LambdaComb is an interdisciplinary ANR project whose broad goal is to deepen connections between lambda calculus and logic on the one hand and combinatorics on the other. One important motivation for the project is the discovery over recent years of a host of surprising links between subsystems of lambda calculus and enumeration of graphs on surfaces, or “maps”, the latter being an active subfield of combinatorics (cf. another recent LIX seminar!) with roots in W. T. Tutte’s work in the 1960s. In the talk I will give a broad overview of these connections, as well as some indications of what we can hope to learn by exploring them further.