Let B be the unit ball in the standard 13-dimensional complex vector space. We shall talk about a ball quotient obtained by removing a locally finite collection of complex hyperplanes from B and then quotienting the rest by the action of a discrete subgroup of U(13,1). We shall state a conjecture that relates the fundamental group of this ball quotient and the monster simple group and describe our results towards this conjecture. This is joint work with Daniel Allcock.