Title: Towards generalized spectral determinacy of random graphs
| Speaker: | Alexander Van Werde |
| Affiliation: | Eindhoven University of Technology |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: Wang and Xu (2006, 2017) discovered sufficient conditions for a graph to be uniquely characterized by the spectra of its adjacency matrix and of its complement graph. They conjectured that these conditions are satisfied with nonvanishing frequency, but this remains open and it was not clear what proof techniques could be used. I will present a new line of attack which approaches the problem as a question about random groups. This allows making connections to proof techniques from combinatorial random matrix theory. The results which I will present are in a toy case, but it is expected that the employed perspective will generalize.
This talk is based on my paper “Cokernel statistics for walk matrices of directed and weighted random graphs” [Combinatorics, Probability and Computing (2025)]