12 problems

Quantum Hikita conjecture. For conical theories, the specialized quantum D-modules on Higgs branches and the D-modules of graded traces for Coulomb branches are isomorphic as D-mod…

Let $X$ be a smooth projective variety equipped with an algebraic $T_\mathbb{C}$-action, and let $Y$ be a smooth GIT quotient of $X$ without orbifold singularities. Let…

A symplectic reduction $X/\!/\mathbb{K}$ is obtained from a space $X$ with a $\mathbb{K}$-action, and one may consider both the quantum $D$-module of the reduction and the…

In the setting of the formal decomposition conjecture, let $\mathscr{R}$ be the complementary quantum-D-module summand with connection $\nabla^{\mathscr{R}}$ and pairing…

In the setting of the formal decomposition conjecture, let $\mathscr{A}_{\pm,\tau}$ denote the analytically continued ancestor potentials and let $\mathscr{R}_\tau$ be the fiber of…

Let $\mathfrak{X}_+$ and $\mathfrak{X}_-$ be smooth Deligne–Mumford stacks related by a birational transformation through a smooth stack $hat{\mathfrak{X}}$, with projective birati…

Sanda–Shamoto's Dubrovin conjecture. There exists an irregular perverse schober whose nearby cycle is $D^b(X)$ and whose Hochschild decategorification gives Stokes data that is the…

Let $X$ and $Y$ be smooth projective varieties related by a primitive extremal transition. Denote by $\mathcal{H}(X)$ the ambient part of the quantum $D$-module of $X$. After analy…

A primitive extremal transition is a transition between Calabi–Yau $3$-folds satisfying the hypotheses specified in the paper. The quantum D-module conjecture. The statement of The…

Let $cmathcal{X}$ and $Y$ be the orbifold and its crepant resolution, with $cmathrm{QDM}(cmathcal{X})$ and $cmathrm{QDM}(Y)$ their quantum $D$-modules. A global quantum $D$-module…

Let $\mathcal{X}_1$ and $\mathcal{X}_2$ be K-equivalent spaces connected by a global quantum $D$-module, and let $\gamma$ be a path in the Kähler moduli space from a point of the c…

Let $(F,\nabla)$ be the global quantum $D$-module over the Kähler moduli space $\mathcal{M}$, and let $V_i$ be a cusp neighborhood corresponding to $X_i$. An integral local system…