10 problems

A solenoid by holomorphic curves is a compact solenoid in the complex projective plane whose leaves are holomorphic curves. Holomorphic-solenoid conjecture. There exists a compact…

Let $B^{2n}(a)$ be the symplectic ball of capacity $a$, let $L$ be a Lagrangian submanifold in $B^{2n}(a)$, and let $J$ be an admissible almost-complex structure. Holomorphic-disk…

Generalized-quiver partition-function conjecture. After this substitution, the generalized-quiver partition function equals the generating function of Gromov-Witten invariants coun…

Let $K$ be a fibered knot, and write $F_K(x,q)$ as a series in $x$. Fibered-knot Laurent polynomial conjecture. For any fibered knot $K$, the coefficients of $F_K$ are Laurent poly…

Green–Griffiths conjecture. $X$ contains no algebraically non-degenerate holomorphic curves.

Let $M$ be a closed manifold of dimension at least $4$, and let $\omega=d^{\alpha}\lambda$ be an exact locally conformally symplectic form on $M$ whose Lee form $\alpha$ is rationa…

Holomorphic Seifert–Weinstein conjecture. For any l.c.s. pair $(\omega,J)$ on $S^{2k+1}\times S^1$ or on $C\times S^1$ for $C$ a threefold, there is an elliptic, non-constant $J$-h…

Zalcman space conjecture. $\mathbb C^n$ is a Zalcman space for each $n\geq 2$.

The exploded Dolbeault-bundle conjecture. The space $\mathfrak E_{g,n}(\mathfrak B,\omega)$ has the structure of a Fréchet orbifold exploded fibration and is a vector bundle over…

The moduli-space structure conjecture. The moduli space