Pure Maths Colloquium: Prime geodesics and spectral theory
12 January 2009 16:15 in CM221
There is an analogy between prime numbers and lengths of (prime) geodesics in hyperbolic manifolds. We discuss the distribution of these lengths and its refinements when we impose (co)homological restrictions. The Selberg trace formula is a good tool for such investigations. It relates these lengths to the eigenvalues of the Laplace operator. We will explain why this is so and what seem to be the limits of the analogies with prime numbers.