3 problems

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…

Smoothness conjecture. If a gauged linear $\sigma$-model is defined by pointsets ${\Scr A}$ and ${\Scr B}$ which are both ${\Scr A}$-complete and ${\Scr B}$-complete, then this mod…

Extremal transition conjecture. The following hold: (1) the structure constants of the small quantum product of $X_{\rm res}$ are polynomials in $q_1,\dots,q_l$ with coefficients r…