7 problems

Let $S$ be a del Pezzo surface, let $E$ be a suitable anticanonical divisor, and let $M_{\beta}$ be the moduli space of stable one-dimensional sheaves of class $\beta$ and Euler ch…

Enriques perverse Hodge generating-series conjecture. The perverse Hodge numbers satisfy the displayed generating-series identity involving the theta functions, eta functions, and…

Refined Gopakumar–Vafa conjecture. One has

Let $g^{\rm (ref)}_n(\{\check\gamma_i,c_i\},y)$ be defined by the refined generating-function construction and the reference solution $F^{\rm (ref)}_n$, with coefficients $b_n$ fix…

Degree-independence conjecture. For fixed $r$, both $\overline H(r,e)(y)$ and $\overline H(r,e)(u,v)$ are independent of $e$; equivalently, they have the same value for all pairs…

Doubly refined wallcrossing and multicover conjecture. Under the same conditions as the preceding refined wallcrossing conjecture, there exist doubly refined invariants in…

Refined multicover conjecture. One has