6 problems

Affine Calabi conjecture. For every pair of polarizations $(\omega,\nu)$, there is a unique choice for $\phi^\vee\circ\phi^{-1}$ such that the local potentials solve the real Monge…

Let $\nabla=\nabla^{(1)}+\dots+\nabla^{(r)}\subset\mathbb R^d$ and $\Delta$ be dual nef-partitions, and let integer-valued functions $\omega:\nabla^\vee_\mathbb Z\to\mathbb R$ and…

Kontsevich–Soibelman's conjecture. For maximal degenerating polarized algebraic Calabi–Yau varieties, the IAMS structure induced by the Collapse Picture coincides with the IAMS str…

Let $\mathcal{R}$ be a simple eigenray diagram, let $B_{\mathcal{R}}$ be its nodal integral affine manifold, and let $\mathcal{F}_{\mathcal{R}}$ be the sheaf defined on the Grothen…

Let $K=\mathbf{C}((t))$, let $X/K$ be a Calabi–Yau variety, and let $\operatorname{Sk}(X)$ be its essential skeleton. Let $\Gamma\subset\operatorname{Sk}(X)$ be a codimension $2$ p…

Let $d$ be a positive integer. A maximally degenerating family of Calabi–Yau manifolds is a family whose Ricci-flat Kähler metrics are considered in the maximally degenerating limi…