27 problems

Let a cohomological field theory be given, and let its double ramification hierarchy be the Hamiltonian integrable system constructed from double ramification cycles. Let its Dubro…

Let $w^{\alpha}$ be the normal coordinates for the Dubrovin–Zhang hierarchy, let $\tilde u^{\alpha}$ be the normal coordinates for Buryak's double ramification hierarchy, let…

Buryak–Dubrovin–Guéré–Rossi conjecture. The DR hierarchy and the DZ hierarchy should be equivalent by a normal Miura transformation in the semisimple case.

Let $\{\mathrm{Cl}_{g,n}\}$ be a conformal P-CohFT, let $G$ be any density of $\overline{G}$, and let $\overline{\mathrm{Br}}_{1}$ and $\overline{\mathrm{Br}}_{2}$ be the bivectors…

Recursion conjecture for homogeneous F-CohFT. A recursion similar to the bi-Hamiltonian recursion for the double ramification hierarchy holds also for homogeneous F-CohFT.

Let a tau-symmetric deformation of the Riemann hierarchy be given. A normal Miura transformation is a Miura transformation of the type defined in the source that preserves the rele…

A tau-symmetric deformation of the Riemann hierarchy is a deformation of the hierarchy of evolutionary equations that retains tau-symmetry, namely the property that a single tau-fu…

Minimal-level conjecture. The correlator vanishes if

Minimal-level conjecture. There exists a minimal level for these correlators, and the paper gives an explicit formula for it.

Buryak–Rossi–Shadrin's conjecture. The operator $K^\mathrm{DR}$ is Poisson and compatible with $\eta^{-1}\partial_x$. It endows the DR hierarchy with a bihamiltonian structure sati…

Burman's conjecture. For an arbitrary CohFT, the DR and DZ hierarchies are Miura equivalent; the required Miura transformation is described precisely in terms of the partition func…

Let a cohomological field theory have semisimple genus-zero Frobenius-manifold data. Let the double ramification (DR) hierarchy be the integrable hierarchy constructed from the coh…

Dubrovin–Zhang hierarchy conjecture. (1) For every $1\leq\alpha,\beta\leq N$ and $a,b\geq0$, there is $\Omega_{\alpha,a;\beta,b}\in\widehat{\mathcal A}_{w;0}$ such that

DR–DZ equivalence conjecture. One has

Let $(W,G)$ be an admissible LG pair with $W$ an invertible Calabi–Yau polynomial of three variables, and let $(q_1,q_2,q_3)$ be its weight system. Weight-and-rank determination co…

Let $c_{g,n}:V^{\otimes n}\to H^*({\overline{\mathcal{M}}}_{g,n},\mathbb C)$ be a semisimple cohomological field theory with metric on $V$ and unit, so that its Dubrovin–Zhang hier…

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 cohomological field theory be given, together with its double ramification hierarchy and a particular solution of that hierarchy. Let the reduced potential be obtained from t…

Buryak's conjecture. The reduced free energy $\mathcal{F}^{\mathrm{red}}$ is the free energy of the double ramification deformation.

For a cohomological field theory, let $F^{\mathrm{DR}}$ denote the potential of the double ramification hierarchy and let $F^{\mathrm{red}}$ denote the reduced potential. DR and re…

Let $M$ be an $N$-dimensional semisimple Frobenius manifold such that it possesses a holomorphic genus one potential $\mathrm dG$. Global extension conjecture. There exists a conve…

Let $V$ be the state space of a cohomological field theory with metric $\eta$, and let $R=1+O(z)$ be an endomorphism-valued power series satisfying $\eta(R(z)v,R(-z)w)=\eta(v,w)$.…

Let an $ADE$ singularity determine its associated cohomological field theory, and let Gromov–Witten theory for a $\mathbb{P}^{1}$-orbifold of $ADE$ type be given. Genus-2 G-functio…

Let $(W,{\bf G},\theta)$ be a semi-positive triple, let $W/\!/{\bf G}$ be its GIT quotient, and let $\Lambda$ be the Novikov ring. For each stability parameter $\varepsilon\geq 0+$…

Let $(W,{\bf G},\theta)$ be a semi-positive triple, let $W/\!/{\bf G}$ be its GIT quotient, and let $\Lambda$ be the Novikov ring. For each stability parameter $\varepsilon\geq 0+$…