5 problems

Christ's conjecture. The restriction of $\Phi$ to ${\mathcal H}$ is an equivalence of $k$-linear categories

Christ's conjecture. The Higgs category should be equivalent to the cosingularity category:

Smith's conjecture. There is an equivalence of triangulated categories

Let $\Gamma$ be any tree, let $\mathscr{B}_\Gamma$ be the DG-algebra arising from the plumbing construction, and let $\mathscr{G}_\Gamma$ be the corresponding Ginzburg DG-algebra.…

Let $\Gamma$ be a tree of Dynkin type $E_6$, $E_7$, or $E_8$, let $\mathscr{B}_\Gamma$ be the DG-algebra arising from the plumbing construction, and let $\mathscr{G}_\Gamma$ be the…