4 problems

Gamayun–Iorgov–Lisovyy conjecture. The tau functions should admit explicit formal series solutions of the form

Conjecture centrale. Pour tout entier $n\geq1$,

Convergent matrix-integral decomposition conjecture. The convergent matrix integral $Z_{\rm conv}$ is a finite linear combination of convergent formal solutions of the loop equatio…

Let $P[[t]]$ be the set of formal series … whose coefficients are monotone nondecreasing nonnegative functions on $2^X$. Let $\mu$ be a probability measure on $2^X$ satisfying the…