5 problems

Folklore conjecture generalizing Kontsevich–Soibelman's conjecture. The collapsing boundary densely parametrizes singular tropical metric spaces homeomorphic to essential skeleta…

Let $\mathfrak{X}$ be a Calabi–Yau family as in Setup II that does not satisfy the equivalent conditions in Theorem. Logarithmic diameter growth conjecture. There exist constants…

Let $f\colon \mathcal{X}\to S$ be a family of Calabi–Yau manifolds with a semi-stable singular fiber $X_0=f^{-1}(0)$. Let $a_0$ be the coefficient of the Dirac current in the curre…

Let $f\colon \mathcal{X}\to S$ be a relatively minimal family, let $s_i\in S$ be a point such that the singular fiber $f^{-1}(s_i)$ is semi-stable, let $a_i$ denote its BCOV invari…

Wang's conjecture. $X$ has finite Weil–Petersson distance if and only if