Let $\Gamma$ be a discrete group, let $1\leq p\leq 2$, and let $q$ be its conjugate exponent, so that … Let $B_p(\Gamma)$ denote the coefficient space associated with isometric rep…

Let $G$ be a finitely presented textsc{qsf} group, and consider the locally finite 3-dimensional and 2-dimensional textsc{wgsc-representations} supplied by the preceding theorem, w…

Classification conjecture. If $G\in\mathfrak{T}$ is a simple group, then it is one of the sporadic groups.

Rank-five dilation criterion. The subgroup $E$ contains a dilation of $\mathbb{F}_{p^3}$ if and only if it belongs to the variety determined by

Let $M$ be a closed hyperbolic 3-manifold with infinite first homology, and let $a\in H^2(M;\mathbb{R})$ be an integral class satisfying the parity condition and having dual norm e…

Let $G$ be a discrete group and let $X$ be a real Banach space with … An equivalent renorming of $X$ is a norm $|||\cdot|||$ equivalent to its original norm, and…