Maxime Ingremeau

Metric graphs (also known as quantum graphs) have been studied by physicists and mathematicians for a long time, since they are a good toy model to understand quantum chaos. In particular, much attention has been devoted to study the asymptotic behaviour of eigenvalues and eigenfunctions on a fixed quantum graph, when the frequency goes to infinity.
In this talk, we will study another interesting regime : when the frequency is fixed, but the graph becomes larger, and more and more complicated. In particular, we will show a quantum ergodicity result for large quantum graphs which are expanders and locally look like trees.
This is joint work with Nalini Anantharaman, Mostafa Sabri and Brian Winn.