05C50 Online Seminar: Sebastian Cioaba

It is known that non-isomorphic strongly regular graphs with the same parameters must be cospectral (have the same eigenvalues). We investigate whether the spectra of higher order Laplacians associated with these graphs can distinguish them. In this paper, we study the clique complexes of strongly regular graphs and determine the spectra of the triangle complexes of Hamming graphs, Triangular graphs and several other strongly regular graphs. In many cases, the spectrum of the triangle complex distinguishes between strongly regular graphs with the same parameters, but we find some examples where that is not the case. This is joint work with Krystal Guo, Chunxu Ji and Mutasim Mim.