Geometric spectral theory of quantum graphs
arXiv:2310.02707 · doi:10.46298/cm.12380
Abstract
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be accessible to doctoral level students, and include background chapters on Laplacians on domains and quantum graphs before moving on to specialised topics involving the dependence and optimisation of operator eigenvalues on a metric graph in function of the graph geometry, drawn in part from the recent literature.
Final version, to appear in Communications in Mathematics
References in corpus (7)
- Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
- On the Spectral Gap of a Quantum Graph
- Spectral gap for quantum graphs and their connectivity
- Finite pseudo orbit expansions for spectral quantities of quantum graphs
- Extremal Eigenvalues of the Laplacian on Euclidean domains and closed surfaces
- On The Spectrum Of Infinite Quantum Graphs
- Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap