14 problems

Let $X$ be a Calabi--Yau manifold equipped with a symplectic form $\omega$, and let $\{Z_t\}_{t\in \Delta^\ast}$ be a family of Calabi--Yau manifolds parametrized by $t$ in a small…

Mirror symmetric Gamma conjecture. The following identity should hold:

Let $X$ be a Fano manifold, let $\mathcal M_X$ be its quantum/Kahler moduli space, and let $A_X(\tau)$ denote the principal asymptotic class at a point ${\mathbf q}=e^\tau$ where t…

Let $X$ be a Fano manifold. Let $S(z)$ be the quantum differential-equation fundamental solution, $\mu$ the grading operator, $c_1$ act by quantum multiplication, and…

Let $X$ be a Fano manifold. Let $S(z)$ be the quantum differential-equation fundamental solution, $\mu$ the grading operator, $c_1$ act by quantum multiplication, and…

Let $X$ be a Fano manifold satisfying Property $\mathcal O_A$, where $T_{\mathrm{A,con}}$ is a simple rightmost eigenvalue of $\hat c_1$. Let $A_X$ be the principal asymptotic clas…

Let $X$ be a Fano manifold. Its quantum cohomology defines a linear operator $\hat c_1$ on the even cohomology, and Property $\mathcal O$ requires that the spectral radius of…

Let $F$ be an $n$-dimensional Fano manifold mirror to a Laurent polynomial $W=W(x_1,\dots,x_n)$ whose Newton polytope contains the origin in its interior and whose non-vanishing co…

Gamma conjecture I. There exists a constant $C\in\mathbb{C}$ such that

Let $X$ be a Fano manifold. Write $H(X)=H^{even}(X)$, let $\rho$ be its Fano index, and let $\boldsymbol{c_1(X)\star_0}$ denote the linear operator on the unital commutative ring…

Let $\Delta$ be a flag 3-manifold, and let $\beta_1(\Delta)$ denote its first Betti number. 3-dimensional manifold Charney–Davis conjecture. … The conjecture extends the Davis–Okun…

The gamma2 conjecture.

Let $\mathfrak{X}_{\mathbf{\Sigma}}$ be a weak-Fano compact toric stack, and let $V_i$ be the $K$-theory classes whose $hat{\Gamma}$-integral flat sections give an asymptotic basis…

Let $X$ be a Calabi–Yau manifold equipped with a symplectic form $\omega$, and let $\{Z_t\}_{t\in \Delta^*}$ be a family of Calabi–Yau manifolds parametrized by $t$ in a small punc…