5 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 $\widetilde{\mathcal{N}}$ be the Springer resolution, let $u(G_q)$ be the small quantum group, let $\operatorname{PrinBlock}_{\mathrm{dg}}(u(G_q))$ be its principal block, and…

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…

Formality-implies-equivalence conjecture. If the Formality Conjecture holds, then this non-monoidal pushforward restricts, via the Kempf embedding, to an equivalence

Formality conjecture. The $E_3$-scheme $\mathscr{X}$ is $E_2$-formal, so that there is a monoidal equivalence