Student Analysis Seminar

Quantum mechanics provides a framework for turning questions about certain dynamics systems into questions about eigenfunctions of certain operators. For example, the Laplacian on a manifold is the operator of interest corresponding to the geodesic flow. A natural question is what the quantum mechanical analogue of ergodicity is. In particular if the geodesic flow on a manifold is ergodic, how does this "show up" in the eigenfunctions of the Laplacian? The answer is that, in a precise sense, "most" eigenfunctions of the Laplacian tend to be "equidistributed" over the entire manifold. In this talk I will motivate, make precise, and sketch a proof of this statement. I hope to keep the talk self-contained; in particular I will not assume that the audience has any background in quantum mechanics or dynamics. Speaker(s): Carsten Peterson (University of Michigan)