6 problems

Let $M$ be a Weil–Petersson variety, and let $X$ be a Weil–Petersson subvariety of dimension $q$ in $M$. Let $c_k(\omega_{WP})$ denote the $k$-th elementary polynomial of the curva…

Let the moduli space of a Calabi–Yau threefold be equipped with its Weil–Petersson geometry, and consider its geodesics. Stability conjecture. All Weil–Petersson geodesics on the m…

Let $\mathbb{P}_g^{\mathrm{\scriptsize{WP}}}$ denote the Weil–Petersson probability measure on compact hyperbolic surfaces of genus $g$, and let $\lambda_1>0$ be the smallest non-z…

Weil–Petersson random prime geodesic conjecture. Theorem 1.1 still holds after replacing the exponent $3/4$ by $1/2$; equivalently, there is a universal constant $c>0$ such that fo…

Let $X$ be a projective Calabi–Yau $n$-fold, let $\mathcal{M}_{\mathrm{Kah}}(X)$ be its stringy Kähler moduli space, and let $\mathcal{D}_X=\mathrm{D^bCoh}(X)$. Let…

Short Curve conjecture. If $g$ is a Weil–Petersson geodesic with end invariant $(\nu^{-},\nu^{+})$, then: