36 problems

Let $g,n,k$ be as above, let $\overline{\operatorname{DRC}}$ denote the pluricanonical double ramification cycle on $\overline{\mathcal{M}}_{g,n}$, and let…

Let $R_{g,A}\in CH^g(\overline{\mathcal{M}}_{g,n})$ be the double ramification cycle, and let $\Omega_{g,A}\in CH^*(\overline{\mathcal{M}}_{g,n})$ be Pixton's mixed-degree graph-su…

Let the double ramification (DR) and Dubrovin–Zhang (DZ) constructions associate integrable hierarchies of partial differential equations to a cohomological field theory. A Miura t…

Let $r$ be the auxiliary weighting parameter in the Chiodo-class expression for the DR-completed volume, and consider the Chiodo coefficient needed in that expression at top codime…

Let $d$ be the degree, let $\boldsymbol{\nu}$ be the ramification data, and let $\operatorname{logDR}_0(d,-\boldsymbol{\nu})$ denote the logarithmic double ramification cycle. Let…

Let $d$ be the degree, let $\boldsymbol{\nu}$ be the ramification data, and let $\operatorname{logDR}_0(d,-\boldsymbol{\nu})$ denote the logarithmic double ramification cycle. Let…

Let $d$ be the degree, let $\boldsymbol{\nu}$ be the ramification data, and let $\operatorname{logDR}_0(d,-\boldsymbol{\nu})$ denote the non-leaky logarithmic double ramification c…

Let $g$, $k$, and $u$ be non-negative integers, and let $(a_1,\dots,a_n)\in\mathbb{Z}^n$ satisfy … Write $\omega_{\mathsf{log}}$ for the logarithmic dualizing sheaf on…

Consider the three classes associated with the DR/DZ correspondence and its quantization: the $A$-class on the DR side, the $B$-class on the DZ side, and the…

Let the quantum tau functions of the quantized double ramification hierarchy be defined from the quantization of the double ramification hierarchy. Let the Omega-class and the lamb…

For $g\geq0$ and $m,n\geq1$ with $2g-2+n+m>0$, let $\Xi^m_{g,n}$ be the Laurent polynomial in $u$ with coefficients in the tautological ring of $\overline{\mathcal{M}}_{g,n+m}$ obt…

Let $A^1_{g,n}$ and $B^1_{g,n}$ be the polynomial-valued tautological classes associated with the rubber and corresponding constructions in the paper, and let $B^m_{g,n}$ and…

Let $Q=\mathbb{Q}[a_1,\dots,a_n]$, let $\pi\colon {\overline{\mathcal{M}}}_{g,n+1}\to {\overline{\mathcal{M}}}_{g,n}$ forget the last marked point, and define … Let…

Let $Q=\mathbb{Q}[a_1,\dots,a_n]$. For a stable rooted tree with one frozen leg, let $A^1_{g,n}\in R^*({\overline{\mathcal{M}}}_{g,n+1})\otimes_{\mathbb{Q}}Q$ be the sum of the cla…

Let $g,n\geq 0$ and let $k$ be a positive odd integer. Let $\mu=(m_1,\ldots,m_n)\in\mathbb{Z}^n\setminus k\mathbb{Z}^n_{\geq 0}$ satisfy … with all entries of $\mu$ even. Let…

Let $g,n\geq 0$, let $k>0$, and let $\mu=(m_1,\ldots,m_n)$ be a signature for $k$-differentials. Denote by $[\widetilde{H}_g(\mu)]$ the weighted fundamental class of the moduli spa…

Identification conjecture. For any such $g$, $n$, and $\overline{d}$,

Identification conjecture. For any such $g$, $n$, and $\overline{d}$,

Let the double Hodge integrals be the integrals involving products of Hodge classes and cotangent-line classes on moduli spaces of curves discussed in the paper. Blot's conjecture.…

Let $\overline{\mathcal{M}}_{g,2}$ be the moduli space of stable curves with two marked points, let $\lambda_g$ denote the top Chern class of the Hodge bundle, and let…

Let $g,n\geq 0$, let $k>0$, and let $a\in\mathbb{Z}^n$ satisfy $|a|=k(2g-2+n)$, $a\notin k\mathbb{Z}_{>0}^n$, and the condition that all entries of $a$ and $k$ are odd. For odd sta…

Let $g\geq 1$ and let $a$ be a parameter. On $\overline{\mathcal{M}}_{g,2}$, write $\mathrm{DR}_{g}(a,-a)$ for the double ramification cycle with weights $a$ and $-a$, let…

DR–DZ equivalence conjecture. One has

Let $\overline{\mathcal{M}}_{g,n}$ be the moduli space of stable curves with $n$ markings, and let $A=(a_1,\ldots,a_n)$ be a vector of integers satisfying … Let…

Main conjecture. The operator $K_2$ is Poisson and compatible with $K_1$. Moreover, the Poisson brackets associated with $K_2$ and $K_1$ give a bihamiltonian structure for the doub…