15 problems

Let … where $i$ is an integer, and let $s$ be the unique formal power series in $x$ and $p$ satisfying … For the Hurwitz generating series $H_g(x,p)$, and for a partition $\theta$…

Let $G^\bullet_{\mu^+,\mu^-}(\lambda;\tau)$ be the disconnected generating function of two-partition Hodge integrals for partitions $\mu^+$ and $\mu^-$. Let…

Sine formula conjecture. For all $d\geq 1$,

Let ${\mathcal P}_+$ denote the set of nonempty partitions, let $\mu^+$, $\mu^-$, $\nu^+$, and $\nu^-$ be partitions, and let $G_{\mu^+,\mu^-}(\tau)$ be the specialization defined…

Let ${\mathcal P}$ be the set of partitions, let $\mu^+$ and $\mu^-$ be partitions, and let $G_{\mu^+,\mu^-}(x,y)$, $p^+_{\mu^+}$, and $p^-_{\mu^-}$ denote the corresponding genera…

For the Deligne–Mumford moduli space of stable curves $\overline{{\mathcal M}}_{g,h}$, let $\Lambda_g^\vee(u)$ denote the total Chern polynomial of the Hodge bundle and let…

Virasoro conjecture for Hodge integrals. For any smooth projective variety,

Let $X$ be a smooth projective variety, and let $\Psi_{g,n}$ denote the universal expression for Hodge integrals with one $\lambda_{g-1}$ or $\lambda_g$ insertion defined in the so…

Let … is a consequence of the degree-$g$ topological recursion relations proposed in the cited work. This proposed connection relates universal equations for higher-genus Gromov–Wi…

Let $g>0$ and let $\vec{\ell}\in\mathbb{Z}_{\geq0}^n$ satisfy $|\vec{\ell}|\leq g-1$, where $|\vec{\ell}|$ is the sum of the entries of $\vec{\ell}$. Let $D_{(\vec{\ell},i),2g+2}$…

Nonnegativity and log-concavity conjecture. The integers $c_{\vec{i},k}$ and $\widetilde{c}_{\vec{i},k}$ are nonnegative, and, for fixed $\vec{i}$, the sequences…

Let $\vec{i}$ be a tuple of nonnegative integers, with $|\vec{i}|$ denoting the sum of its entries. Let $D_{(\vec{i}),2g+2}$ and $d_{(\vec{i}),2g+2}$ denote the corresponding…

Let $Z_{q,p}({\bf T})$ be the generating function of triple Hodge integrals … with … The parameters satisfy the Calabi–Yau condition, and $\mathbf T$ denotes the Hodge-integral var…

Let $X$ be the target, let $T_a$ and $T^a$ be dual cohomology bases, let $g$ be a genus, and let $B_{2g}$ be the Bernoulli number. Two-point universal-equations conjecture. For…

Let $g\geq2$, let $n$ be a positive integer, and let $d_j\geq1$ satisfy … Let $\lambda_i$ denote the Chern classes of the Hodge bundle, let $\tau_d$ denote a psi-class insertion, l…