3 problems

Liu–Xia localization conjecture. Under the specific conditions considered by Liu and Xia, the formulas for sums of local contributions should localize in the precise sense they con…

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…