10 problems

Factorization and stability conjecture. There exists a unique $i\in\{1,\ldots,s\}$ such that the Higgs field factors through

Let $(X,Y)$ be a geometric mirror pair, meaning that there is a parameter space $U$ and, for each $t\in U$, a correspondence $Z_t\subset X\times Y$, sections of the projections, Ri…

Nonabelian Hodge conjecture. The points of $NL(X_s,GL(n))$, that is, the $\mathbb Z$-variations of Hodge structure, are motivic representations on $X_s$.

Let $Y$ be a Calabi–Yau manifold with $h^{2,0}(Y)=0$, and let $\pi:\mathcal{Y}\to S$ be a family of complex structures on $Y$ whose Kodaira–Spencer map is an isomorphism everywhere…

Let $(\mathbb{V},\mathscr{F}^{\bullet})$ be an integral polarized variation of Hodge structures on a smooth connected quasi-projective variety $S$. The Baldi–Klingler–Ullmo conject…

Arakelov equality characterization. The general fiber has Kodaira dimension zero, and the family is Shimura in the following sense: $Y$ parameterizes a compactified universal famil…

Let $\mathbb V$ be a $\mathbb Z$-variation of Hodge structure defined over a number field $L\subset\mathbb C$. Let…

For each index $\alpha$, let $G_\alpha^1$ be a de Rham stratum and let $\big(G_\alpha^1\big)^{\rm VHS}\subset G_\alpha^1$ be the subset of polarized complex variations of Hodge str…

Let $X$ be a smooth projective variety and let $D\subset X$ be an ample divisor. Let $\mathscr{H}\to D$ be a polarized variation of Hodge structure, and let its numerical invariant…

Let $C$ be a Teichmüller curve of genus $g$, with Lyapunov exponents $\lambda_1\geq\cdots\geq\lambda_g$ and normalized Harder–Narasimhan numbers $w_1\geq\cdots\geq w_g$. Let $k$ be…