9 problems

Let $(\overline{X},\omega_{CS},\rho_{CS})$ be a nearly Kähler conifold with a singularity at $x_0$ modelled on the Calabi--Yau cone $(C=C(L),\omega_C,\rho_C)$. An obstruction conje…

Let the central Hirzebruch scroll be the limiting member of the deformation family of Hirzebruch scrolls described above, and let its Calabi–Yau hypersurface be Tyurin-degenerate,…

Let $r^{\prime}:H^{\operatorname{LG}}\to H^{\operatorname{CY}}$ be the correspondence map, and let … and … be the Landau–Ginzburg and Calabi–Yau $tt^*$ structures. Conjectural…

Let $M_{mar}$ be the marginal-deformation subspace of the deformation space $M$. Let…

Let $(X,g,\omega)$ be a compact Kähler manifold, and fix $R\in\Omega^{1,1}(X)$ such that $[R]=c_1(T_X)\in H^{1,1}(X)$. Then there exists a unique Kähler metric $\widetilde{g}$ with…

Let ${\mathcal M}_{\rm par}$ be the moduli space of singular parabolic Higgs bundles with $n$ simple poles in their connection, and let ${\mathcal M}_{\rm wild}$ be the moduli spac…

Let a compact singular elliptically fibered Calabi–Yau $3$-fold have singular fibers associated to ${\mathcal G}$-symmetry in codimension $1$ over the base, admit a crepant resolut…

Let $X\in\widetilde{\mathscr{KS}}(n,\kappa)$ be a Calabi–Yau conifold and let $x_0\in X$. The tangent space at $x_0$ is the limiting tangent object associated with the conifold str…

Metric contraction conjecture. The singular AC metrics on the $r$-th root of $K_{\mathbb{P}(E)}$ contract along one-parameter families to the smooth AC metrics on $E\otimes L$ by s…