37 problems

Let $E$ be a directed graph and let $L_K(E)$ be its Leavitt path algebra with its natural grading. The talented monoid of $L_K(E)$ is the graded monoid associated with the graded f…

Drinfeld-center classification conjecture. The map

Bounded Morita Frobenius number conjecture. Amongst all finite groups $G$ and blocks $B$ of $kG$ with defect group isomorphic to $D$, the Morita Frobenius number…

Let $P_1$ and $P_2$ be Morita equivalent Poisson manifolds, with dimensions $m_1=\dim P_1$ and $m_2=\dim P_2$. The preceding result gives an isomorphism … when $P_1$ is unimodular.…

Let $R$ be a finitely generated smooth commutative algebra over $\mathbb Z$, let $g\in\operatorname{Aut}(P_{n,R})$, and for each sufficiently large prime $p$ let $M_{g,p}$ be a bim…

Let $A_{n,\mathbb C}$ be the Weyl algebra of index $n$ over $\mathbb C$, and let $P_{n,\mathbb C}$ be the Poisson algebra of polynomial functions on the $2n$-dimensional affine sym…

Differential-equivalence conjecture. Differential equivalence should imply that $X$ and $Y$ are isomorphic.

Rieffel–Schwarz conjecture. If two matrices in $\mathcal{T}_n$ lie in the same orbit of this action, then they define strongly Morita equivalent noncommutative tori, both at the…

Let $R$ and $S$ be rings, let $L$ be a $\times_R$-bialgebra, and let $P$ and $Q$ implement the Morita equivalence between $R$ and $S$. Write…

Lifting conjecture. The set $X$ is a complete set of exact $H$-equivariant Morita equivalence class representatives.

Splendid Morita equivalence conjecture. The endoscopic equivalence of Theorem $$ induces a splendid Morita equivalence in the sense of Rickard.

Let $\Bbbk$ be a field, let the Morita equivalence in Theorem be the equivalence associated with the cyclotomic web construction, and let the Morita equivalence in Theorem be the e…

Let $F\colon\mathcal{S}\to\mathcal{T}$ be a morphism of limit sketches. A test Morita equivalence is a morphism of sketches that induces an equivalence … for every test sketch. Set…

Let $\mathsf{B}^{n+1}$ be a background phase and let $\mathsf{C}^{n+1}$ be an $(n+1)$D anomaly-free topological order. An MCLP lattice model over $\mathsf{B}^{n+1}$ has a local spi…

Let $F$ be an algebraically closed field of characteristic $p>0$, let $G$ be a finite group, and let $B$ be a block of $FG$ with fusion system $\mathcal{F}=\mathcal{F}_D(B)$. Write…

Let $D=(C_2)^6$ and consider purely nonprincipal blocks with defect group $D$. For each group in the following list, there is one relevant Morita equivalence class of nonprincipal…

Let $G=(C_2)^6\rtimes\operatorname{SmallGroup}(729,122)$, where $\operatorname{SmallGroup}(729,122)=((C_3)^2\times 3^{1+2}_+)\rtimes C_3$ and $(C_3)^2$ acts trivially on $(C_2)^6$.…

Let $M=(C_2)^4\rtimes (C_3)_2\times A_4$, and let a central extension by $C_3$ produce the group $(C_2)^6\rtimes 3^{1+2}_+$. Let $3^{1+2}_-$ denote the other central extension cons…

Let $D=(C_2)^6$ be an elementary abelian defect group of order $64$. Consider the known blocks with defect group $D$, including those determined in Theorem 1.1 of the paper. Comple…

Sambale's conjecture. No two blocks in this list are Morita equivalent.

Let $({}_{dg}^{red}Q_b^{{\underline{N}}},0)$ be the reduced dg-quiver Schur algebra and let $({}_{dg}Q_b^{{\underline{N}}},0)$ be the non-reduced dg-quiver Schur algebra. Dg-Morita…

Representability conjecture. All orbifolds are representable.

Central-charge conjecture. The central charge is the only Morita invariant of a holomorphic VOA; equivalently, holomorphic VOAs with the same central charge should be Morita equiva…

Complementary Morita-class count conjecture.

Weight-two Morita-class count conjecture.