9 problems

Let $\Sigma$ be a closed oriented surface of genus $g$, let $s^i\Sigma$ denote its $i$-th symmetric product, and let $HF_g^*$ be the Floer cohomology ring associated with…

Ample-cone conjecture. If $C$ is a very general curve of genus $g\ge 4$, then

Let $\mathrm{SP}^d(\mathbb{P}^n)$ be the $d$-th symmetric product of complex projective space, and let $cl$ denote the cycle class map from Lawson homology to singular homology wit…

Farber–Oprea conjecture. The formal power series $f_X(t)$ represents a rational function of the form

Let $C$ be a projective smooth curve of genus $g\geq 2$, and let $C_d$ denote its $d$-th symmetric product. Let $D(C_d)$ be its derived category, and call a semi-orthogonal decompo…

Wang's conjecture. One has

Let $X$ be an irreducible smooth complex variety. For a partition $\lambda$ of $k$, let $W_\lambda(X)$ denote the symmetric complement associated with the stratum indexed by…

Let $X$ be an irreducible smooth complex variety, let $^j\lambda$ denote the partition obtained by adjoining $j$ parts equal to $1$ to a partition $\lambda$, and let…

Let $i$ be a nonnegative integer, let $bb$ be a partition, and let $X$ be an irreducible smooth complex variety. For each $j$, let $\bar{w}^c_{1^j\lambda}(X)$ denote the complement…