11 problems

Let $X$ be a Fano manifold whose big quantum cohomology is semisimple, and suppose that $\mathcal{D}^b_{\rm coh}(X)$ admits a full exceptional collection. Let $U\subset B_{ss}$ be…

Let $(Y,(-\log t)\omega)$ and $(Z_t,\Omega_t)$ be a Calabi-Yau mirror pair, and let $C_t\subset Z_t$ be a certain family of $n$-cycles. Let $F$ and…

Let $X$ be a Fano manifold, and let $QH_{\rm sm}(X)$ be its small quantum cohomology with small Dubrovin connection, flat-section space $\mathcal{S}^{\rm sm}$, and…

Let $X$ be a Fano variety of complex dimension $D$ with odd-vanishing cohomology, and let $F_0(\textbf{v})$ be a power series with convergence domain $\Omega$. Let…

Let $X$ be a monotone symplectic manifold. For Chern roots $x_j$ of $TX$, let $u$ be the equivariant parameter, let $J_X^d=ev^d_*\left(\frac{1}{1-u\psi}\right)$, and let…

Let $Y$ be a del Pezzo surface, let $(\mathcal X,W)$ be its Landau–Ginzburg mirror, let $\alpha:K(Y)\to H_2(\mathcal X,W^{-1}(+\infty);\mathbb Z)$ be the map from the preceding cen…

Hosono's Gamma conjecture. There is a map

Let $X$ be an almost complex manifold with Chern roots $\delta_1,\dots,\delta_n$ and Gamma class … The $\widehat{\Gamma}$-integral structure is an integral structure on the symplec…

Let $X$ be a smooth projective variety, let $\tau\in H^*(X)$ be a point where the quantum connection is of exponential type, and let $\mathsf{C}$ index the exponential factors. Let…

Let $X$ be a Fano manifold and let $\mathcal{A}$ be the vector space of flat sections $s(z)$ over the positive real axis such that $e^{T/z}s(z)$ has at most polynomial growth as…

Calabi–Yau Gamma conjecture. The asymptotics of the vanishing periods of $M_{q,t}$ should be given by the Gamma class of the mirror partner $W$, as in