Given a compact manifold and a finite degree, the number of covering spaces of that degree is finite. This leads to the question how many such covers there are and what this tells one about the geometry and topology of the manifold. Answering this question is equivalent to counting finite index subgroups of the fundamental group of the manifold. This counting problem is usually called subgroup growth. In this talk, I will discuss joint work with H. Baik, and J. Raimbault on the subgroup growth of right-angled Coxeter and Artin groups.

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