9 problems

Let $X$ be a hyperkähler variety of K3$^{[n]}$-type with $n\geq 2$. A K3 category is a category of K3 type, and let $\mathcal A_X^{[n]}$ denote its Hilbert-scheme-type construction…

Let $X_1$ and $X_2$ be generalized-dual smooth Gushel–Mukai varieties, and let $\mathcal A_{X_1}$ and $\mathcal A_{X_2}$ denote their K3 categories. Kuznetsov's conjecture. One sho…

Universal filtration conjecture for Gushel–Mukai fourfolds. For every object $\mathcal{E}\in\mathcal{A}_X$, one has

Shen–Yin's universal filtration conjecture. The filtration ${\rm S}_{\bullet}(X)$ should be universal on $K_0(\mathcal{A}_X)$, in the sense that

Let $\mathsf{A}$ be the K3 category of the Debarre–Voisin hyperplane section $Y$, and let $T$ and $P$ be the associated congruence of lines and Peskine variety. Let $\mathcal{U}$ a…

Let $Y\subset\operatorname{Gr}(3,V_{10})$ be a very general hyperplane section, and let $\mathsf{A}$ be the K3 subcategory of $\operatorname{D}^b(Y)$ obtained as the semiorthogonal…

Let $Y\subset G(3,10)$ be a very general hyperplane section, let $K$ be its vanishing-cohomology K3 Hodge structure, and let $P\subset\mathbb{P}^9$ and $T\subset G(2,10)$ be the as…

Sheaf–cycle correspondence conjecture. For any object ${\mathcal E} \in {\mathcal A}_Y$,

Let $W$ be a $7$-dimensional vector space, let $X\subset\operatorname{Gr}(3,W)$ be the $5$-dimensional zero locus of a section of…