6 problems

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…

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…