Abstract
It is believed, following the work of BKL 50 years ago, that the classical dynamics of general relativity greatly simplifies close to  singularities such as those inside black holes or at the Big Bang. Each point in space evolves separately, with dynamics that is equivalent to the motion of a particle bouncing within the fundamental domain of the modular group. I will explain how the emergent conformal and modular symmetries in this regime suggest possible dual formulations of the physics. The mathematical language that pertains is that of L-functions. These share key properties of the Riemann zeta function, including nontrivial zeros and a representation in terms of prime numbers. I will describe the physical consequences of these facts.



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