11 problems

Relative holomorphic anomaly conjecture. The series lies in

Primitive conjecture.

Fiber-class conjecture. Up to a constant, $F^{S^{[n]}}_{g,0}$ is a meromorphic quasi-Jacobi form of weight $k$ and index $0$, with poles at torsion points. Modulo constants it also…

Quasi-Jacobi form property. For all $\ell>0$,

Let $S$ be a smooth projective surface with $b_1(S)=0$, $p_g(S)>0$, $K_S\ne0$, and with only Seiberg–Witten basic classes $0$ and $K_S$. Let $H,c_1,c_2$ be chosen so that there are…

Let $\pi:X\to B$ be an elliptic fibration with section and integral fibers, let $D\subset X$ be a nonsingular divisor restricting to an elliptic fibration $\pi_D:D\to A$ over a non…

Oberdieck–Pixton's conjecture. The relative Gromov–Witten potentials of elliptic fibrations are cycle-valued lattice quasi-Jacobi forms and satisfy a holomorphic anomaly equation w…

Let $S$ be an elliptic $K3$ surface, let $\mathcal F(S)$ be its Fock space, let $\mathcal E^{\operatorname{Hilb}}$ and $\mathcal E^{(0)}$ be the Hilbert-scheme and recursively defi…

Let $S$ be a nonsingular projective $K3$ surface, let $\mathcal F(S)$ be its Nakajima Fock space, and let $F(y,q)$ and $\Delta(q)$ be the functions defined in the paper. For functi…

Conjecture C. For every $(m,\ell)\in\mathbb Z^2\setminus\{0\}$, the series

Conjecture J. For all $d\geq 1$ and all $\mu,\nu\in H^{\ast}(\operatorname{Hilb}^d(S))$, there is a quasi-Jacobi form $\psi(z,\tau)$ of index $d-1$ and weight at most $2+2d$ such t…