Abstract:

A hyperbolic manifold is a quotient of hyperbolic space H^n by a discrete group of isometries. In particular, an arithmetic hyperbolic manifold is a quotient of H^n by a group which is in some sense arithmetic. For example, taking the quotient of H^2 by an action of SL_2(Z) yields more or less the (level 1) modular curve, which is a beloved object of number theorists around the world. Starting from the beginning, I will try to explain some of the rich structure of these arithmetic hyperbolic manifolds which make them particularly nice to study.

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