5 problems

Let $\mathcal{F}_{2d}$ be the moduli space of polarized K3 surfaces of degree $2d$, and let $\overline{\mathcal{F}_{2d}}^{{\rm Sat},\tau_{\rm ad}}$ be its Satake compactification f…

Let $(M,g)$ be a compact Riemannian $n$-manifold with $obreakoperatorname{Ric}ggeq -(n-1)$ and bounded diameter, and let $widetilde{B1(x)}$ denote the local universal cover of the…

Let $M$ be the moduli space of polarized irreducible holomorphic symplectic varieties, let $\lambda$ be the polarization class, let $\lambda^{\perp}$ be its orthogonal lattice, and…

Let $\mathcal{M}_{\rm K3}$ be the moduli space of Ricci-flat Kähler K3 surfaces modulo hyperKähler rotation, and let $\overline{\mathcal{M}_{\rm K3}}^{\rm Sat,\tau_{\rm ad}}$ be it…

Let $D$ be a bounded domain with bounded principal curvatures. A semi-stable rubber band in $D$ is a minimal rubber band, without requiring it to be strictly minimal. Consider the…