14 problems

Let $X_q$ be the half-quantum flag variety, let $\widetilde{\mathcal{N}}$ be the Springer resolution, let $\mathcal{N}$ be the nilpotent cone, and use…

Let $G$ be an almost-simple algebraic group with dual group $\check{G}$, let $q$ be a chosen complex root of unity, let $X_q$ be the half-quantum flag variety, let…

Kontsevich's tangent-map conjecture. The induced map

Let $K$ be a finitely generated free ${\cal D}_X$-module, and let $SK$ denote the associated chiral algebra. Let $\mathrm{def}_{SK}$ be its deformation pro-$*$-Lie algebra, and let…

Compatibility conjecture. The diagram of curved $L_\infty$-morphisms

Let $G$ be a connected graph, and let ${\mathscr A}_G$ denote its connected subgraph arrangement. For an arrangement ${\mathscr A}$, $k$-formality is the hierarchy of formality pro…

For $n\in{\mathbb N}$, let ${\mathscr H}_n$ denote the hyperpolygonal arrangement. An arrangement is $k$-formal when it has the stronger formality property indexed by $k$, with…

Let $\mathcal{K}$ be a flag simplicial complex, and consider the grading on $H^*(\mathcal{Z}_\mathcal{K};\mathbb{Q})$ specified in the source's preceding theorem. Koszul formality…

Let a Lie-quasi bialgebroid be a quasi-bialgebroid generalising Lie bialgebroids and quasi-bialgebras, and let a quasi-quantum groupoid be a topological deformation of the standard…

Let $M$ be a connected, oriented, closed Riemannian manifold with $\HDR^1(M)=0$, and suppose that $M$ is formal. In the situation of the equivalence conjecture, let $\PMC$ be the C…

Let $V$ be a differential Poincaré duality algebra with \H^0(V)=\operatorname{Span}\{1\} and \H^1(V)=0, and suppose that $V$ is formal as a differential graded algebra. A Poinc…

Higher-dimensional framed compatibility conjecture. If the framed little $n$-disks operad $\mathtt{fe}_{n}$ is formal, then the pair…

Let $k$ be a field of characteristic $p$, let $r$ be a nonnegative integer, and let $G$ belong to the category of homogeneous strict polynomial functors of degree $d$. Let…

Let $X_{{\bullet}}$ be a connected simplicial smooth projective variety satisfying the finite index condition. Let $P$ be a $G$-principal bundle with $\lambda$-connection, or a $G$…