15 problems

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…

Noncommutative resolution conjecture. This phase should reduce to a $\mathbb{Z}_{N}$ orbifold of some noncommutative resolution of $CGr(2,N)$.

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…

NCCR summand-count conjecture. The number of non-isomorphic indecomposable summands of $M$ is equal to

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

NCCR categorical-resolution conjecture. Every NCCR of $R$ yields a strongly crepant categorical resolution of $X$.

Let $X$ be a singular algebraic variety and let a noncommutative resolution of $X$ mean a suitable categorical resolution of singularities, with admissible subcategories regarded a…

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

Let $V$ be a vector space, let $n=\dim V$, and for an integer $0\le r\le n$ define … The varieties $X_r(V)$ parameterize symmetric $2$-tensors of rank at most $r$. Hori–Knapp–Kuzne…

Suppose a noncommutative resolution admits the point objects considered by Toen and Vaquie, and let the resulting moduli space exist. In the setting described, this moduli space is…

The paper considers abelian gauged linear sigma models whose infrared limits may be smooth branched double covers or noncommutative resolutions. In the latter case, D-brane probes…