21 problems

Let $S$ be a Noetherian scheme and let $G$ be an isotrivial reductive group over $S$, meaning that $G$ becomes split after a finite étale cover of $S$. A $G$-equivariant $S$-fiberw…

Fiber-wise duality conjecture. This fiber-wise duality should work remarkably well when there is some residual supersymmetry and an underlying adiabaticity.

Let $U$) be an $n$-dimensional contractible complex manifold and let $(M,D)$ be a Kähler smooth compactification. Fujita's conjecture $A_n$. Then … and $(M,D)$ is the standard exam…

Let $n\geq 4$. A bilipschitz bundle is a fiber bundle whose structure group lies in $\operatorname{bilipschitz}(X)$. The high-dimensional non-compactification conjecture. There exi…

Quantum toric stacks are considered with fixed dimension and a fixed number of generators, and their moduli spaces with fixed combinatorics are the spaces under consideration. Tori…

Let $C_0$ denote the coefficient appearing in the large-genus expansion of the index for a genus $g$ compactification with no flux and no punctures, so that … The index counts, wit…

An $ALG$ or $ALG^*$ gravitational instanton may, after a suitable hyperKähler rotation, admit a compactification obtained by adding a canonical cycle to a rational surface. Compact…

Bapat–Deopurkar–Licata's boundary-density conjecture. There is a suitable class $\mathcal{S}$ of objects such that the functionals $\overline{\mathrm{hom}}(s)$ for…

Let $\mathsf{C}$ be a ${\mathbf{k}}$-linear triangulated category, and consider the quotient of its stability space by the natural $\mathbb{C}$-action, together with the mass map ……

Geometric interpretation conjecture. The coefficients $w_j$ can be interpreted geometrically in terms of the compactified space.

Let $\mathcal C$ be the 2-Calabi--Yau category associated to the quiver under consideration, and let $M$ and $P$ be the images of $\operatorname{Stab}(\mathcal C)/\mathbb C$ and th…

Let $\mathcal C$ be a triangulated category, let $q>0$, and let $m_q\colon\operatorname{Stab}(\mathcal C)/\mathbb C\to\mathbb P^{\mathcal C}$ be the continuous map defined using th…

Let $\mathcal C$ be a triangulated category satisfying the mild conditions assumed in the paper, and let $\operatorname{Stab}(\mathcal C)/\mathbb C$ be its moduli space of Bridgela…

Let $X^{o}$ be a complex manifold carrying a complete Ricci-flat Kähler metric. A compactification should consist of a compact Kähler manifold $X$ and an anticanonical divisor $D$…

Consider the quiver obtained by gluing $g-1$ two-punctured tori in a circle, equivalently using the Seiberg-dual frame of an $SU(2)$ gauge node with three flavors to obtain the qui…

Let $G$ be a real reductive Lie group with compact center, and let an hd-compactification of $G$ be a compact manifold with corners $\overline{G}$ containing $G$ as its interior an…

A hd-compactification of a Lie group is a compactification satisfying the properties described in the paper: inversion extends smoothly, right-invariant vector fields extend as smo…

A 5d SCFT is a five-dimensional superconformal field theory, and a 6d SCFT is a six-dimensional superconformal field theory. Circle compactification means compactifying the 6d theo…

Let $M$ be a complete noncompact Kähler manifold with positive Ricci curvature. Yau's quasiprojective compactification conjecture. The manifold $M$ is biholomorphic to a Zariski op…

Let $M$ be a complete Ricci-flat Kähler manifold with finite topological type. Yau's compactification conjecture. The manifold $M$ can be compactified complex analytically. The pap…

Yau's compactification conjecture. Every complete Calabi–Yau manifold can be compactified in the complex analytic sense.