Zeev Rudnick

Prime numbers, closed geodesics, and random hyperbolic surfaces

There is a close analogy between the theory of closed geodesics on a hyperbolic surface and prime number theory. This has been known since the 1950s. After surveying the two theories, I will discuss a recent perspective, when we consider the surface as being random in the moduli space of hyperbolic surfaces of large genus, using Mirzakhani’s work.