14 problems

Let $X$ be a complex manifold elliptically fibered with at worst $I_{1}$ fibers over a normal analytic variety $B$ such that … Let $\alpha,\beta\in\mathop{\mathcal{S}h}_{an}(X)$ be…

Let $X\to\mathbb P^n$ be an abelian fibration, let $P\to\mathbb P^n$ be its relative Picard, and let $X_0$ be the relative Picard of $P$. Let…

Let $W$ be the coarse projective variety in the KSBA moduli problem, let ${\mathfrak W}\to W$ be a $\mu_N$-gerbe, and let $M$ be the associated KSBA moduli space. Suppose that the…

Gerbe decomposition conjecture. For the Ruan–Zhang/Chern–Simons level corresponding to ordinary quantum $K$-theory,

Drinfeld's gerbe isomorphism conjecture. These two gerbes are isomorphic.

Let $\mathcal{Y}$ be a gerbe with dual $\widehat{\mathcal{Y}}$ and associated $\mathbb{C}^*$-gerbe $c$. Let $D\subset \mathcal{B}$ be a smooth irreducible divisor, and define its i…

Let $G$ be a finite group, let $Q$ act on the finite set of isomorphism classes of irreducible $G$-representations, and let $\mathcal{Y}$ be a gerbe with dual…

Let $S$ be a smooth projective surface and let $r\in{\mathbb Z}_{>0}$. For $L\in\operatorname{Pic}(S)$, define the $\operatorname{SU}(r)$ Vafa–Witten partition function by … Define…

Let $X$ be the smooth scheme considered above, let $G$ be the reductive group with maximal torus $T$, and let $\ell$ be the chosen prime. Consider the diagram … The horizontal and…

Formality-independence claim. The quasi-classical limit $\widetilde{\operatorname{gr}^\times}\mathcal{C}$ is equivalent to $\operatorname{gr}^\times\mathcal{C}$ equipped with the…

Let $G$ be a compact Lie group acting smoothly on a compact manifold $M$, and let $b1\in H^3_G(M,\mathbb Z)$. For each $g\in G$, let $P^g\to M^g$ be the associated $G$-equivariant…

Let $cmathcal{Y}$ be a $G$-gerbe over a compact symplectic orbifold $cmathcal{B}$, and let $(cmathcal{\widehat{Y}},c)$ be its dual pair, where $c$ is the flat $U(1)$-gerbe defining…

Modified Ruan crepant resolution conjecture. There are a flat gerbe $$ over $Y$ and elements

Modified cohomological crepant resolution conjecture. There is a flat gerbe … -twisted small quantum product of $Y$ by analytic continuation in $Q_{s+1},\ldots,Q_r$, if necessary,…