9 problems

Let $X$ be a Calabi–Yau threefold with only terminal conifold singularities and no Kähler small resolution. Let $\mathcal{S}$ be the set of all small resolutions $\widehat{X}$ of…

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 $X$.

Let $0 \in J \subseteq J' \subseteq I$, set $K \coloneqq I \setminus J$ and $K' \coloneqq I \setminus J'$, and let $\sigma_{K,K'}$ be the cone defined by … Let…

Let $X$ be the base of the Calabi–Yau double cover $Y$, let $Cl_{0}$ be the even part of the sheaf of Clifford algebras obtained from the quadratic GLSM superpotential, and write…

Stringy Euler-characteristic conjecture. The stringy Euler characteristic of $X$ can be computed as the Euler characteristic of an NCCR, computed via periodic cyclic homology.

Stringy E-function polynomiality conjecture. The stringy $E$-function $E_{st}(X,u,v)$ is a polynomial.

Toric summand-count conjecture. The number of indecomposable summands in the reflexive module defining an NCCR of $R$ is equal to

Homological projective duality conjecture. The homological projective dual variety of the Cayley plane is a non-commutative resolution of the Cartan cubic hypersurface in…