Combinatorics of the lambda-calculus and maps: bijections and limit properties

This talk concerns maps (graphs embedded on surfaces), the linear lambda-calculus, and their combinatorial interactions. Using a combination of new bijective and analytic techniques, we will explore the structure of large random cubic maps and linear lambda-terms, focusing on the study of various statistics on such objects, in particular those related to the presence of various patterns and their connection with the dynamics of beta-reduction on linear terms.