a cartographic quest between lambda-calculus, logic, and combinatorics – LambdaComb

This project aims to advance a remarkable connection between computer science and mathematics that was discovered by the lead researchers in 2013/2014. On one side of this interdisciplinary correspondence is the lambda calculus, a classical model of computation that remains highly influential on the design & analysis of modern programming languages. On the other side is the study of graphs on surfaces (or "maps"), a deep branch of mathematics with a long history. The unexpected discovery of a host of enumerative and bijective links between these two domains presents a real opportunity for transferring knowledge and techniques in both directions, and for making new advances. This project aims to deepen our scientific understanding by using these new bijective connections to: 1. develop rigorous logical perspectives on maps and related combinatorial objects; and 2. develop precise quantitative perspectives on lambda calculus and related systems.