7 problems

Let $A_1$ be a first-order Hamiltonian operator of Ferapontov type for a first-order WDVV system, compatible with the third-order Hamiltonian operator supplied by the Hamiltonian t…

Let $N$ be the dimension of the WDVV system, let $S_L$ denote its linear subsystem, and let $S_{\lambda amu b}$ denote the remaining equations indexed by $2<\lambda<\mu\leq N$ and…

Polynomiality conjecture. If $P$ and $R$ are compatible, meaning that their Schouten bracket vanishes, $[P,R]=0$, then every entry of $Q^{\alpha\beta}$ is a polynomial of degree tw…

A WDVV system is a system of first-order PDEs considered together with its projective-geometric structures. A quadratic line complex is the associated family of lines in projective…

Let $F(v)$ be a solution of the WDVV equations, let $\hat F(\hat v)$ be its inversion, and let $\tilde{\mathcal F}_g$ and $\hat{\mathcal F}_g$ be the corresponding genus-$g$ free e…

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 $W$ be a Weyl group, let $\Omega$ be the relevant domain, and let $J(W)$ be the Jacobi group acting on it. Write $\mathcal{R}_W$ for the root system of $W$, let…