7 problems

Let $(A,\Theta)\in\mathcal A_g$ be a principally polarized abelian variety, and let a $d$-dimensional subvariety of $A$ have minimal cohomology class, meaning the class is the mini…

Let $J_g$ be the Jacobian locus in $\mathcal A_g$, and let $\mathcal S_g$ be the small Schottky–Jung locus, defined as the intersection of the Schottky–Jung loci associated with al…

Let $J_{g,h}$ be the universal Jacobian locus in $\mathcal A_{g,h}$, equipped with the Riemannian metric $ds^2_{g,h;A,B}$. Universal geodesic noncontainment conjecture. For a suffi…

Let $J_{g,h}$ be the universal Jacobian locus in $\mathcal A_{g,h}$, equipped with the Riemannian metric $ds^2_{g,h;A,B}$. Universal totally geodesic subvariety conjecture. For a s…

Let $J_g$ be the Jacobian locus in $\mathcal A_g$ and let $\overline J_g$ be its closure. Geodesic noncontainment conjecture. For a sufficiently large integer $g$, there does not e…

Let $J_g$ be the Jacobian locus in $\mathcal A_g$, and let a totally geodesic subvariety mean an irreducible subvariety arising as the image of a totally geodesic subvariety of the…

Let $g\geq 5$. Let $\mathcal{A}_g$ be the moduli space of principally polarized abelian varieties, let $\mathcal{J}_g$ be the Jacobian locus, and let $\mathcal{S}_g$ be the locus c…