Two applications of Grothendieck's algebraicity conjecture

Abstract: In 1984 D.Chudnovsky and G.Chudnovsky proved Grothendieck's algebraicity conjecture in the abelian case: if the derivative of logarithm of a series with integer coefficients is algebraic, then the series itself is algebraic.

One of applications is in the hypergeometric setting, by É.Delaygue and T.Rivoal.

Another one (by me) is in the free probability theory of large random unitary matrices, based on theory of formal grammars and algebraic noncommutative series by N.Chomksy and M.Schützenberger. There are interesting parallels between these two cases.