14 problems

Let ${\mathsf r}\geq 2$, and let $\check{\mathsf{QM}}^{\mathsf a}_{{\mathsf d},0}$ and $\hat{\mathsf{QM}}^{\mathsf a}_{{\mathsf d},0}$ denote the zero-degree quasimap invariants in…

Let $g\geq 2$ be the genus, let ${\mathsf{r}}=2$ be the rank, and let ${\mathsf{d}}$ be the degree. Define the generating series $\check{\mathsf{QM}}^i_{\mathsf{d}}(q)$ and…

Expected transversality conjecture. The intersection $I$ is generically smooth and pure of codimension

Let $Fl$ be a partial flag variety. Denote by $QK(Fl)$ its stable-map quantum $K$-ring and by $QK^{QM}(Fl)$ its quasimap quantum $K$-ring. The quasimap–stable-map conjecture. In th…

Fix cycles $c_i^X$ in the source $X=\mathbb{P}^k$ and cycles $c_i^Y$ in the target $Y=\mathbb{P}^n$, for $i=1,\ldots,l$. Let $\mathrm{Maps}_d(\mathbb{P}^k,\mathbb{P}^n)$ be the spa…

For a fixed rank ${\mathsf r}$, define the generating series obtained by summing over the flux index,…

Let $G$ be an abelian group acting in a CI-GIT presentation, and let $Y\mathord{/{\mkern-6mu/}}G$ be the corresponding quotient with projective coarse moduli space. Let…

Ciocan-Fontanine–Kim wall-crossing conjecture.

Let $Z$ be a complete intersection in projective space, and fix $g,n\geq 0$. For each effective degree $\beta$, let $q^\beta$ be the corresponding Novikov monomial, let…

Let $E\sslash \textbf{G}$ be the relevant GIT quotient, let $I(\mathbf{t},z)$ be the quasimap I-function, let $P^Q(\mathbf{t},z)$ be the corresponding quasimap input, and let…

Let $E\to E\sslash \textbf{G}$ be the GIT quotient in the paper, let $H^*(E\sslash \textbf{G},\Lambda)$ be its cohomology with coefficient ring $\Lambda$, and let…

Let $G$ act on a $G$-space $V$, and let $W\subset V$ be the zero locus of $G$-semi-invariant polynomials $f_i$, for $i=1,\ldots,r$. For $P\in\mathbb{C}[\mathfrak{t}]^{\mathcal{W}}$…

Quasimap–Gromov–Witten comparison conjecture. One has

Twisted big $J$-function conjecture. The function $\tilde{\mathds{J}}^{\theta,\varepsilon,E}$ lies on the Lagrangian cone encoding the genus-zero, ${\bf T}$-equivariant,…