Spectral theory: hypergraphs and lattice models
by Zuhe Zhang
Abstract: I will first present what I have obtained during the first year of my PhD study. The work is about the application of spectral theory on graphs and lattice models. It includes the investigation of the resistance distance, energy, dimer problem, spanning trees and expansion property of clique-inserted-lattices, the entropy of hard-core model and the spectrum of the subdivison-vertex join and subdivsion-edge join of regular graphs. I will then list some research topics for next two years, focusing on spectral hypergraph theory, that is, studying hypergraphs by using the properties of associated hypermatrices.