18 problems

Logarithmic double ramification tautologicality conjecture. The logarithmic double ramification cycle belongs to

Let $g,k,u\geq 0$ and let $A=(a_1,\ldots,a_n)\in\mathbb{Z}^n$ satisfy … Let $\overline{{\mathcal M}}_{g,A}^{k,r}$ be the moduli space of twisted $r$-spin structures, 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 logarithmic double ramification cycle. Let…

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…

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

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

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 $g,n,k$ be as above, let $A=(a_1,\ldots,a_n)$ satisfy $\sum_{i=1}^n a_i=k(2g-2)$, and let $\widetilde A=(a_1+k,\ldots,a_n+k)$. For $k\geq 1$, assume that $A$ is not of the form…

Let $F^{\mathrm{DR}}$ denote the DR potential and let $F^{\mathrm{red}}$ denote the reduced potential associated to a cohomological field theory. Generalized strong DR/DZ equivalen…

Let a semisimple CohFT be given, and let its associated Dubrovin–Zhang (DZ) and double ramification (DR) hierarchies be the corresponding tau-symmetric integrable hierarchies. Bury…

Let $G,d,m$ be as in the moduli problem, let $x$ be the marked point, and let $\overline{\mathcal M}^0_{G,1,d}(\mathbb{CP}^1)$ denote the relevant moduli space of stable maps. For…

Let ${\rm DR}_g(a_1,\dots,a_n)$ be the double ramification cycle in $\overline{\mathcal M}_{g,n}$ associated with labels $a_1,\dots,a_n$. The class has codimension $g$, so its Poin…