An Application of the Ramanujan Bounds to Communication Networks

Theoretical computer science is a domain which poses many interesting problems to mathematicians. In many instances, their solutions involve important results from well-developed areas of mathematics like probability theory or number theory. The problem that I will present in this article is of this type. Starting from the design of communication networks, one passes to a problem about graphs which is solved thanks to a fundamental result of number theory. However, this is not the end of the story, for along the road we will encounter several unsolved mathematical questions which stem from the close analogy between graphs and Riemannian manifolds.