9 problems

Let $g_{ij}$ be a solution of the linear system … associated with a diagonal semi-Hamiltonian system, and let $w^i_{(\alpha)}$ be the characteristic velocities of its symmetries. F…

Let an integrable diagonalizable quasilinear system of partial differential equations be given, also called a semi-Hamiltonian system. Consider the limiting case of Ferapontov's Ha…

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.

Dubrovin–Zhang uniqueness conjecture. Associated to any semisimple 2d topological field theory, there canonically exists a unique integrable hierarchy of topological type such that…

Polynomiality and monodromy-invariance conjecture. Under these hypotheses, every function $u^i(\boldsymbol{v})$ belongs to the invariant polynomial ring…

Let $P_2^{[0]}$ be the second Hamiltonian structure of the principal hierarchy, and let $P_2$ denote its image under the quasi-Miura transformation … Here a Hamiltonian structure h…

Let $\mathcal{P}$ be the local Hamiltonian operator for the Mikhailov–Novikov–Wang system (1). The system also has the nonlocal Hamiltonian operators…

Reciprocal invariance conjecture. For a general Hamiltonian system, respectively bihamiltonian system, with dispersion terms, the transformation above preserves the locality proper…