4 problems

Painlevé I limit conjecture. There exists a choice of constant $C = C(P_0,{\bf u})>0$ and a polynomial $Q(t_1,t_2,t_5)$ such that, defining $\hat{\tau}_0:= e^{Q}$, considered as a…

String-equation characterization. All critical points of the $2$-matrix model are characterized by the so-called $(q,p)$-string equations, which arise as symmetry constraints of th…

Benjamin–Ono uniqueness conjecture. The function $U(X,T)$ is uniquely characterized as the solution of the string equation satisfying this boundary behaviour.

Benjamin–Ono string-equation conjecture. The critical behaviour of solutions to the Benjamin–Ono equation is described by a particular solution of this singular integro-differentia…