Appears in collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

Integrals on the space U(N) of unitary matrices have a large N expansion whose coefficients count factorisations of permutations into "monotone" sequences of transpositions. We will show how this classical story can be adapted to integrals on the complex Grassmannian Gr(M,N), which leads to a 1-parameter deformation of the aforementioned enumeration. The resulting polynomials obey remarkable properties, some known and some conjectural. The notion of topological recursion inspired this work and we will briefly attempt to explain how and why. (This is joint work with Xavier Coulter and Ellena Moskovsky.)