8 problems

Kuznetsov's conjecture. For any $k$ and $n$, the Pfaffian variety

Generalized Pfaffian HPD conjecture. For every $0\leq t\leq \lfloor n/2\rfloor$, there exist noncommutative resolutions of singularities of $X$ and $Y$ which are Homologically Proj…

Higher-dimensional Pfaffian HPD conjecture. There exists a noncommutative resolution of singularities $(Y,\CR)$ of $Y$ which is Homologically Projectively Dual to $X$.

Categorical crepant resolution conjecture. The categorical crepant resolution $\widetilde{D}^b({\mathrm {Pf}}(2k,V^{\vee}))$ has the non-rectangular Lefschetz decomposition

Let $V$ be a vector space of dimension $N$ over an algebraically closed field $k$ of characteristic zero, and consider the Plücker embedding…

Let $W$ be a vector space of dimension $m$, and let $\operatorname{Pf}(2k,W)$ denote the closure of the locus of bivectors in $\Lambda^2W$ of rank $2k$. Let…

Let $X_i$ be the Pfaffian Calabi–Yau threefold for $i\in\{5,7,10\}$, and let $\{n_d^g\}_{d\in\mathbb{N}}$ be the numbers listed in the Appendix. BPS-invariant conjecture. The BPS i…

Let $W$ be a vector space of dimension $2n$, let $V\subset\Lambda^2W^*$ satisfy $\dim V=2n=\dim W$, and let $V^\perp\subset\Lambda^2W$ be its orthogonal. Define the Pfaffian hypers…