8 problems

Octagon-poset tau-sequence conjecture. For each octagon poset $P$, the $R$-system associated with $G(P)$ admits a strong $\tau$-sequence consisting of irreducible Laurent polynomia…

Eigenvalue read-off conjecture. If the deautonomisation is sufficiently general, then the value of the largest eigenvalue of the linear map on the Picard group, and hence the algeb…

Picard-action conjecture. For any confining mapping of the plane, the behaviour of the parameters satisfying the confinement constraints is governed by the linear action on the Pic…

The source discusses irreducibility and co-primeness of iterated terms for discrete mappings, and relates these properties to singularity structure and integrability. In particular…

Consider a non-autonomous mapping regularised by blowing up its indeterminacy points, and the induced map on the exceptional curves. The singularity-confinement conditions are obta…

Let $\ell$ and $\ell'$ be the non-negative integers specifying the blow-up patterns, and let the matrix governing the evolution of the mapping's parameters be compared with the mat…

A nonlinear partial difference equation is said to have singularity confinement when its singularities do not propagate indefinitely, and two terms are co-prime when they share no…

Singularity confinement conjecture. Singularity confinement holds generically on $X_S$ unless