8 problems

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…

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…

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…

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

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 $M$ 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 $\eta(R(z)v,R(-z)w)=\eta(v,w)$.…