Quantum unique ergodicity and random waves on graphs
The proposal aims to address two important conjectures of Quantum Chaos,  Quantum Unique Ergodicity and the Random Wave hypothesis, via the analysis of eigenfunctions of the Laplacian on discrete graphs. It will provide a better understanding of two difficult problems of mathematical physics through an original approach, while developing spectral theory on graphs. The latter has a strong potential of applications in the study of networks, whose understanding is of great importance in the modern world. The expertise of the experienced researcher on analysis on graphs will be ideally complemented by the quantum chaos and ergodic theory specialists of the University of Bristol, to ensure the success of this project.