5 problems

Soliton-condensate conjecture. Models outside the stability regime should correspond to a soliton condensate.

Let $\Psi$ be the wave function associated with the trigonometric Gaudin model, and let $g_a^{(\alpha)}$ be the eigenvalues of the trigonometric Calogero Lax matrix arranged in str…

Let $\Psi=\langle\Omega\mid\Phi\rangle$ be the wave function obtained from a solution of the KZ equations, and let $\hat{\cal H}_k$ denote the higher Calogero Hamiltonians. Suppose…

Generator-count conjecture. Assuming superintegrability, the number of ring generators is $2r-3$ for the first structure and $r-1$ for the second structure.

Odd-rank B-series nonexistence conjecture. There are no complex solutions for the constraints based on the Ansatz in the case of odd rank in the $B$-series.