Automorphic forms and geometric group theory

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Newtonian mechanics provides a very accurate description of many everyday phenomena. Nevertheless, physicists believe that a more fundamental description is available in quantum mechanics. It follows that the quantum-mechanical description of a system in which quantum effects are small should behave like the classical description. In many cases, well-defined mathematical models of the classical and quantum descriptions exist. The physics just mentioned leads to mathematical predictions about these models, predictions which can be proven or disproven rigorously.