15 problems

For an admissible LG pair $(W,G)$, let the Fan–Jarvis–Ruan–Witten, Polishchuk–Vaintrob, and Chang–Li–Li–Kiem–Li constructions define three cohomological field theories. Folklore eq…

Cohomological-field-theory deformation conjecture. The non-degenerate part of the cohomological field theory described by $f$ is the deformation of the Frobenius algebra of the inv…

Sector correspondence conjecture. The Neveu–Schwarz sectors are in one-to-one correspondence with the one-dimensional twisted sectors, while the Ramond sectors are in one-to-one co…

Let $\mathcal{D}({\bf t};\hbar)$ be the homogeneous total descendent potential of a calibrated homogeneous CohFT with vacuum, and let the generalized Virasoro constraints denote th…

The $HT$ twist of a three-dimensional $\mathcal{N}=2$ theory equipped with an $R$-symmetry is a cohomological twist on a three-dimensional theory with a holomorphic direction, and…

Let $\mathcal C=(\Sigma,x,y)$ be a spectral curve and let $\gamma\subset\Sigma\setminus{\bf b}$ be an admissible path associated with $e^{-x/\mathfrak u}$. Let $\eta$ be the CohFT…

Let $\overline{\mathcal{H}}_g^{\operatorname{res}}(a_1,\ldots,a_n)$ denote the moduli stack compactification of meromorphic differentials with prescribed orders $a_1,\ldots,a_n$ an…

Costello's conjecture. The Lie bracket does not vanish on the fermionic part of the doubled BPS Lie algebra.

Let $(a_1,\ldots,a_n)$ be a partition of $2g-2$ with non-negative parts, and let $\overline{\mathcal{H}}_{g}(a_1,\ldots,a_n)$ be the closure in $\overline{\mathcal{M}}_{g,n}$ of th…

Let $\tilde W:\mathbb{C}^N\to\mathbb{C}$ be a hypersurface singularity, and let $\zeta_\infty$ and $\zeta_0$ be the two specified choices of primitive form. Write…

Let a cohomological field theory (CohFT) be given on ${\overline{\mathcal{M}}}_{g,n}$. For integers $a_1,\ldots,a_n$ with sum zero, let…

For genus $g$ and the general multi-backbone case, let $\widehat b^{(g)}_{\vec k,\vec\beta}$ denote the coefficients identified with combinations of ancestor invariants, where…

Let $T^{\pm}_{2n}$ denote the even times used to express the Kontsevich–Penner matrix model, let $\overline{\mathcal M}_{g,s}$ be the Deligne–Mumford compactification of the moduli…

DR–Dubrovin–Zhang hierarchy conjecture. If a cohomological field theory is semisimple, then the DR hierarchy is related to the Dubrovin–Zhang hierarchy by a Miura transformation.

Manin–Zograf conjecture. The classes $\kappa_j$, $j\geq 0$, and $\mu_j$, for $j>0$ odd, are the only primitive classes on $\overline{M}_g^n$. Consequently, any rank $1$ theory shou…